+
    LV-j‹{ ã                   óL  € ^ RI Ht ^ RIt^ RIt^ RIt^ RIHtHtH	t	 ^ RIH
t ^ RIHtHt ^ RIHt ^ RIHtHtHtHtHtHtHt ^ RIHtHtHt ^ R	IHt ^ R
IH t! ^ RI"H#t#H$t$H%t%H&t& ^ RI'H(t(H)t) ^ RI*H+t+H,t, ]#! ]4       ! R R4      4       t-]#! ]P&                  4       ! R R4      4       t.]#! ]P4                  4       ! R R4      4       t/ ! R R]4      t0 ! R R4      t1 ! R R4      t2]#! ]4       ! R R4      4       t3 ! R R4      t4 ! R R4      t5 ! R  R!4      t6 ! R" R#4      t7R# )$é    )ÚproductN)Úassert_Úassert_equalÚassert_allclose)Úraises)ÚstatsÚspecial)Údistributions)Úepps_singleton_2sampÚcramervonmisesÚ_cdf_cvmÚcramervonmises_2sampÚ_pval_cvm_2samp_exactÚbarnard_exactÚboschloo_exact)ÚmannwhitneyuÚ
_mwu_stateÚ_MWU)Ú_TestPythranFunc)Úarray_api_extra)Úmake_xp_test_caseÚxp_default_dtypeÚis_numpyÚeager_warns)Úxp_assert_equalÚxp_assert_close)ÚSmallSampleWarningÚtoo_small_1d_not_omitc                   ó€   a € ] tR t^t o ]P
                  P                  R. R	O4      R 4       tR tR t	R t
R tRtV tR# )
ÚTestEppsSingletonÚdtypeNc                óž  € \        V4      '       d/   VP                  R 8  d   VR8X  d   \        P                  ! R4       Vf   \	        V4      M
\        W!4      pVP                  . R
OVR7      pVP                  . ROVR7      p\        W44      w  rV\        WRP                  RVR7      RR7       \        WbP                  RVR7      R	R7       R# )ú2.0Úfloat32ú!Pre-NEP 50 doesn't respect dtypesN©r!   gHáz®G.@g¸…ëQ¸ž?©Úatolg˜Q,·´r?ç-Cëâ6?)
gffffffÖ¿gffffff@g®Gáz®û?ç\�Âõ(\ç?çffffffÖ?g…ëQ¸…@gq=
×£pÝ?g®Gázî¿g®Gáz®×¿g¤p=
×#(@)
gffffffò¿g333333Ã¿g×£p=
×@g      
@g®Gáz®@g)\�Âõ(@ç      @gö(\�Âõ@gÃõ(\�Â @ç333333!@)	r   Ú__version__ÚpytestÚskipr   ÚgetattrÚasarrayr   r   )Úselfr!   ÚxpÚxÚyÚwÚps   &&&    Úq/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/stats/tests/test_hypotests.pyÚtest_statistic_1Ú"TestEppsSingleton.test_statistic_1   s´   € ô �B�<Š<˜BŸN™N¨UÔ2°uÀ	Ô7IÜ�KŠKÐ;Ô<Ø(-ªÔ  Ô$¼7À2Ó;MˆØ�J‰Jò 9Ø@Eð ó Gˆà�J‰Jò 3Ø:?ð ó Aˆä# AÓ)‰ˆÜ˜Ÿ:™: e°5˜:Ó9ÀÕEÜ˜Ÿ:™: g°U˜:Ó;À&×Ió    c                óÜ   € VP                  . RO4      pVP                  . RO4      p\        W#4      w  rE\        WAP                  R4      RR7       \        WQP                  R4      RR7       R# )	r   gÍÌÌÌÌÌ!@çü©ñÒMbP?r'   g&ª·¶J°?g-Cëâ6
?N)r   é   é   r@   r@   r@   é   rA   rA   rA   é   é   rC   rC   rC   é   é
   rE   rE   rE   )rE   rB   r   rC   rE   rE   r   rC   rD   é   rE   rA   r?   rF   r   é   r?   rC   rG   rE   )r2   r   r   )r3   r4   r5   r6   r7   r8   s   &&    r9   Útest_statistic_2Ú"TestEppsSingleton.test_statistic_2+   sZ   € à�J‰Jò 7ó 8ˆà�J‰Jò 8ó 9ˆä# AÓ)‰ˆÜ˜Ÿ:™: eÓ,°4Õ8Ü˜Ÿ:™: gÓ.°T×:r<   c                óz  € \         P                  ! ^4      \         P                  ! ^4      r!\        \        V4      \        V4      4      w  r4\        \	        V4      \	        V4      4      w  rV\        W4      w  rx\        Y5u;8H  ;'       d    V8H  Mu 4       \        YFu;8H  ;'       d    V8H  4       R# u 4       R# )é   N)ÚnpÚaranger   ÚlistÚtupler   )	r3   r5   r6   Úw1Úp1Úw2Úp2Úw3Úp3s	   &        r9   Útest_epps_singleton_array_likeÚ0TestEppsSingleton.test_epps_singleton_array_like5   sv   € Ü�yŠy˜‹}œbŸiši¨›mˆ1ä%¤d¨1£g¬t°A«wÓ7‰ˆÜ%¤e¨A£h´°a³Ó9‰ˆÜ% aÓ+‰ˆä�—”˜B”ÔÜ�—”˜B‘Ö‘Ör<   c                ó”  € VP                  . RO4      VP                  ^
4      r2\        \        \        VR7      ;_uu_ 4        \        W#4      p\        VP                  VP                  VP                  4      4       \        VP                  VP                  VP                  4      4       RRR4       R#   + '       g   i     R# ; i)r?   ©Úmatchr4   N©r?   r@   rA   rB   )
r2   rM   r   r   r   r   r   Ú	statisticÚnanÚpvalue©r3   r4   r5   r6   Úress   &&   r9   Útest_epps_singleton_sizeÚ*TestEppsSingleton.test_epps_singleton_size?   s{   € à�z‰zš,Ó'¨¯©°2«ˆ1ÜÔ+Ô3HÈR×PÖPÜ& qÓ,ˆCÜ˜CŸM™M¨2¯:©:°b·f±fÓ+=Ô>Ü˜CŸJ™J¨¯
©
°2·6±6Ó(:Ô;÷ Q×P×PÒPús   ÁA*B6Â6C	c                óŽ  € \         P                  P                  R 4      pVP                  RR7      pVP                  RR7      p\         P                  ! . RO4      p\	        W4RR7      w  rg\         P
                  We&   \         P
                  Wu&   \         P
                  W5^ ,          ^ 3&   \         P                  W5^,          ^3&   \         P                  ) WE^,          ^3&   VP                  V4      VP                  V4      rC\	        W4RR7      w  r‰\        W�P                  V4      4       \        W‘P                  V4      4       R# )l   2$>Ü. ©Úsize©ÚaxisN)rE   é   )rE   é   )r?   rB   é	   éÿÿÿÿ)rL   ÚrandomÚdefault_rngr2   r   r]   Úinfr   )
r3   r4   Úrngr5   r6   ÚiÚw_refÚp_refÚw_resÚp_ress
   &&        r9   Útest_epps_singleton_nonfiniteÚ/TestEppsSingleton.test_epps_singleton_nonfiniteG   sê   € Ü�i‰i×#Ñ# NÓ3ˆØ�J‰J˜HˆJÓ%ˆØ�J‰J˜HˆJÓ%ˆÜ�JŠJ’yÓ!ˆä+¨A°rÔ:‰ˆÜ—6‘6ˆ‰Ü—6‘6ˆ‰ä—V‘VˆˆA�$�ˆ'‰
Ü—V‘VˆˆA�$�ˆ'‰
Ü—f‘f�WˆˆA�$�ˆ'‰
à�z‰z˜!‹}˜bŸj™j¨›mˆ1Ü+¨A°rÔ:‰ˆÜ˜Ÿz™z¨%Ó0Ô1Ü˜Ÿz™z¨%Ó0Ö1r<   © ©Nr$   Úfloat64)Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__r/   ÚmarkÚparametrizer:   rH   rV   ra   ru   Ú__static_attributes__Ú__classdictcell__©Ú__classdict__s   @r9   r    r       sE   ø‡ € à‡[�[×Ñ˜WÒ&BÓCñJó DðJò ;ò ò<÷2ð 2r<   r    c            
       ó”  a € ] tR t^[t o ]P
                  P                  R^. RO. RO3^
. RO. RO3R. RO. RO3R. RO. RO3.4      R 4       tR tR t	R t
R t]P
                  P                  R	R
R7      ]P
                  P                  RRR..4      R 4       4       t]P
                  P                  R. RO4      R 4       tR tRtV tR# )ÚTestCvmz	n, x, reféè  Nc                ór   € \        \        VP                  V4      V4      VP                  V4      R R7       R# ©r)   r'   N)r   r   r2   )r3   Únr5   Úrefr4   s   &&&&&r9   Útest_cdf_refÚTestCvm.test_cdf_ref`   s'   € ô 	œ §¡¨A£°Ó2°B·J±J¸s³OÈ$×Or<   c                óæ   € \        \        VP                  RR.4      R4      VP                  RR.4      4       \        \        VP                  RR.4      ^4      VP                  RR.4      4       R# )	r?   i  ç        ç      ð?Ng²Xª(~$?gUUUUU5f@g†a†ah?g«ªªªªª"@)r   r   r2   )r3   r4   s   &&r9   Útest_cdf_supportÚTestCvm.test_cdf_supporti   s`   € äœ §¡¨Z¸Ð,?Ó!@À#ÓFØŸ
™
 B¨ 8Ó,ô	.äœ §¡¨_¸jÐ,IÓ!JÈBÓOØŸ
™
 B¨ 8Ó,ö	.r<   c                ón   € VP                  . RO4      p\        \        VR4      \        V4      RR7       R# )çaÃÓ+e™?é'  r)   r'   N)r“   ç+û®þ·¢?çÉ&pën¾?ç+MJA·—ò?éd   )r2   r   r   ©r3   r4   r5   s   && r9   Útest_cdf_large_nÚTestCvm.test_cdf_large_np   s(   € à�J‰JÒ@ÓAˆÜœ  EÓ*¬H°Q«K¸d×Cr<   c                ó¶   € VP                  R VP                  R7      pR\        VR4      u;8  d	   R8  g   Q h Q hR\        V4      u;8  d	   R8  g   Q h Q hR# )gÍÌÌÌÌÔt@r&   gwJëÿï?r†   r�   N)r2   ry   r   r™   s   && r9   Útest_large_xÚTestCvm.test_large_xu   sW   € ð �J‰J�u B§J¡JˆJÓ/ˆØœ( 1 dÓ+Ö1¨cÔ1Ð2Ñ1Ð2Ð1Øœ( 1›+Ö+¨Ô+Ð,Ñ+Ð,Ò+r<   c                óð   € ^p\        VP                  V4      R,          \        P                  4      p\	        VP
                  W!R7      R8”  g   Q h\        VP                  VP                  R4      4       R# )ri   çš™™™™™é?)r4   r�   rŽ   N)	r   Úonesr	   Úndtrr   r\   r   r^   r2   )r3   r4   r‰   r`   s   &&  r9   Ú
test_low_pÚTestCvm.test_low_p   sT   € ð ˆÜ˜RŸW™W Q›Z¨�^¬W¯\©\Ó:ˆÜ˜Ÿ™ qÔ0°3Ô6Ð6Ð6Ü˜Ÿ
™
 B§J¡J¨r£NÖ3r<   ú	jax.numpyúlazy -> no _axis_nan_policy©Úreasonr5   ç      ø?c                óž  € \         P                  ! \        \        R 7      ;_uu_ 4        \	        VP                  V4      \        P                  4      p\        VP                  VP                  VP                  4      4       \        VP                  VP                  VP                  4      4       RRR4       R#   + '       g   i     R# ; i)©rZ   N)r/   Úwarnsr   r   r   r2   r	   r¢   r   r\   r]   r^   )r3   r5   r4   r`   s   &&& r9   Útest_invalid_inputÚTestCvm.test_invalid_input‡   su   € ô �\Š\Ô,Ô4I×JÖJÜ  §¡¨A£´·±Ó=ˆCÜ˜CŸM™M¨2¯:©:°b·f±fÓ+=Ô>Ü˜CŸJ™J¨¯
©
°2·6±6Ó(:Ô;÷ K×J×JÒJús   ©BB;Â;C	r!   c                óp  a€ \        S4      '       d/   SP                  R 8  d   VR8X  d   \        P                  ! R4       Vf   \	        S4      M\        SV4      p\        SP                  . ROVR7      \        P                  4      p\        VP                  SP                  RVR7      4       \        VP                  SP                  RVR7      4       \        SP                  . ROVR7      R 4      p\        VP                  SP                  RVR7      4       \        VP                  SP                  R	VR7      4       \        SP                  . ROVR7      V3R
 l4      p\        VP                  SP                  RVR7      4       \        VP                  SP                  RVR7      4       R# )r#   r$   r%   Nr&   gÓˆk&qÒ?gDC+·šÂ?c                 óJ   € \         P                  ! V ^,
          R,          4      # )rA   r©   )r	   r¢   )r5   s   &r9   Ú<lambda>Ú'TestCvm.test_values_R.<locals>.<lambda>Ÿ   s   € ¤w§|¢|°Q¸µU¸CµKÔ'@r<   g�ºrW*î?g¤ju2´™`?c                 ó*   <€ SP                  V ) 4      ) # ©N)Úexpm1)r5   r4   s   &€r9   r±   r²   ¦   s   ø€ �r—x‘x  “|‘mr<   g  ¹Ð.óê?góûÎ`Ã(r?)g333333û¿r@   r   gÍÌÌÌÌÌô?rB   çš™™™™™¹?ç333333ã?)	r?   r@   rC   çffffffö?gìQ¸…ëÁ?rh   é   çÍÌÌÌÌÌì?ç      @)r   r.   r/   r0   r   r1   r   r2   r	   r¢   r   r\   r^   )r3   r!   r4   r`   s   &&f r9   Útest_values_RÚTestCvm.test_values_R�   sO  ø€ ä�B�<Š<˜BŸN™N¨UÔ2°uÀ	Ô7IÜ�KŠKÐ;Ô<Ø(-ªÔ  Ô$¼7À2ÀuÓ;Mˆô
 ˜RŸZ™ZÒ(FÈe˜ZÓTÜ$Ÿ\™\ó+ˆä˜Ÿ™ r§z¡zÐ2BÈ% zÓ'PÔQÜ˜Ÿ
™
 B§J¡J°Àu JÓ$MÔNô ˜RŸZ™ZÒ(FÈe˜ZÓTÙ@óBˆä˜Ÿ™ r§z¡zÐ2BÈ% zÓ'PÔQÜ˜Ÿ
™
 B§J¡JÐ/@È JÓ$NÔOô Ø�J‰JÒ=ÀUˆJÓKÜ#ó%ˆô 	˜Ÿ™ r§z¡zÐ2BÈ% zÓ'PÔQÜ˜Ÿ
™
 B§J¡JÐ/@È JÓ$NÖOr<   c                ó¾  € \        V4      '       gO   R p\        P                  ! \        VR7      ;_uu_ 4        \	        VP                  . RO4      R4       RRR4       R# \        P                  ! ^4      RrC\	        V\        P                  P                  4      p\	        VR4      p\        VP                  VP                  3VP                  VP                  34       \	        V\        P                  P                  V4      p\	        VRV4      p\        VP                  VP                  3VP                  VP                  34       R#   + '       g   i     R# ; i)z7`cdf` must be a callable if `rvs` is a non-NumPy array.r«   ÚbetaNÚexpon©r?   r@   rA   )r¸   çffffffæ?)r   r/   r   Ú
ValueErrorr   r2   rL   rM   r
   rÀ   Úcdfr   r\   r^   r¿   )r3   r4   Úmessager5   ÚargsrŠ   r`   s   &&     r9   Útest_str_cdfÚTestCvm.test_str_cdfª   së   € Ü˜�|Š|ØOˆGÜ—’œz°×9Ö9Ü˜rŸz™zª)Ó4°fÔ=÷ :áä—)’)˜A“, 
ˆ4Ü˜Q¤× 3Ñ 3× 7Ñ 7Ó8ˆÜ˜Q Ó(ˆÜ�c—m‘m S§Z¡ZÐ0°3·=±=À#Ç*Á*Ð2MÔNä˜Q¤× 2Ñ 2× 6Ñ 6¸Ó=ˆÜ˜Q ¨Ó-ˆÜ�c—m‘m S§Z¡ZÐ0°3·=±=À#Ç*Á*Ð2MÖN÷ :Ö9áús   ¸EÅE	rw   )gy;ÂiÁ‹ž?g#¾³^¥?gþE�>‘¿?gåD»
)î?)ç{®Gáz„?çš™™™™™©?ç      à?g+‡ÙÎ÷ï?)g…8„*5›?g@¤ß¾œ£?g÷Hmâä¾?g%¯Î1 â?)rÉ   rÊ   rË   g333333ï?)g€}têÊg™?g˜`�º¢?gäIÒ5“o¾?gÜ×�sF”ò?)r“   r•   r–   r—   rx   )rz   r{   r|   r}   r/   r~   r   r‹   r�   rš   r�   r£   Úskip_xp_backendsr­   r¼   rÇ   r€   r�   r‚   s   @r9   r…   r…   [   sô   ø‡ € ð
 ‡[�[×Ñ˜[Ø	
Ò0Ò2JÐKØ	Ò1Ò3KÐLØ	Ò3Ò5MÐNØ	Ò3Ò5MÐNð	+ó ñPóðPò.òDò
-ò4ð ‡[�[×!Ñ! +Ð6SÐ!ÓTØ‡[�[×Ñ˜S 2¨ u +Ó.ñ<ó /ó Uð<ð ‡[�[×Ñ˜WÒ&BÓCñPó DðP÷4Oð Or<   r…   c                   óN  a € ] tR t^»t o ]P
                  P                  RRR7      R 4       tR tR t	. R7Ot
. R8OtRRR	R
/R9.RRR	R
/R:.RRR	R
/R;.RRR	R/R<.RRR	R/R=.RRR	R/R>..t]P
                  P                  R?]4      ]P
                  P                  R. R@O4      R 4       4       tRRRR/RA.RRRR/RB.RRRR/RC.RRRR/RD.RRRR/RE.RRRR/RF..t]P
                  P                  R?]4      R 4       tR t^. RGO^. RHO^. RIO/t^. RJO^. RKO^. RLO^. RMO/t^. RNO^. ROO^. RPO^. RQO^. RRO/t^. RSO^. RTO^. RUO^. RVO^. RWO^. RXO/tR tR tR tRRR	R
/RY.RRR	R
/RZ.RRR	R
/R[.RRR	R/R\.RRR	R/RZ.RRR	R/R\..t]P
                  P                  R]]4      R 4       tR t]P
                  P                  RRR7      ]P
                  P                  R	R
R.4      R 4       4       tR t]P
                  P                  RRR7      R 4       t. R^O^^^^]P@                  ^^^^^^.RR 3. R^O^^^^]P@                  ]P@                  ^^^^^.R!R"3^^]P@                  ^.^^^^]P@                  ^^^^^^.R#R$3^^]P@                  ^.^^^^]P@                  ]P@                  ^^^^^.RR%3^]P@                  ]P@                  ^.^^^^]P@                  ]P@                  ^^^^^.R&R'3.t!]P
                  P                  R_]!4      R( 4       t". R`O. RaO. RbO. RcO. RdO. ReO. RfO. RgO. RhO.	t#]P
                  P                  Ri]#4      R) 4       t$]P
                  P                  RRR7      R* 4       t%. RjOR+R,.RRk.. RjOR+R,.RRk.. RjOR+R,.RRl.. RmO^.RRn.. RmO^.RRn.. RmO^.RRo.^^.^^.RRp.^^.^^.RRp.^^.^^.RRq..	t&]P
                  P                  . RrO]&4      R- 4       t'R. t(]P
                  P                  R. RsO4      R/ 4       t). RtOt*. RuOt+R0t,R1 t-R2 t.R3 t/R4 t0R5 t1R6t2V t3R# )vÚTestMannWhitneyUr¥   r¦   r§   c                ó¦  € VP                  ^^.4      pVP                  ^^.4      pVP                  . VP                  R7      pVP                  VP                  4      p\        P                  ! \
        \        R7      ;_uu_ 4        \        W$4      p\        VP                  V4       \        VP                  V4       RRR4       \        P                  ! \
        \        R7      ;_uu_ 4        \        WC4      p\        VP                  V4       \        VP                  V4       RRR4       \        P                  ! \
        \        R7      ;_uu_ 4        \        WD4      p\        VP                  V4       \        VP                  V4       RRR4       R#   + '       g   i     Lâ; i  + '       g   i     L�; i  + '       g   i     R# ; i)r?   r&   r«   N)r2   r!   r]   r/   r¬   r   r   r   r   r\   r^   )r3   r4   r5   r6   Úemptyr]   r`   s   &&     r9   Ú
test_emptyÚTestMannWhitneyU.test_emptyÃ   s3  € à�J‰J˜˜1�vÓˆØ�J‰J˜˜1�vÓˆØ—
‘
˜2 Q§W¡W�
Ó-ˆØ�j‰j˜Ÿ™Ó ˆä�\Š\Ô,Ô4I×JÖJÜ˜qÓ(ˆCÜ˜CŸM™M¨3Ô/Ü˜CŸJ™J¨Ô,÷ Kô
 �\Š\Ô,Ô4I×JÖJÜ˜uÓ(ˆCÜ˜CŸM™M¨3Ô/Ü˜CŸJ™J¨Ô,÷ Kô
 �\Š\Ô,Ô4I×JÖJÜ˜uÓ,ˆCÜ˜CŸM™M¨3Ô/Ü˜CŸJ™J¨Ô,÷ KÑJ÷ K×Jú÷
 K×Jú÷
 K×JÐJús$   Â8FÃ/8F,Å8F?ÆF)	Æ,F<	Æ?G	c                ód  € VP                  ^^.4      pVP                  ^^.4      p\        \        RR7      ;_uu_ 4        \        W#RR7       RRR4       \        \        RR7      ;_uu_ 4        \        W#RR7       RRR4       \        \        RR7      ;_uu_ 4        \        W#R	R
7       RRR4       \        \        RR7      ;_uu_ 4        \        W#RR7       RRR4       R#   + '       g   i     LŸ; i  + '       g   i     Lƒ; i  + '       g   i     Lg; i  + '       g   i     R# ; i)r?   z`use_continuity` must be oner«   Úekki)Úuse_continuityNz`alternative` must be one of©Úalternativez`axis` must be an integerr©   rf   z`method` must be one of©Úmethod)r2   Úassert_raisesrÃ   r   )r3   r4   r5   r6   s   &&  r9   Útest_input_validationÚ&TestMannWhitneyU.test_input_validationÙ   sÃ   € Ø�J‰J˜˜1�vÓˆØ�J‰J˜˜1�vÓˆÜœ:Ð-K×LÖLÜ˜¨fÕ5÷ Mäœ:Ð-K×LÖLÜ˜¨6Õ2÷ Mäœ:Ð-H×IÖIÜ˜ CÕ(÷ Jäœ:Ð-F×GÖGÜ˜ fÕ-÷ HÑG÷ M×LúçL×LúçI×IúçG×GÐGús0   Á C%Á/C8ÂDÃDÃ%C5	Ã8D	ÄD	ÄD/	c                óÔ  € \         P                  P                  R 4      p^pVP                  VP                  V^,
          4      4      pVP                  VP                  V^,
          4      4      p\	        WE4      p\	        WERR7      p\	        WERR7      pVP
                  VP
                  8X  g   Q hVP
                  VP
                  8w  g   Q hVP                  VP                  V^,
          4      4      pVP                  VP                  V^,           4      4      p\	        WE4      p\	        WERR7      p\	        WERR7      pVP
                  VP
                  8X  g   Q hVP
                  VP
                  8w  g   Q h\	        WT4      p\	        WERR7      p\	        WERR7      pVP
                  VP
                  8X  g   Q hVP
                  VP
                  8w  g   Q hVP                  VP                  V^,           4      4      pVP                  VP                  V^,           4      4      p\	        WE4      p\	        WERR7      p\	        WERR7      pVP
                  VP
                  8w  g   Q hVP
                  VP
                  8X  g   Q hVP                  VP                  V^,
          4      4      pVP                  VP                  V^,
          4      4      p\        P                  ! V4      ^,          P                  V^,          4      p\	        WE4      p\	        WERR7      p\	        WERR7      pVP
                  VP
                  8w  g   Q hVP
                  VP
                  8X  g   Q hR# )l   nE QWS�fÚ
asymptoticrØ   ÚexactN)	rL   rl   rm   r2   r   r^   ÚxpxÚatÚset)	r3   r4   ro   r‰   r5   r6   ÚautorÞ   rß   s	   &&       r9   Ú	test_autoÚTestMannWhitneyU.test_autoå   s¨  € ô �i‰i×#Ñ#Ð$6Ó7ˆØˆð �J‰J�s—z‘z ! A¥#“Ó'ˆØ�J‰J�s—z‘z ! A¥#“Ó'ˆÜ˜AÓ!ˆÜ! !¨|Ô<ˆ
Ü˜Q¨'Ô2ˆØ�{‰{˜eŸl™lÔ*Ð*Ð*Ø�{‰{˜j×/Ñ/Ô/Ð/Ð/ð �J‰J�s—z‘z ! A¥#“Ó'ˆØ�J‰J�s—z‘z ! A¥#“Ó'ˆÜ˜AÓ!ˆÜ! !¨|Ô<ˆ
Ü˜Q¨'Ô2ˆØ�{‰{˜eŸl™lÔ*Ð*Ð*Ø�{‰{˜j×/Ñ/Ô/Ð/Ð/ô ˜AÓ!ˆÜ! !¨|Ô<ˆ
Ü˜Q¨'Ô2ˆØ�{‰{˜eŸl™lÔ*Ð*Ð*Ø�{‰{˜j×/Ñ/Ô/Ð/Ð/ð �J‰J�s—z‘z ! A¥#“Ó'ˆØ�J‰J�s—z‘z ! A¥#“Ó'ˆÜ˜AÓ!ˆÜ! !¨|Ô<ˆ
Ü˜Q¨'Ô2ˆØ�{‰{˜eŸl™lÔ*Ð*Ð*Ø�{‰{˜j×/Ñ/Ô/Ð/Ð/ð �J‰J�s—z‘z ! A¥#“Ó'ˆØ�J‰J�s—z‘z ! A¥#“Ó'ˆÜ�FŠF�1‹I�a�L×Ñ˜Q˜q�TÓ"ˆÜ˜AÓ!ˆÜ! !¨|Ô<ˆ
Ü˜Q¨'Ô2ˆØ�{‰{˜eŸl™lÔ*Ð*Ð*Ø�{‰{˜j×/Ñ/Ô/Ð/Ò/r<   r×   ú	two-sidedrÙ   rÞ   ç      0@ÚlessÚgreaterrß   r!   Nc                óú  € \        V4      '       d/   VP                  R 8  d   VR8X  d   \        P                  ! R4       Vf   \	        V4      M
\        WC4      pVP                  V P                  VR7      VP                  V P                  VR7      re\        WV3/ VB p\        VP                  VP                  V^ ,          VR7      4       \        VP                  VP                  V^,          VR7      4       R# )r#   r$   z*Scalar dtypes only respected after NEP 50.Nr&   )r   r.   r/   r0   r   r1   r2   r5   r6   r   r   r\   r^   )r3   ÚkwdsÚexpectedr!   r4   r5   r6   r`   s   &&&&&   r9   Ú
test_basicÚTestMannWhitneyU.test_basic;  s¸   € ô �B�<Š<˜BŸN™N¨UÔ2°uÀ	Ô7IÜ�KŠKÐDÔEØ(-ªÔ  Ô$¼7À2Ó;MˆØ�z‰z˜$Ÿ&™&¨ˆzÓ.°·
±
¸4¿6¹6È°
Ó0Oˆ1Ü˜1Ñ( 4Ñ(ˆÜ˜Ÿ™ r§z¡z°(¸1µ+ÀU zÓ'KÔLÜ˜Ÿ
™
 B§J¡J¨x¸­{À% JÓ$HÖIr<   rÕ   TFc                ó<  € VP                  V P                  4      VP                  V P                  4      rT\        WT3R R/VB p\	        VP
                  VP                  V^ ,          4      4       \	        VP                  VP                  V^,          4      4       R# )rÙ   rÞ   N)r2   r5   r6   r   r   r\   r^   )r3   rë   rì   r4   r5   r6   r`   s   &&&&   r9   Útest_continuityÚ TestMannWhitneyU.test_continuityS  so   € ð �z‰z˜$Ÿ&™&Ó! 2§:¡:¨d¯f©fÓ#5ˆ1Ü˜1Ñ=¨Ð=¸Ñ=ˆÜ˜Ÿ™ r§z¡z°(¸1µ+Ó'>Ô?Ü˜Ÿ
™
 B§J¡J¨x¸­{Ó$;Ö<r<   c           
     óö  € VP                  . RO4      pVP                  . RO4      pVP                  . RO4      R,          pVP                  . RO4      R,          pVP                  VR,
          W4,
          W5,
          W3V,           W4,           VR,           .4      p\        W&R	RR7      p. R
Op. ROp	\        VP                  VP                  V4      4       \        VP                  VP                  V	4      4       R# )r�   rÉ   rÞ   )rg   rÙ   N©r�   ç       @ç      @ç      @)r�   rô   rõ   rö   r,   )rŽ   r�   rŽ   r�   rŽ   )rŽ   rŽ   r�   rŽ   rŽ   rk   )rE   rj   ç      !@rG   r»   rF   rD   )r?   g]�UÄÚì?g…æ[»é?giœ…\­æ?g°ZX<_Õã?gãžxº.á?gåß ê…
Ù?)r2   Ústackr   r   r\   r   r^   )
r3   r4   r5   Úy0ÚdyÚdy2r6   r`   Ú
U_expectedÚ
p_expecteds
   &&        r9   Útest_tie_correctÚ!TestMannWhitneyU.test_tie_correctc  sÀ   € ð �J‰JÒ'Ó(ˆØ�Z‰ZÒ,Ó-ˆØ�Z‰ZÒ,Ó-¨dÕ2ˆØ�j‰jÒ-Ó.¨tÕ3ˆØ�H‰H�b˜•g˜r�u b¥f¨b°Sµ&¸"½%ÀÀDÅÐIÓJˆÜ˜1 b°Ô>ˆÚ/ˆ
òIˆ
ä˜Ÿ™ r§z¡z°*Ó'=Ô>Ü˜Ÿ
™
 B§J¡J¨zÓ$:Ö;r<   c           	     ó  € \        \        R \        ^ ^ 4      4       ^V P                  ^V P                  ^V P
                  ^V P                  /pVP                  4        EF£  w  r#VP                  4        EFˆ  w  rE\        P                  ! ^ \        V4      4      p\        P                  P                  WB4       \        \        P                  P                  VR7      VRR7       \        P                  ! ^ WB,          ^,           4      p\        \        P                  P                  VR7      \        P                  P                  VR7      ,           \        P                  P!                  VR7      ,
          ^4       \        P                  P!                  VR7      p\        WˆRRR1,          4       \        P                  P                  W$4       \        P                  P!                  VR7      p	\        W‰4       EK‹  	  EK¦  	  R# )Ús)Úkr>   r'   Nrk   )Úsetattrr   r   Úpn3Úpn4Úpm5Úpm6ÚitemsrL   rM   Úlenr  Ú
set_shapesr   rÄ   ÚsfÚpmf)
r3   Úp_tablesr‰   ÚtableÚmr8   ÚuÚu2r  Úpmf2s
   &         r9   Útest_exact_distributionÚ(TestMannWhitneyU.test_exact_distribution“  sg  € ä”
˜C¤ a¨£Ô,à�t—x‘x  D§H¡H¨a°·±¸1¸d¿h¹hÐGˆØ Ÿ™×(‰HˆAØŸ™Ÿ‘�ä—I’I˜a¤ Q£Ó(�Ü—‘×'Ñ'¨Ô-Ü¤
§¡× 0Ñ 0°1Ð 0Ó 5°q¸tÕDô —Y’Y˜q !¥# a¥%Ó(�Ü¤
§¡× 0Ñ 0°2Ð 0Ó 6Ü",§,¡,§/¡/°B /Ó"7õ!8ä",§,¡,×"2Ñ"2°RÐ"2Ó"8õ!9à:;ô=ô
 !—l‘l×&Ñ&¨Ð&Ó,�Ü ©¨2¨¥YÔ/ô —‘×'Ñ'¨Ô-Ü!—|‘|×'Ñ'¨"Ð'Ó-�Ü ×*ô) &ó )r<   c                óì  € \         P                  P                  R 4      pVP                  VP                  ^4      4      pVP                  VP                  ^4      4      p\	        W4RR7      p\	        W4RR7      pVP
                  VP
                  8X  g   Q hVP                  VP                  VP                  ,
          4      R8”  g   Q hVP                  VP                  ^(4      4      pVP                  VP                  ^(4      4      p\	        W4RR7      p\	        W4RR7      pVP
                  VP
                  8X  g   Q hVP                  VP                  VP                  ,
          4      R8  g   Q hR# )iÿ0  rß   rØ   rÞ   rÉ   r>   N)rL   rl   rm   r2   r   r\   Úabsr^   )r3   r4   ro   r5   r6   Úres1Úres2s   &&     r9   Útest_asymptotic_behaviorÚ)TestMannWhitneyU.test_asymptotic_behavior¯  s  € Ü�i‰i×#Ñ# EÓ*ˆð �J‰J�s—z‘z !“}Ó%ˆØ�J‰J�s—z‘z !“}Ó%ˆÜ˜A¨Ô1ˆÜ˜A¨Ô6ˆØ�~‰~ §¡Ô/Ð/Ð/Ø�v‰v�d—k‘k D§K¡KÕ/Ó0°4Ô7Ð7Ð7ð �J‰J�s—z‘z "“~Ó&ˆØ�J‰J�s—z‘z "“~Ó&ˆÜ˜A¨Ô1ˆÜ˜A¨Ô6ˆØ�~‰~ §¡Ô/Ð/Ð/Ø�v‰v�d—k‘k D§K¡KÕ/Ó0°4Ô7Ð7Ò7r<   c                óž  € VP                  . RO4      VP                  RR.4      r2\        W#RRR7      p\        W#RRR7      p\        VP                  VP                  4       VP                  R8”  g   Q h\        W#R	RR7      p\        VP                  VP                  R4      4       \        VP                  VP                  R 4      4       R
# )r�   rõ   r©   ç      @rè   rß   )r×   rÙ   ré   rË   ræ   N©r�   rô   rõ   )r2   r   r   r^   r\   )r3   r4   r5   r6   Úres_lÚres_gr`   s   &&     r9   Útest_exact_U_equals_meanÚ)TestMannWhitneyU.test_exact_U_equals_meanÄ  s›   € ð �z‰zš,Ó'¨¯©°S¸#°JÓ)?ˆ1Ü˜Q¨v¸gÔFˆÜ˜Q¨yÀÔIˆÜ˜Ÿ™ e§l¡lÔ3Ø�|‰|˜cÔ!Ð!Ð!ä˜1¨[ÀÔIˆÜ˜Ÿ™ r§z¡z°"£~Ô6Ü˜Ÿ
™
 B§J¡J¨r£NÖ3r<   c                ó0   € \        \        R/ VB V4       R# )r?   N©r?   r@   )r   r   )r3   rë   Úresults   &&&r9   Útest_scalar_dataÚ!TestMannWhitneyU.test_scalar_dataß  s   € ô 	œÑ2¨TÑ2°FÖ;r<   c           	     ó¸   € \        \        ^^RR7      R4       \        \        ^^RR7      R4       \        \        ^^RRR7      R\        P                  34       R# )	r?   rß   rØ   rË   rÞ   F)rÙ   rÕ   N)rË   r?   )r   r   rL   r]   ©r3   s   &r9   Útest_equal_scalar_dataÚ'TestMannWhitneyU.test_equal_scalar_dataä  sP   € ô
 	”\ ! Q¨wÔ7¸ÔBÜ”\ ! Q¨|Ô<¸hÔGô 	”\ ! Q¨|Ø16ô8Ø:=¼r¿v¹v¸ö	Hr<   c                ó¸  € \         P                  P                  R 4      pRp^^
reVP                  V^^34      pVP                  ^V^^34      R,           p\        VP	                  V4      VP	                  V4      WR7      p	Rp
V	P
                  P                  V
8X  g   Q hV	P                  P                  V
8X  g   Q h\         P                  ! WtR	4      \         P                  ! W„R	4      r‡VR
,          pVP                  VP                  8X  g   Q h\         P                  ! WzV3,           4      p\         P                  ! WŠV3,           4      pVP                  RR	 V
8X  g   Q hVP                  RR	 V
8X  g   Q h\         P                  ! V
4      p\         P                  ! V
4      p\        V
 Uu. uF  p\        V4      NK  	  up!   F=  pW~,          pWŽ,          p\        VVVR7      pVP                  W¾&   VP
                  WÎ&   K?  	  \        V	P
                  VP	                  V4      RR7       \        V	P                  VP	                  V4      RR7       R# u upi )l   2=U r¶   )rÙ   rg   NrØ   ç¼‰Ø—²Òœ<r'   éýÿÿÿ)rD   rA   rG   rk   )N.)rL   rl   rm   r   r2   r^   Úshaper\   ÚmoveaxisÚndimÚbroadcast_toÚzerosr   Úranger   )r3   rÙ   r4   ro   rg   r  r‰   r5   r6   r`   r.  Ú
statisticsÚpvaluesrp   ÚindicesÚxiÚyiÚtemps   &&&               r9   Útest_gh_12837_11113Ú$TestMannWhitneyU.test_gh_12837_11113ó  sé  € ô �i‰i×#Ñ# JÓ/ˆð ˆØ�"ˆ1Ø�J‰J˜˜1˜a�yÓ!ˆØ�J‰J˜˜1˜a �|Ó$ sÕ*ˆÜ˜2Ÿ:™: a›=¨"¯*©*°Q«-ÀÔRˆàˆØ�z‰z×Ñ 5Ô(Ð(Ð(Ø�}‰}×"Ñ" eÔ+Ð+Ð+ô �{Š{˜1 BÓ'¬¯ª°Q¸bÓ)Aˆ1àˆi�LˆØ�v‰v˜Ÿ™ÔÐÐä�OŠO˜A¨ t�|Ó,ˆÜ�OŠO˜A¨ t�|Ó,ˆØ�w‰w�s˜ˆ|˜uÔ$Ð$Ð$Ø�w‰w�s˜ˆ|˜uÔ$Ð$Ð$ô —X’X˜e“_ˆ
Ü—(’(˜5“/ˆÜ±5Ó 9±5¨a¤ q¦±5Ñ 9Ô:ˆGØ•ˆBØ•ˆBÜ  B¨vÔ6ˆDØ"&§.¡.ˆJÑØ#Ÿ{™{ˆGÓñ ;ô 	˜Ÿ
™
 B§J¡J¨wÓ$7¸eÕDÜ˜Ÿ™ r§z¡z°*Ó'=ÀE×Jùò !:s   Æ-Ic                ón  € . ROp. ROp\        VP                  V4      VP                  V4      4      pRV^ &   \        P                  V^&   \        VP                  V4      VP                  V4      4      p\	        VP
                  VP
                  4       \	        VP                  VP                  4       R# )r?   r�   Nr[   )rA   rD   rF   rG   rj   rA   r@   r?   rB   rB   rC   )r   r2   rL   rn   r   r\   r^   )r3   r4   r5   r6   r  r  s   &&    r9   Útest_gh_11355ÚTestMannWhitneyU.test_gh_11355   s€   € âˆÚ-ˆÜ˜BŸJ™J q›M¨2¯:©:°a«=Ó9ˆð ˆˆ!‰Ü�v‰vˆˆ!‰Ü˜BŸJ™J q›M¨2¯:©:°a«=Ó9ˆä˜Ÿ™¨¯©Ô7Ü˜Ÿ™ T§[¡[Ö1r<   c                óT  € . ROp^^^\         P                  ^	^^^^^^.p\        VP                  V4      VP                  V4      4      p\	        VP
                  VP                  VP                  4      4       \	        VP                  VP                  VP                  4      4       R# )r�   Nró   )rL   r]   r   r2   r   r\   r^   )r3   r4   r5   r6   Úres3s   &&   r9   Útest_gh11355_nanÚ!TestMannWhitneyU.test_gh11355_nan.  s{   € ò ˆØ��1”b—f‘f˜a  A q¨!¨Q°Ð2ˆÜ˜BŸJ™J q›M¨2¯:©:°a«=Ó9ˆÜ˜Ÿ™¨¯
©
°2·6±6Ó(:Ô;Ü˜Ÿ™ R§Z¡Z°·±Ó%7Ö8r<   ç      $@g+z’¿QœÀ?r÷   g}$kù\¶?g     €1@g!Ë›G*ã?g›Á,ÖsÿÝ?ç     €8@gêFÏHïQé?c                óú   € \        VP                  V4      VP                  V4      R R7      p\        VP                  VP                  V4      RR7       \        VP                  VP                  V4      RR7       R# )rÞ   rØ   çê-�™—q=r'   N)r   r2   r   r\   r^   )r3   r5   r6   r\   r^   r4   r`   s   &&&&&& r9   Útest_gh_11355bÚTestMannWhitneyU.test_gh_11355bG  sT   € ô ˜2Ÿ:™: a›=¨"¯*©*°Q«-ÀÔMˆÜ˜Ÿ™ r§z¡z°)Ó'<À5ÕIÜ˜Ÿ
™
 B§J¡J¨vÓ$6¸U×Cr<   c                ó  € R pVP                  . RO4      pVP                  . RO4      p\        WxVW#R7      p	\        V	P                  VP                  V4      4       \	        V	P
                  VP                  V4      4       R# )g     €A@©rÕ   r×   rÙ   N)
r    g�Âõ(\�ê?g=
×£p=þ?g¤p=
×£ð?g333333÷?g®Gázö?g�Âõ(\�þ?g=
×£p=ú?r*   g\�Âõ(\÷?)gffffffò?g)\�Âõ(ì?rº   g®Gáz®ç?g\�Âõ(\ó?)r2   r   r   r\   r   r^   )
r3   rÕ   r×   rÙ   Ú
pvalue_expr4   Ústatistic_expr5   r6   r`   s
   &&&&&&    r9   Útest_gh_9184ÚTestMannWhitneyU.test_gh_9184X  sg   € ð. ˆØ�J‰JÒSÓTˆØ�J‰JÒ5Ó6ˆÜ˜1°Ø'2ôCˆä˜Ÿ™ r§z¡z°-Ó'@ÔAÜ˜Ÿ
™
 B§J¡J¨zÓ$:Ö;r<   c                ó  € VP                  VP                  4      pVP                  W"W"V.4      pVP                  W"W"V.4      p\        W44      p\	        VP
                  VP                  V4      4       \	        VP                  V4       R # r´   )r2   r]   rø   r   r   r\   r^   )r3   r4   r]   ÚaÚbr`   s   &&    r9   Útest_gh_4067ÚTestMannWhitneyU.test_gh_4067w  sn   € ð �j‰j˜Ÿ™Ó ˆØ�H‰H�c ¨#Ð.Ó/ˆØ�H‰H�c ¨#Ð.Ó/ˆÜ˜1Ó ˆÜ˜Ÿ™ r§z¡z°#£Ô7Ü˜Ÿ
™
 CÖ(r<   r©   r  c                óV  € \        VP                  V4      VP                  V4      R VRR7      p\        V4      VP                  8X  d   RMRp\	        VP
                  VP                  V^ ,          4      VR7       \	        VP                  VP                  V^,          4      VR7       R# )TrÞ   rJ  ç�íµ ÷Æ°>rF  ©ÚrtolN)r   r2   r   r$   r   r\   r^   )r3   r5   r6   r×   rì   r4   r`   rW  s   &&&&&&  r9   Útest_gh_2118ÚTestMannWhitneyU.test_gh_2118‘  s{   € ô ˜2Ÿ:™: a›=¨"¯*©*°Q«-ÈØ'2¸<ôIˆä'¨Ó+¨r¯z©zÔ9‰t¸uˆÜ˜Ÿ™ r§z¡z°(¸1µ+Ó'>ÀTÕJÜ˜Ÿ
™
 B§J¡J¨x¸­{Ó$;À$×Gr<   c                ó  € \         P                  P                  R 4      p^^r2VP                  VR7      pVP                  VR7      p\        \        R\        ^ ^ 4      4       \        P                  P                  4        \        P                  ! WERR7      p\        P                  P                  P                  pVR,          \        VP                  W#,          VP                  ,
          4      ^,           8X  g   Q h\        P                  ! WTRR7       V\        P                  P                  P                  8X  g   Q h\        P                  P                  4        \        P                  ! V^ V,          RRR7       \        P                  P                  P                  pVR,          ^8X  g   Q h\        P                  ! ^ V,          VRRR7       V\        P                  P                  P                  8X  g   Q hR# )	ì   g>·mŽjÑK rd   r  rß   rØ   ré   )rÙ   r×   Nrk   )rL   rl   rm   r  r   r   r  Úresetr   r   Úconfigurationsr.  Úminr\   )r3   ro   r  r‰   r5   r6   r`   r.  s   &       r9   Útest_gh19692_smaller_tableÚ+TestMannWhitneyU.test_gh19692_smaller_table›  si  € ô
 �i‰i×#Ñ#Ð$7Ó8ˆØ�"ˆ1Ø�J‰J˜AˆJÓˆØ�J‰J˜AˆJÓˆä”
˜C¤ a¨£Ô,Ü�‰×ÑÔä× Ò  ¨gÔ6ˆÜ—‘×+Ñ+×1Ñ1ˆØ�R�yœC §¡¨q­s°S·]±]Õ/BÓCÀaÕGÔGÐGÐGÜ×Ò˜1¨Õ0Øœ
Ÿ™×3Ñ3×9Ñ9Ô9Ð9Ð9ô
 	�‰×ÑÔÜ×Ò˜1˜a �c¨'¸yÕIÜ—‘×+Ñ+×1Ñ1ˆØ�R�y˜AŒ~Ðˆ~Ü×Ò˜1˜Q�3 ¨'¸yÕIØœ
Ÿ™×3Ñ3×9Ñ9Ô9Ð9Ò9r<   c                ó¢  € \         P                  P                  R 4      pVP                  RR7      pVP                  RR7      p\        P                  ! W4\        P
                  ! 4       V^R7      p\        P                  ! W4RV^R7      p\        VP                  VP                  RR7       \        VP                  VP                  RR7       R# )	r[  rd   )rÙ   r×   rg   rß   çVçž¯Ò<rV  N)r@   rC   )r@   rD   )	rL   rl   rm   r   r   ÚPermutationMethodr   r\   r^   )r3   r×   ro   r5   r6   r`   r  s   &&     r9   Útest_permutation_methodÚ(TestMannWhitneyU.test_permutation_method¸  sœ   € ä�i‰i×#Ñ#Ð$7Ó8ˆØ�J‰J˜FˆJÓ#ˆØ�J‰J˜FˆJÓ#ˆÜ× Ò  ¬e×.EÒ.EÓ.GØ-8¸qôBˆä×!Ò! !¨wØ.9ÀôCˆä˜Ÿ™ t§~¡~¸EÕBÜ˜Ÿ
™
 D§K¡K°e×<r<   g›+¡†›„=c                ó$  € VP                  V P                  4      VP                  V P                  4      r2\        P                  ! W#R R7      w  rE\        P                  ! W2RR7      w  rg\        P                  ! W#RR7      w  r‰\        P                  ! W2R R7      w  r«\        WW4       \        W›4       WY8w  g   Q h\        WAP                  R4      4       \        WaP                  R4      4       \        W�P                  R4      4       \        W¡P                  R4      4       \        WQP                  R4      V P                  R7       VP                  VP                  8X  d   V P                  MRp\        W‘P                  R4      VR	R
7       R# )rè   rÖ   ré   ç      @ç     €Y@g=_A§ÿï?rV  çü©ñÒMb@?glP†z.?r,  ©rW  r(   N)
r2   ÚXÚYr   r   r   r   rW  r!   ry   ©r3   r4   rk  rl  Úu1rQ   r  rS   Úu3rU   Úu4Úp4rW  s   &&           r9   Útest_mannwhitneyu_one_sidedÚ,TestMannWhitneyU.test_mannwhitneyu_one_sidedÖ  s  € Ø�z‰z˜$Ÿ&™&Ó! 2§:¡:¨d¯f©fÓ#5ˆ1Ü×#Ò# A°fÔ=‰ˆÜ×#Ò# A°iÔ@‰ˆÜ×#Ò# A°iÔ@‰ˆÜ×#Ò# A°fÔ=‰ˆä˜ÔÜ˜ÔØŒxˆˆxÜ˜ŸJ™J tÓ,Ô-Ü˜ŸJ™J tÓ,Ô-Ü˜ŸJ™J tÓ,Ô-Ü˜ŸJ™J tÓ,Ô-Ü˜ŸJ™JÐ'8Ó9ÀÇ	Á	ÕJØŸG™G r§z¡zÔ1ˆt�yŠy°tˆÜ˜ŸJ™JÐ':Ó;À$ÈU×Sr<   c                óâ  € VP                  V P                  4      VP                  V P                  4      r2\        P                  ! W#R R7      w  rE\        P                  ! W2R R7      w  rg\        WW4       \        WAP                  R4      4       \        WaP                  R4      4       VP                  VP                  8X  d   V P                  MRp\        WQP                  R4      VRR7       R# )	ræ   rÖ   rg  rh  ri  glP†z.?r,  rj  N©
r2   rk  rl  r   r   r   r!   ry   rW  r   ©	r3   r4   rk  rl  rn  rQ   r  rS   rW  s	   &&       r9   Útest_mannwhitneyu_two_sidedÚ,TestMannWhitneyU.test_mannwhitneyu_two_sidedè  s¥   € Ø�z‰z˜$Ÿ&™&Ó! 2§:¡:¨d¯f©fÓ#5ˆ1Ü×#Ò# A°kÔB‰ˆÜ×#Ò# A°kÔB‰ˆä˜ÔÜ˜ŸJ™J tÓ,Ô-Ü˜ŸJ™J tÓ,Ô-ØŸG™G r§z¡zÔ1ˆt�yŠy°tˆÜ˜ŸJ™JÐ'9Ó:ÀÈE×Rr<   c                ó  € VP                  V P                  4      VP                  V P                  4      r2\        P                  ! W#R RR7      w  rE\        P                  ! W2R RR7      w  rg\        P                  ! W#R RR7      w  r‰\        P                  ! W2R RR7      w  r«\        WW4       \        W›4       WY8w  g   Q h\        WAP                  R4      4       \        WaP                  R4      4       \        W�P                  R4      4       \        W¡P                  R4      4       VP                  VP                  8X  d   V P                  MRp\        WQP                  R4      VRR	7       \        W‘P                  R
4      VRR	7       R# )Frè   rÖ   ré   rg  rh  ri  gii5‡£ÿï?r,  rj  g¬2¥¥2?Nru  rm  s   &&           r9   Ú&test_mannwhitneyu_no_correct_one_sidedÚ7TestMannWhitneyU.test_mannwhitneyu_no_correct_one_sidedó  s  € Ø�z‰z˜$Ÿ&™&Ó! 2§:¡:¨d¯f©fÓ#5ˆ1Ü×#Ò# A¨%¸VÔD‰ˆÜ×#Ò# A¨%¸YÔG‰ˆÜ×#Ò# A¨%¸YÔG‰ˆÜ×#Ò# A¨%¸VÔD‰ˆä˜ÔÜ˜ÔØŒxˆˆxÜ˜ŸJ™J tÓ,Ô-Ü˜ŸJ™J tÓ,Ô-Ü˜ŸJ™J tÓ,Ô-Ü˜ŸJ™J tÓ,Ô-ØŸG™G r§z¡zÔ1ˆt�yŠy°tˆÜ˜ŸJ™JÐ'8Ó9ÀÈ5ÕQÜ˜ŸJ™JÐ';Ó<À4Èe×Tr<   c                óæ  € VP                  V P                  4      VP                  V P                  4      r2\        P                  ! W#R RR7      w  rE\        P                  ! W2R RR7      w  rg\        WW4       \        WAP                  R4      4       \        WaP                  R4      4       VP                  VP                  8X  d   V P                  MRp\        WQP                  R4      VRR7       R	# )
Fræ   rÖ   rg  rh  ri  g¬2¥¥2?r,  rj  Nru  rv  s	   &&       r9   Ú&test_mannwhitneyu_no_correct_two_sidedÚ7TestMannWhitneyU.test_mannwhitneyu_no_correct_two_sided  s©   € Ø�z‰z˜$Ÿ&™&Ó! 2§:¡:¨d¯f©fÓ#5ˆ1Ü×#Ò# A¨%¸[ÔI‰ˆÜ×#Ò# A¨%¸[ÔI‰ˆä˜ÔÜ˜ŸJ™J tÓ,Ô-Ü˜ŸJ™J tÓ,Ô-ØŸG™G r§z¡zÔ1ˆt�yŠy°tˆÜ˜ŸJ™JÐ';Ó<À4Èe×Tr<   c                óÞ  € VP                  . R NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NRNR NR NRNR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR N4      pVP                  . R NR NR NR NR NR NR NRNR NRNR NR NR NR NRNR NR NR NRNR NR NR NR NR NRNR NR NRNR NR NR NR NR NR NR NR NR NR NRNR NRNR NR NR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NRNRNR NR NRNR NR NRNR NRNR NR NR NR NRNRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NR NR NRNRNRNR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NRNR NR NR NR NRNR NR NR NR NR NR NR NR NR NR NR NR NRNR NR NR NRNR NR NR NR NR NR N4      p\        P                  ! W#RR7      p\        VP                  VP                  R4      4       \        VP
                  VP                  R4      4       \        P                  ! W#RR7      p\        VP                  VP                  R4      4       \        VP
                  VP                  R4      4       \        P                  ! W#R	R7      p\        VP                  VP                  R4      4       \        VP
                  VP                  R
4      4       R# )r�   rô   rõ   rè   rÖ   g     •Ð@g €?Õ¹•ý>ré   gÜ&)EÅÿï?ræ   g�Ž?Õ¹•?N)r2   r   r   r   r\   r^   r_   s   &&   r9   Útest_mannwhitneyu_onesÚ'TestMannWhitneyU.test_mannwhitneyu_ones  sŽ  € à�J‰Jð 0˜ð 0˜Bð 0 ð 0 Bð 0¨ð 0¨Bð 0°ð 0°Bð 0¸ð 0¸Bð 0Àð 0ÀBð 0Èð 0ÈBð 0Øð0Øð0Ø "ð0Ø$&ð0Ø(*ð0Ø,.ð0Ø02ð0Ø46ð0Ø8:ð0Ø<>ð0Ø@Bð0ØDFð0ØHJð0ØLNð0àð0àð0à "ð0à$&ð0à(*ð0à,.ð0à02ð0à46ð0à8:ð0à<>ð0à@Bð0àDFð0àHJð0àLNð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð	0ð ð	0ð !#ð	0ð %'ð	0ð )+ð	0ð -/ð	0ð 13ð	0ð 57ð	0ð 9;ð	0ð =?ð	0ð ACð	0ð EGð	0ð IKð	0ð MOð	0ð
 ð0ð
 ð0ð
 !#ð0ð
 %'ð0ð
 )+ð0ð
 -/ð0ð
 13ð0ð
 57ð0ð
 9;ð0ð
 =?ð0ð
 ACð0ð
 EGð0ð
 IKð0ð
 MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð ð0ð ð0ð !#ð0ð %'ð0ð )+ð0ð -/ð0ð 13ð0ð 57ð0ð 9;ð0ð =?ð0ð ACð0ð EGð0ð IKð0ð MOð0ð  ð!0ð  ð!0ð  !#ð!0ð  %'ð!0ð  )+ð!0ð  -/ð!0ð  13ð!0ð  57ð!0ð  9;ð!0ð  =?ð!0ð  ACð!0ð  EGð!0ð  IKð!0ð  MOð!0ð" ð#0ð" ð#0ð" !#ð#0ð" %'ð#0ð" )+ð#0ð" -/ð#0ó 1ˆð& �J‰Jð (˜ð (˜Bð ( ð ( Bð (¨ð (¨Bð (°ð (°Bð (¸ð (¸Bð (Àð (ÀBð (Èð (ÈBð (Øð(Øð(Ø "ð(Ø$&ð(Ø(*ð(Ø,.ð(Ø02ð(Ø46ð(Ø8:ð(Ø<>ð(Ø@Bð(ØDFð(ØHJð(ØLNð(àð(àð(à "ð(à$&ð(à(*ð(à,.ð(à02ð(à46ð(à8:ð(à<>ð(à@Bð(àDFð(àHJð(àLNð(ð ð(ð ð(ð !#ð(ð %'ð(ð )+ð(ð -/ð(ð 13ð(ð 57ð(ð 9;ð(ð =?ð(ð ACð(ð EGð(ð IKð(ð MOð(ð ð	(ð ð	(ð !#ð	(ð %'ð	(ð )+ð	(ð -/ð	(ð 13ð	(ð 57ð	(ð 9;ð	(ð =?ð	(ð ACð	(ð EGð	(ð IKð	(ð MOð	(ð
 ð(ð
 ð(ð
 !#ð(ð
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 )+ð(ð
 -/ð(ð
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 =?ð(ð
 ACð(ð
 EGð(ð
 IKð(ð
 MOð(ð ð(ð ð(ð !#ð(ð %'ð(ð )+ð(ð -/ð(ð 13ð(ð 57ð(ð 9;ð(ð =?ð(ð ACð(ð EGð(ð IKð(ð MOð(ð ð(ð ð(ð !#ð(ð %'ð(ð )+ð(ð -/ð(ð 13ð(ð 57ð(ð 9;ð(ð =?ð(ð ACð(ð EGð(ð IKð(ð MOð(ð ð(ð ð(ð !#ð(ð %'ð(ð )+ð(ð -/ð(ð 13ð(ð 57ð(ð 9;ð(ð =?ð(ð ACð(ð EGð(ð IKð(ð MOð(ð ð(ð ð(ð !#ð(ð %'ð(ð )+ð(ð -/ð(ð 13ð(ð 57ð(ð 9;ð(ð =?ð(ð ACð(ð EGð(ð IKð(ð MOð(ð ð(ð ð(ð !#ð(ð %'ð(ð )+ð(ð -/ð(ð 13ð(ð 57ð(ð 9;ð(ð =?ð(ð ACð(ð EGð(ð IKð(ð MOð(ð ð(ð ð(ð !#ð(ð %'ð(ó )ˆô × Ò  °6Ô:ˆÜ˜Ÿ™ r§z¡z°'Ó':Ô;Ü˜Ÿ
™
 B§J¡JÐ/DÓ$EÔFÜ× Ò  °9Ô=ˆÜ˜Ÿ™ r§z¡z°'Ó':Ô;Ü˜Ÿ
™
 B§J¡J¨Ó$?Ô@Ü× Ò  °;Ô?ˆÜ˜Ÿ™ r§z¡z°'Ó':Ô;Ü˜Ÿ
™
 B§J¡JÐ/@Ó$AÖBr<   rw   )gm9—âªAj@g¼è+H3Œ[@gi¢²>s@)g›#ëhA{@gð±lËûz@gcžÚDf@gÇ³*âú¹h@gZ¬£ÿõA@gI9^¿YQa@g­ò§Ü`@g©î£ÞÕžp@gÑ¥Š–:q@gõó&º‚‚@g§Zµ|@g’`À×ÖÉr@gM‡cä3g@)rç   ç
+ž×÷å?)rç   ç
+ž×÷Õ?)rç   ç¼ŒÉ%c�æ?)rç   g9§ƒ:¨ƒæ?)rç   g9§ƒ:¨ƒÖ?)rç   g*…:¨ƒ:æ?)rë   rì   rx   )ç      7@r‚  )r…  r„  )r…  rƒ  )r…  gl,KÎNhä?)r…  gÊiÚ˜ØËå?)r…  gl,KÎNhÔ?)g      Ð?rË   g      è?)r¶   çš™™™™™É?çš™™™™™Ù?r·   )rÊ   r¶   r†  r+   rË   gÍÌÌÌÌÌä?)r†  r‡  r·   )gôýÔxé&±?g /Ý$Á?gJ+‡Ñ?r‡  r·   )çyé&1¬œ?çÉv¾Ÿ/­?gÉv¾Ÿ/½?r†  gj¼t“Ô?çÛù~j¼tÛ?çƒÀÊ¡Eâ?)	gyé&1¬Œ?gV-²�?r‰  r¶   gÙÎ÷SãÅ?g´Èv¾ŸÏ?gÁÊ¡E¶óÕ?g'1¬ZÜ?gmçû©ñÒá?)gÇK7‰A`Å?gZd;ßOÕ?rË   gòÒMbXå?)çªñÒMb¨?çR¸…ëQ¸?çR¸…ëQÈ?ççû©ñÒMÒ?rŠ  r‹  )	g;ßO�—n’?ç;ßO�—n¢?ç“V-²?g      À?gJ+‡É?r�  gôýÔxé&Ù?rË   g�•C‹lã?)çü©ñÒMb€?çü©ñÒMb�?çü©ñÒMb ?gyé&1¬¬?r�  ççû©ñÒMÂ?g‘í|?5^Ê?g˜nƒÀÊÑ?g\�Âõ(\×?ç!°rh‘íÜ?çð§ÆK7‰á?)çü©ñÒMbp?r’  r“  rˆ  çú~j¼t“¨?g333333³?gÑ"Ûù~j¼?ç×£p=
×Ã?gáz®GáÊ?çð§ÆK7‰Ñ?g®GázÖ?g‹lçû©ñÚ?rË   gºI+‡â?)r•  r�  g1¬ZdÛ?r‹  )r�  r‘  r•  ç1¬ZdË?g%�•C‹Ô?rŠ  r‹  )
gú~j¼t“ˆ?gú~j¼t“˜?r™  gsh‘í|?µ?gøSã¥›ÄÀ?rŽ  r›  g+‡ÙÖ?r–  r—  )g{®Gázt?rÉ   gÛù~j¼t“?gL7‰A`å ?r‰  gj¼t“¶?gP�—nƒÀ?gºI+‡Æ?gX9´ÈvÎ?g…ëQ¸…Ó?gü©ñÒMbØ?gsh‘í|?Ý?gÇK7‰A`á?)çü©ñÒMb`?r˜  g;ßO�—n‚?g¸…ëQ¸Ž?g9´Èv¾Ÿš?gË¡E¶óý¤?gTã¥›Ä °?gbX9´È¶?g°rh‘í|¿?g…ëQ¸Å?rœ  gôýÔxé&Ñ?gÉv¾Ÿ/Õ?gòÒMbXÙ?gÃõ(\�ÂÝ?g…ëQ¸á?)r>   r�  r˜  r’  g9´Èv¾ŸŠ?g/Ý$�•?r”  rŒ  gL7‰A`å°?g
×£p=
·?g¸…ëQ¸¾?rš  gžï§ÆK7É?g`åÐ"ÛùÎ?g7‰A`åÐÒ?r+   g“V-Ú?gj¼t“Þ?gË¡E¶óýà?©rŽ   r�   )rŽ   rË   )rŽ   g‹·éƒ¡Eï?)rŽ   r?   )rë   r$  )r�   r@   rA   rB   )r5   r6   r\   r^   )Trè   rÞ   g¾ˆ²Ò&Óì?)Tré   rÞ   g„Ïì‡ÓO¿?)Træ   rÞ   g„Ïì‡ÓOÏ?)Frè   rÞ   g9@VN!xì?)Fré   rÞ   g9þM�õ>¼?)Fræ   rÞ   g9þM�õ>Ì?)Trè   rß   g ?UÈV²ì?)Tré   rß   gßºVJHÀ?)Træ   rß   gèÁVJHÐ?)rÕ   r×   rÙ   rK  r  )rõ   ga×€}¢ã?)rõ   r�   rÁ   )r©   g¤Û?hÍå?)r©   r�   )rô   gæ5&#\å?)rô   r�   )r5   r6   r×   rì   )rè   ré   ræ   )g®Þ	ÂUå3@g^û�Â–‹3@g™òtÇ3@g½¢™]o·5@g·z³S4@gÔtÆ< 4@gM	‚«X3@gXÄmCók4@gLìo&£3@gfÉ˜ÊâÇ2@gžý{m;^3@ga A$|3@gMÑ¢Á_À4@gŽÌ#é3@g19T•_3@gg§„Cÿ2@gúqïR4@g˜Kk/±4@gè—Ü�Š3@gÌZ†û2@g„_
À²ƒ3@g«ÝÀ$`Ó3@g
ŒÃx„4@g3ƒ#Ð»5@g;VND÷ò1@g >®ƒåH2@g—µâr4@g³»ØyÜ¤2@gèà’?4@g=bòÉ‡Ž3@)gÔäìpG3@g„Lä:jþ0@gýî„¨Š2@g«¹JNnC1@gRÀ;`(3@g+Pi,ƒ2@g6:Z›2@gZ"3=ùÕ2@gF	uSa	3@gXâÒ€2@g¥ÙX3^83@g§2¡Õ1@g÷��J2@gZ)Eû‡ª2@g¦U8ø3@g°»°50@g�ˆ³Ô†3@gFz‰™33@gøèãz3@g¨¢²Ú´3@)4rz   r{   r|   r}   r/   r~   rÌ   rÑ   rÛ   rä   r5   r6   Úcases_basicr   rí   Úcases_continuityrð   rþ   r  r  r  r  r  r  r   Úcases_scalarr%  r)  r:  r=  rA  rL   rn   Úcases_11355rG  Ú
cases_9184rM  rR  Ú
cases_2118rX  r_  rd  rk  rl  rW  rr  rw  rz  r}  r€  r€   r�   r‚   s   @r9   rÎ   rÎ   »   s…  ø‡ € ð ‡[�[×!Ñ! +Ð6SÐ!ÓTñ-ó Uð-ò*
.ò10òj 	-€Aò	€Að& # K°¸<ÐHØ*ð,à" F¨H°lÐCØ*ð,à" I¨x¸ÐFØ*ð,à" K°¸7ÐCØ*ð,à" F¨H°gÐ>Ø*ð,à" I¨x¸ÐAØ*ð,ð-€Kð ‡[�[×ÑÐ1°;Ó?Ø‡[�[×Ñ˜WÒ&BÓCñJó Dó @ðJð (¨Ð6FÈÐMØ/ð1à'¨Ð1AÀ4ÐHØ/ð1à'¨Ð4DÀdÐKØ/ð1à'¨Ð6FÈÐNØ/ð1à'¨Ð1AÀ5ÐIØ/ð1à'¨Ð4DÀeÐLØ/ð1ð2Ðð ‡[�[×ÑÐ1Ð3CÓDñ=ó Eð=ò<ð, Ò Ò$8ØÒ.ð0€CàŠo˜qÒ"AØÒ<ØÒKðM€Cð Ò(ØÒ7ØÒKØò 2àò <ð=€Cð Ò*ØÒ?Øò 1àò 9ð ò Gàò $ð%€Cò+ò88ò*4ð" $ [°(¸LÐIØðà# V¨X°|ÐDØð à# Y°¸,ÐGØ)ð+à# [°(¸GÐDÀgÐNØ# V¨X°wÐ?ÀÐKØ# Y°¸'ÐBÀGÐLðN€Lð ‡[�[×ÑÐ/°Ó>ñ<ó ?ð<òHð ‡[�[×!Ñ! +Ð6SÐ!ÓTØ‡[�[×Ñ˜X¨°gÐ'>Ó?ñ)Kó @ó Uð)KòV2ð ‡[�[×!Ñ! +Ð6SÐ!ÓTñ9ó Uð9ò "Ø˜˜1˜a §¡¨¨A¨q°!°Q¸Ð:Ø˜ð*ò "Ø˜˜1˜a §¡¨¯©°°A°q¸!¸QÐ?ØÐ)ð+ð ˜˜2Ÿ6™6 1Ð%Ø˜˜1˜a §¡¨¨A¨q°!°Q¸Ð:Ø˜/ð+ð ˜˜2Ÿ6™6 1Ð%Ø˜˜1˜a §¡¨¯©°°A°q¸!¸QÐ?Ø˜ð*ð ˜Ÿ™ §¡¨Ð*Ø˜˜1˜a §¡¨¯©°°A°q¸!¸QÐ?Ø˜/ð+ð,€Kð  ‡[�[×ÑÐ>ÀÓLñDó MðDò ?ÚBÚCÚ@ÚCÚEÚ:Ú=Ú?ðA€Jð ‡[�[×Ñð 6Ø7AóCñ<óCð<ð: ‡[�[×!Ñ! +Ð6SÐ!ÓTñ)ó Uð)ò   # s ¨YÐ8MÐNÚ # s ¨VÐ5JÐKÚ # s ¨[¸)ÐDÚ˜q˜c 9Ð.CÐDÚ˜q˜c 6Ð+@ÐAÚ˜q˜c ;°	Ð:Ø�q�6˜A˜q˜6 9Ð.BÐCØ�q�6˜A˜q˜6 6Ð+?Ð@Ø�q�6˜A˜q˜6 ;°Ð9ð;€Jð ‡[�[×ÑÒBÀJÓOñHó PðHò:ð: ‡[�[×Ñ˜]Ò,LÓMñ	=ó Nð	=ò	-€Aò	N€Að €DòTò$	SòUò$	U÷+Cð +Cr<   rÎ   c                   ó¬   a € ] tR tRt o R tR tR tR tR tR t	R t
R	 tR
 tR tR t]P                   P#                  RR4      R 4       tR tRtV tR# )ÚTestSomersDi>  c                ó  € V P                   V P                  ,           V n        ^ \        P                  ! ^
4      V P                   V P                  ,           3^\        P                  ! ^
4      V P                   V P                  ,           3/V n        V P
                   Uu. uF  qP
                  V,          ^ ,          NK  	  pp\        P                  ! \        P                  RR7      V n
        V P                  ! V!  V n        R# u upi )r   ræ   rÖ   N)ÚALL_INTEGERÚ	ALL_FLOATÚdtypesrL   rM   Ú	argumentsÚ	functoolsÚpartialr   ÚsomersdÚpartialfuncrì   )r3   ÚidxÚinput_arrays   &  r9   Úsetup_methodÚTestSomersD.setup_method?  sÌ   € Ø×&Ñ&¨¯©Õ7ˆŒØœbŸiši¨›mØ"×.Ñ.°·±Õ?ðAàœbŸiši¨›mØ"×.Ñ.°·±Õ?ðAðBˆŒð :>¿ºÓH¹°#—~‘~ cÕ*¨1×-Ð-¹ˆÐHô
 %×,Ò,¬U¯]©]Ø9DôFˆÔà×(Ò(¨+Ñ6ˆŽùò Is   Â"Dc                óÖ   € V P                   ! V!  p\        VP                  V P                  P                  R R7       \        VP                  V P                  P                  R R7       R# )rb  r'   N)r¯  r   r\   rì   r^   )r3   rÆ   r`   s   &* r9   ÚpythranfuncÚTestSomersD.pythranfuncN  sF   € Ø×Ò Ñ%ˆÜ˜Ÿ™ t§}¡}×'>Ñ'>ÀUÕKÜ˜Ÿ
™
 D§M¡M×$8Ñ$8¸u×Er<   c                ó<  € . RO. RO. RO.p\         P                  ! V4      pV P                  \         P                  4      p\         P                  ! V3/ VB p\        VP                  VP                  RR7       \        VP
                  VP
                  RR7       R# )é   rb  r'   N)r¸  é   é   rF   r   )rF   rº  é   é#   ri   )r?   rA   r@   rF   é   )r   r®  Úget_optional_argsr   r\   r^   )r3   r  r  Úoptional_argsr  s   &    r9   Útest_pythranfunc_keywordsÚ%TestSomersD.test_pythranfunc_keywordsS  sm   € â#Ò%8Ò:JÐKˆÜ�}Š}˜UÓ#ˆà×.Ñ.¬u¯}©}Ó=ˆÜ�}Š}˜UÑ4 mÑ4ˆä˜Ÿ™¨¯©¸UÕCÜ˜Ÿ™ T§[¡[°u×=r<   c                óŠ  € . ROp. ROpRp\         P                  ! W4      p\        VP                  V^ ,          RR7       \        VP                  V^,          RR7       . R	Op. R
OpRp\         P                  ! W4      p\        VP                  V^ ,          RR7       \        VP                  V^,          RR7       . ROp. ROpRp\         P                  ! W4      p\        VP                  V^ ,          RR7       \        VP                  V^,          RR7       \
        P                  ! ^
4      p\
        P                  ! ^
4      pRp\         P                  ! W4      p\        VP                  V^ ,          RR7       \        VP                  V^,          RR7       \
        P                  ! ^
4      p\
        P                  ! . RO4      pRp\         P                  ! W4      p\        VP                  V^ ,          RR7       \        VP                  V^,          RR7       \
        P                  ! ^
4      p\
        P                  ! ^
4      RRR1,          pRp\         P                  ! W4      p\        VP                  V^ ,          RR7       \        VP                  V^,          RR7       \
        P                  ! ^
4      p\
        P                  ! . RO4      pRp\         P                  ! W4      p\        VP                  V^ ,          RR7       \        VP                  V^,          RR7       . ROp. ROpRp\         P                  ! WV4      p\        VP                  V^ ,          RR7       \        VP                  V^,          RR7       \         P                  ! . RO. RO4      p\        VP                  \
        P                  4       \        VP                  \
        P                  4       \         P                  ! . RO. RO4      p\        VP                  \
        P                  4       \        VP                  \
        P                  4       \         P                  ! . RO. RO4      p\        VP                  \
        P                  4       \        VP                  \
        P                  4       \         P                  ! ^ .^ .4      p\        VP                  \
        P                  4       \        VP                  \
        P                  4       \         P                  ! . . 4      p\        VP                  \
        P                  4       \        VP                  \
        P                  4       \
        P                  ! R4      p\
        P                  ! R4      p\        \        \         P                  W4       R# )rC   rb  r'   NrC  ç      4@)rC   r@   r?   rA   rD   rB   rF   rG   )rC   r@   rD   rA   r?   rG   rF   rB   rž  )	r   rC   r@   r?   rA   rD   rB   rF   rG   )	rC   r@   r   rD   rA   r?   rG   rF   rB   )rC   r@   r?   rA   rD   rB   rF   )rC   r@   rD   rA   r?   rF   rB   )g+$I’$IÂ¿g=/3n£+ä?©r�   r   )
r   r@   r?   rA   rB   rD   rC   rF   rG   rj   )gsÒ'}Ò'í?rŽ   rk   )g      ð¿r   )
rj   rF   rG   rD   rC   rA   rB   r@   r?   r   )g}Ò'}Ò'í¿rŽ   )ri   r@   r?   ri   r@   )r?   rB   rF   r?   r   )ç      à¿gÞ.Ê‚ƒÓ?)r@   r@   r@   )r@   r   r@   )r   r®  r   r\   r^   rL   rM   Úarrayr]   rÚ   rÃ   )r3   r5   r6   rì   r`   Úx1Úx2s   &      r9   Útest_like_kendalltauÚ TestSomersD.test_like_kendalltau^  sÃ  € ò %ˆÚ$ˆà9ˆÜ�mŠm˜AÓ!ˆÜ˜Ÿ™ x°¥{¸Õ?Ü˜Ÿ
™
 H¨Q¥K°eÕ<ò (ˆÚ'ˆà9ˆÜ�mŠm˜AÓ!ˆÜ˜Ÿ™ x°¥{¸Õ?Ü˜Ÿ
™
 H¨Q¥K°eÕ<ò "ˆÚ!ˆà:ˆÜ�mŠm˜AÓ!ˆÜ˜Ÿ™ x°¥{¸Õ?Ü˜Ÿ
™
 H¨Q¥K°eÕ<ô �IŠI�b‹MˆÜ�IŠI�b‹Mˆð *ˆÜ�mŠm˜AÓ!ˆÜ˜Ÿ™ x°¥{¸Õ?Ü˜Ÿ
™
 H¨Q¥K°eÕ<ô �IŠI�b‹MˆÜ�HŠHÒ3Ó4ˆà9ˆÜ�mŠm˜AÓ!ˆÜ˜Ÿ™ x°¥{¸Õ?Ü˜Ÿ
™
 H¨Q¥K°eÕ<ô �IŠI�b‹MˆÜ�IŠI�b‹M™$˜B˜$Õˆð +ˆÜ�mŠm˜AÓ!ˆÜ˜Ÿ™ x°¥{¸Õ?Ü˜Ÿ
™
 H¨Q¥K°eÕ<ô �IŠI�b‹MˆÜ�HŠHÒ3Ó4ˆà;ˆÜ�mŠm˜AÓ!ˆÜ˜Ÿ™ x°¥{¸Õ?Ü˜Ÿ
™
 H¨Q¥K°eÕ<ò ˆÚˆà:ˆÜ�mŠm˜BÓ#ˆÜ˜Ÿ™ x°¥{¸Õ?Ü˜Ÿ
™
 H¨Q¥K°eÕ<ô �mŠmšI¢yÓ1ˆÜ˜Ÿ™¤r§v¡vÔ.Ü˜Ÿ
™
¤B§F¡FÔ+ä�mŠmšI¢yÓ1ˆÜ˜Ÿ™¤r§v¡vÔ.Ü˜Ÿ
™
¤B§F¡FÔ+ä�mŠmšI¢yÓ1ˆÜ˜Ÿ™¤r§v¡vÔ.Ü˜Ÿ
™
¤B§F¡FÔ+ä�mŠm˜Q˜C ! Ó%ˆÜ˜Ÿ™¤r§v¡vÔ.Ü˜Ÿ
™
¤B§F¡FÔ+ô �mŠm˜B Ó#ˆÜ˜Ÿ™¤r§v¡vÔ.Ü˜Ÿ
™
¤B§F¡FÔ+ô �IŠI�c‹NˆÜ�IŠI�c‹NˆÜ”j¤%§-¡-°Ö6r<   c                óº  € . ROp. R	OpRpRpRp\         P                  ! W4      p\        VP                  VRR7       \        VP                  VRR7       \        VP                  P                  R
4       \         P                  ! W!4      p\        VP                  VRR7       \        VP                  VRR7       \        VP                  P                  R4       R# )r?   gCÑE]tÑ?gâ^ñ_ñÕ?gO((ÄÇ·?rb  r'   r)   N)r?   r?   r?   r@   r@   r@   r@   r@   rA   rA   r?   r@   r@   r@   r@   r@   r@   r@   rA   rA   rA   rA   rA   rA   )r?   r?   r?   r?   r?   r?   r?   r?   r?   r?   r@   r@   r@   r@   r@   r@   r@   r@   r@   r@   r@   r@   r@   r@   )rA   r@   ©r@   rA   )r   r®  r   r\   r^   r   r  r.  )r3   r5   r6   Úd_crÚd_rcr8   r`   s   &      r9   Útest_asymmetryÚTestSomersD.test_asymmetryÍ  s¡   € ò1ˆò1ˆð !ˆØ ˆØˆÜ�mŠm˜AÓ!ˆÜ˜Ÿ™ t°%Õ8Ü˜Ÿ
™
 A¨DÕ1Ü�S—Y‘Y—_‘_ fÔ-Ü�mŠm˜AÓ!ˆÜ˜Ÿ™ t°%Õ8Ü˜Ÿ
™
 A¨EÕ2Ü�S—Y‘Y—_‘_ fÖ-r<   c                ój  € \         P                  ! ^^.^^.^^.^^.^^..4      pVP                  pRp\        \        P
                  ! V4      P                  V4       \         P                  ! ^^ .^U^ .^ ^..4      pRRr#\        \        P
                  ! V4      P                  V4       \        \        P
                  ! VP                  4      P                  V4       \         P                  ! ^^ .^ ^.^U^ ..4      pRp\        \        P
                  ! VP                  4      P                  V4       R# )rG   NgHHHHHHØ?gœÜMî&wã?r�   gtÑE]tá¿)rL   rÆ  ÚTr   r   r®  r\   )r3   r  ÚdyxÚdxys   &   r9   Útest_somers_originalÚ TestSomersD.test_somers_originalæ  sý   € ô
 —’˜1˜a˜& 1 a &¨1¨a¨&°1°a°&¸1¸a¸&ÐAÓBˆà—‘ˆØˆÜœŸš eÓ,×6Ñ6¸Ô<ô —’˜2˜q˜' B¨ 7¨Q°¨GÐ4Ó5ˆØ˜iˆSÜœŸš eÓ,×6Ñ6¸Ô<ÜœŸš e§g¡gÓ.×8Ñ8¸#Ô>ô —’˜2˜q˜' A r 7¨R°¨GÐ4Ó5ˆØˆÜœŸš e§g¡gÓ.×8Ñ8¸#Ö>r<   c                óì  € ^dpRp\         P                  ! V4      p\         P                  P                  ^ 4      p\        P
                  P                  V\         P                  ! V4      V,          VR7      P                  V4      p\        P                  ! V4      p\         P                  ! V^\         P                  ! V^,          4      ^ R7      p\        P                  ! V4      p\         P                  ! V^\         P                  ! V^ ,          4      ^R7      p	\        P                  ! V	4      p
\         P                  ! V^\         P                  ! V^ ,          ^,           4      ^R7      p\        P                  ! V4      p\        VP                  RRR7       \        VP                  VP                  4       \        VP                  V
P                  4       \        VP                  VP                  4       \        VP                  RRR7       \        VP                  VP                  4       \        VP                  V
P                  4       \        VP                  VP                  4       R# )	r˜   ©r8   Úrandom_staterf   rb  r'   gP—j¹$Ä?N©rB   rD   gaƒ¸yò½¿)rL   Úprodrl   ÚRandomStater   ÚmultinomialÚrvsr¡   Úreshaper®  Úinsertr2  r   r\   r^   )r3   ÚNr.  re   ro   r  r`   Ús2r  Ús3r@  Ús4Úres4s   &            r9   Ú*test_contingency_table_with_zero_rows_colsÚ6TestSomersD.test_contingency_table_with_zero_rows_colsü  s™  € ð ˆØˆÜ�wŠw�u‹~ˆä�i‰i×#Ñ# AÓ&ˆÜ×Ñ×!Ñ! !¤r§w¢w¨t£}°TÕ'9Ø/2ð "ó 4ß4;±G¸E³Nð 	
ä�mŠm˜AÓˆä�YŠY�q˜!œRŸXšX e¨A¥hÓ/°aÔ8ˆÜ�}Š}˜RÓ ˆä�YŠY�q˜!œRŸXšX e¨A¥hÓ/°aÔ8ˆÜ�}Š}˜RÓ ˆä�YŠY�r˜1œbŸhšh u¨Q¥x°¥zÓ2¸Ô;ˆÜ�}Š}˜RÓ ˆô 	˜Ÿ™Ð'9ÀÕFÜ˜Ÿ™ t§~¡~Ô6Ü˜Ÿ™ t§~¡~Ô6Ü˜Ÿ™ t§~¡~Ô6ä˜Ÿ
™
Ð$5¸EÕBÜ˜Ÿ
™
 D§K¡KÔ0Ü˜Ÿ
™
 D§K¡KÔ0Ü˜Ÿ
™
 D§K¡KÖ0r<   c                ó  € ^dpRp\         P                  ! V4      p\         P                  P                  ^ 4      p\        P
                  P                  V\         P                  ! V4      V,          VR7      P                  V4      pV^,
          pRp\        \        VR7      ;_uu_ 4        \        P                  ! V4       RRR4       VR,           pRp\        \        VR7      ;_uu_ 4        \        P                  ! V4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        P                  ! . .4       RRR4       \        \        VR7      ;_uu_ 4        \        P                  ! ^..4       RRR4       \         P                  ! R	4      p	\        \        VR7      ;_uu_ 4        \        P                  ! V	4       RRR4       ^V	R
&   \        \        VR7      ;_uu_ 4        \        P                  ! V	4       RRR4       R#   + '       g   i     ELV; i  + '       g   i     EL'; i  + '       g   i     Lÿ; i  + '       g   i     LØ; i  + '       g   i     L�; i  + '       g   i     R# ; i)r˜   rØ  z:All elements of the contingency table must be non-negativer«   NrÉ   z5All elements of the contingency table must be integerz?At least two elements of the contingency table must be nonzero.rÚ  )rA   rA   ©r   r?   )rL   rÛ  rl   rm   r   rÝ  rÞ  r¡   rß  rÚ   rÃ   r®  r2  )
r3   rá  r.  re   ro   r  Ús5rÅ   Ús6Ús7s
   &         r9   Útest_invalid_contingency_tablesÚ+TestSomersD.test_invalid_contingency_tables  s¨  € ØˆØˆÜ�wŠw�u‹~ˆä�i‰i×#Ñ# AÓ&ˆä×Ñ×!Ñ! !¤r§w¢w¨t£}°TÕ'9Ø/2ð "ó 4ß4;±G¸E³Nð 	
ð ��UˆØNˆÜœ:¨W×5Ö5Ü�MŠM˜"Ô÷ 6ð ��XˆØIˆÜœ:¨W×5Ö5Ü�MŠM˜"Ô÷ 6ð,ˆäœ:¨W×5Ö5Ü�MŠM˜2˜$Ô÷ 6ô œ:¨W×5Ö5Ü�MŠM˜A˜3˜%Ô ÷ 6ô �XŠX�fÓˆÜœ:¨W×5Ö5Ü�MŠM˜"Ô÷ 6ð ˆˆ4‰Üœ:¨W×5Ö5Ü�MŠM˜"Ô÷ 6Ñ5÷+ 6×5Ð5ú÷
 6×5Ð5ú÷
 6×5ú÷ 6×5ú÷ 6×5ú÷ 6×5Ð5úsH   Â*HÃ-H"Ä'H6Å I	Æ0IÇ-I/ÈH	È"H3	È6I	É	I	ÉI,	É/J 	c                ó<  € . ROpRR\         P                  .p. ROp^ R\         P                  ) .p\        P                  ! W4      p\        P                  ! W$4      p\	        VP
                  VP
                  4       \	        VP                  VP                  4       R# )r?   gÍÌÌÌÌÌ @NrÁ   rk   )rA   r@   r?   rÅ  )rL   rn   r   r®  r   r\   r^   )r3   r5   rÈ  r6   Úy2r`   r  s   &      r9   Útest_only_ranks_matterÚ"TestSomersD.test_only_ranks_matter@  sn   € âˆØ�#”r—v‘vÐˆÚˆØ�œŸ™�wÐˆÜ�mŠm˜AÓ!ˆÜ�}Š}˜RÓ$ˆÜ�S—]‘] D§N¡NÔ3Ü�S—Z‘Z §¡Ö-r<   c                óÞ   € \         P                  ! ^
4      p\         P                  ! ^
4      p\        P                  ! W4      p\	        VP
                  \         P                  ! ^
4      4       R# )rE   N)rL   rM   r   r®  r   r  Úeye©r3   r5   r6   r`   s   &   r9   Útest_contingency_table_returnÚ)TestSomersD.test_contingency_table_returnK  s@   € ä�IŠI�b‹MˆÜ�IŠI�b‹MˆÜ�mŠm˜AÓ!ˆÜ�S—Y‘Y¤§¢ r£
Ö+r<   c                ó¨  € . R	Op. R
Op\         P                  ! WRR7      pVP                  ^ 8”  g   Q h\         P                  ! WRR7      p\        VP                  VP                  4       \	        VP
                  ^VP
                  ^,          ,
          4       \         P                  ! WRR7      p\        VP                  VP                  4       \	        VP
                  VP
                  ^,          4       VP                  4        \         P                  ! WRR7      pVP                  ^ 8  g   Q h\         P                  ! WRR7      p\        VP                  VP                  4       \	        VP
                  ^VP
                  ^,          ,
          4       \         P                  ! WRR7      p\        VP                  VP                  4       \	        VP
                  VP
                  ^,          4       \        P                  ! \        RR7      ;_uu_ 4        \         P                  ! WRR7       RRR4       R#   + '       g   i     R# ; i)r?   ræ   rÖ   rè   ré   z`alternative` must be...r«   ú	ekki-ekkiN)r?   r@   rA   rB   rC   )rC   rD   rF   rG   rF   )
r   r®  r\   r   r   r^   Úreverser/   r   rÃ   )r3   rÇ  rÈ  rì   r`   s   &    r9   Útest_somersd_alternativeÚ$TestSomersD.test_somersd_alternativeR  s“  € ò ˆÚˆô —=’= °[ÔAˆØ×!Ñ! AÔ%Ð%Ð%ô �mŠm˜B°Ô7ˆÜ�S—]‘] H×$6Ñ$6Ô7Ü˜Ÿ
™
 A¨¯©¸1Õ)<Õ$=Ô>ô �mŠm˜B°	Ô:ˆÜ�S—]‘] H×$6Ñ$6Ô7Ü˜Ÿ
™
 H§O¡O°aÕ$7Ô8ð 	�
‰
Œô —=’= °[ÔAˆØ×!Ñ! AÔ%Ð%Ð%ô �mŠm˜B°	Ô:ˆÜ�S—]‘] H×$6Ñ$6Ô7Ü˜Ÿ
™
 A¨¯©¸1Õ)<Õ$=Ô>ô �mŠm˜B°Ô7ˆÜ�S—]‘] H×$6Ñ$6Ô7Ü˜Ÿ
™
 H§O¡O°aÕ$7Ô8ä�]Š]œ:Ð-G×HÖHÜ�MŠM˜"¨kÕ:÷ I×H×HÒHús   ÈI É I	Úpositive_correlationc                ó&  € \         P                  ! ^
4      pV'       d   TM\         P                  ! V4      pV'       d   ^MRp\        P                  ! W#RR7      pVP
                  V8X  g   Q hVP                  ^ 8X  g   Q h\        P                  ! W#RR7      pVP
                  V8X  g   Q hVP                  V'       d   ^M^ 8X  g   Q h\        P                  ! W#RR7      pVP
                  V8X  g   Q hVP                  V'       d   ^ M^8X  g   Q hR# )rE   ræ   rÖ   rè   ré   Nrk   )rL   rM   Úflipr   r®  r\   r^   )r3   rý  rÇ  rÈ  Úexpected_statisticr`   s   &&    r9   Ú test_somersd_perfect_correlationÚ,TestSomersD.test_somersd_perfect_correlation{  sÙ   € ô �YŠY�r‹]ˆß'‰R¬R¯WªW°R«[ˆß"6™Q¸BÐô �mŠm˜B°Ô<ˆØ�}‰}Ð 2Ô2Ð2Ð2Ø�z‰z˜QŒÐˆô �mŠm˜B°Ô7ˆØ�}‰}Ð 2Ô2Ð2Ð2Ø�z‰z×#7™a¸QÔ?Ð?Ð?ô �mŠm˜B°	Ô:ˆØ�}‰}Ð 2Ô2Ð2Ð2Ø�z‰z×#7™a¸QÔ?Ð?Ò?r<   c                óò   € ^^.pRp\         P                  P                  R4      pVP                  W4      pVP                  W4      pRp\        P
                  ! WE4      P                  p\        WgRR7       R# )r?   l   ÿ.E5 g 0ôÜuD?rb  r'   Né@B )rL   rl   rm   Úchoicer   r®  r\   r   )r3   ÚclassesÚ	n_samplesro   r5   r6   Úval_sklearnÚ	val_scipys   &       r9   Ú!test_somersd_large_inputs_gh18132Ú-TestSomersD.test_somersd_large_inputs_gh18132”  si   € ð �a�&ˆØˆ	Ü�i‰i×#Ñ# JÓ/ˆØ�J‰J�wÓ*ˆØ�J‰J�wÓ*ˆð +ˆô —M’M !Ó'×1Ñ1ˆ	Ü˜°U×;r<   )r«  rª  rì   r¯  N)FT)rz   r{   r|   r}   r²  rµ  rÀ  rÉ  rÏ  rÕ  ræ  rí  rñ  rö  rû  r/   r~   r   r  r
  r€   r�   r‚   s   @r9   r¦  r¦  >  su   ø‡ € ò7òFò
	>òm7ò^.ò2?ò,1ò@"òH	.ò,ò';ðR ‡[�[×ÑÐ3°]ÓCñ@ó Dð@÷0<ð <r<   r¦  c                   óè  a € ] tR tRt o Rt]P                  P                  R^+^(.^
^'..R3^d^.R^..R3^^.^^..R3^^.^
^
..R3^^.^^..R3^^.^^..R3^
^.^
^..R3^^ .^^..R3^ ^.^^..R3^ ^.^^..R3^^.^^..R3.4      R 4       t]P                  P                  R^+^(.^
^'..R3^d^.R^..R3^^.^^..R3^^.^
^
..R 3^^.^^..R!3^^.^^..R"3^
^.^
^..R#3^^ .^^..R$3^ ^.^^..R%3^ ^.^^..R&3^^.^^..R3.4      R 4       t	R t
]P                  P                  R^ ^ .^^..R'3.4      R	 4       t]P                  P                  R^ ^.^ ^
..R]P                  33^^ .^
^ ..R]P                  33.4      R
 4       t]P                  P                  R^^.^^..R(3^^È.R^..R)3^^.R^..R*3.4      ]P                  P                  RRR.4      R 4       4       tRtV tR# )+ÚTestBarnardExacti­  z8Some tests to show that barnard_exact() works correctly.úinput_sample,expectedr†   c                ód   € \        V4      pVP                  VP                  rT\        WE.V4       R# )zÆThe expected values have been generated by R, using a resolution
for the nuisance parameter of 1e-6 :
```R
library(Barnard)
options(digits=10)
barnard.test(43, 40, 10, 39, dp=1e-6, pooled=TRUE)
```
N©r   r\   r^   r   ©r3   Úinput_samplerì   r`   r\   r^   s   &&&   r9   Útest_preciseÚTestBarnardExact.test_precise°  s*   € ô2 ˜LÓ)ˆØŸM™M¨3¯:©:�6Ü˜Ð+¨XÖ6r<   c                óh   € \        VRR7      pVP                  VP                  rT\        WE.V4       R# )zÇThe expected values have been generated by R, using a resolution
for the nuisance parameter of 1e-6 :
```R
library(Barnard)
options(digits=10)
barnard.test(43, 40, 10, 39, dp=1e-6, pooled=FALSE)
```
F)ÚpooledNr  r  s   &&&   r9   Útest_pooled_paramÚ"TestBarnardExact.test_pooled_paramÍ  s,   € ô2 ˜L°Ô7ˆØŸM™M¨3¯:©:�6Ü˜Ð+¨XÖ6r<   c                óŠ  € R p\        \        VR7      ;_uu_ 4        \        ^^.^^..^ R7       RRR4       Rp\        \        VR7      ;_uu_ 4        \        \        P                  ! ^4      P                  ^^4      4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        R^.^^..4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        ^^.^^..R4       RRR4       R#   + '       g   i     LÐ; i  + '       g   i     L�; i  + '       g   i     Ln; i  + '       g   i     R# ; i)	ú7Number of points `n` must be strictly positive, found 0r«   ©r‰   Nú,The input `table` must be of shape \(2, 2\).ú*All values in `table` must be nonnegative.zI`alternative` should be one of {'two-sided', 'less', 'greater'}, found .*únot-correctrk   )rÚ   rÃ   r   rL   rM   rß  ©r3   Ú	error_msgs   & r9   Útest_raisesÚTestBarnardExact.test_raisesê  sý   € ð Fð 	ô œ:¨Y×7Ö7Ü˜A˜q˜6 A q 6Ð*¨aÕ0÷ 8ð Eˆ	Üœ:¨Y×7Ö7Üœ"Ÿ)š) A›,×.Ñ.¨q°!Ó4Ô5÷ 8ð Aˆ	Üœ:¨Y×7Ö7Ü˜B ˜7 Q¨ FÐ+Ô,÷ 8ð
ð 	ô œ:¨Y×7Ö7Ü˜A˜q˜6 A q 6Ð*¨MÔ:÷ 8Ñ7÷% 8×7ú÷
 8×7ú÷
 8×7ú÷ 8×7Ð7úó/   œC8Á0DÂ&DÃD1Ã8D	ÄD	ÄD.	Ä1E	r�   c                ó’   € \        V4      pVP                  VP                  rT\        WR^ ,          4       \        WB^,          4       R# ©r   N©r   r\   r^   r   r  s   &&&   r9   Útest_edge_casesÚ TestBarnardExact.test_edge_cases  s5   € ô ˜LÓ)ˆØŸM™M¨3¯:©:�6Ü�V a�[Ô)Ü�Y¨¥Ö,r<   c                ó’   € \        V4      pVP                  VP                  rT\        WR^ ,          4       \        WB^,          4       R# r%  r&  r  s   &&&   r9   Útest_row_or_col_zeroÚ%TestBarnardExact.test_row_or_col_zero  s5   € ô ˜LÓ)ˆØŸM™M¨3¯:©:�6Ü�V a�[Ô)Ü�Y¨¥Ö,r<   é,  i¥  r×   ré   rè   c                óÌ   € Vw  rEVR8X  d&   \         P                  ! V4      RRRR13,          pV) p\        WR7      pVP                  VP                  r‡\        Wx.WE.RR7       R# )a0  
"The expected values have been generated by R, using a resolution
for the nuisance parameter of 1e-6 :
```R
library(Barnard)
options(digits=10)
a = barnard.test(2, 7, 8, 2, dp=1e-6, pooled=TRUE)
a$p.value[1]
```
In this test, we are using the "one-sided" return value `a$p.value[1]`
to test our pvalue.
ré   :NNNNrÖ   çH¯¼šò×z>r'   rk   )rL   rÆ  r   r\   r^   r   )	r3   r  rì   r×   Úexpected_statÚless_pvalue_expectr`   r\   r^   s	   &&&&     r9   Útest_less_greaterÚ"TestBarnardExact.test_less_greater  sd   € ð, -5Ñ)ˆà˜)Ô#ÜŸ8š8 LÓ1°!±T°r°T°'Õ:ˆLØ*˜NˆMä˜LÔBˆØŸM™M¨3¯:©:�6ÜØÐ -Ð!DÈ4÷	
r<   rw   N)gÏXyq@g{2s&QÇ7?)gøl¯€lü¿gEA]0×KÁ?)ç*õ)1Ö%ÀgØ_  ¬“?)g_½Òc1÷?gèß=ç Ä?)g5PyQ ý¿g�Q@Ì2ý°?)g»ÔÌÑÁù¿g¼ÂJ"¸ò½?)g_½Òc1÷¿gwÝ�Ù„¹Æ?)gý7ŠËé§@g      Œ?)gš~øtñ†ñ¿ç,À�?3Oà?)gÝr?ô~Éø¿çCæ°Yð7É?)gµ’¹7ç\@gAÞÄƒø2?)gXS‘ç;ò¿gÙŽþ hî?)g>!ÉŽ¢Àg6¦  ¨”?)gS¡y@õù?gúÒ^¶ÛFÃ?)g‘ª-º©˜ÿ¿g¼X«I#°?)g°a£ÑÐ�û¿goÇÜðÁ?)gbø]?ü¿gFug¹H	Ð?)g§6Ò­è@g      €?)gi(	Ž˜ó¿r4  )gÓNXèz¶û¿r5  rÄ  )r3  gEç\/?„?)gÐgÑìíQ5ÀrŽ   )gü&çìX}>ÀrŽ   )rz   r{   r|   r}   Ú__doc__r/   r~   r   r  r  r!  r'  rL   r]   r*  r1  r€   r�   r‚   s   @r9   r  r  ­  sx  ø‡ € ÙBà‡[�[×ÑØà�2ˆh˜˜R˜Ð!Ð#CÐDØ�Aˆh˜˜q˜	Ð"Ð$EÐFØ�!ˆf�q˜!�fÐÐ@ÐAØ�!ˆf�r˜2�hÐÐ!AÐBØ�"ˆg˜˜B�xÐ Ð"CÐDØ�"ˆg˜˜B�xÐ Ð"CÐDØ�1ˆg˜˜A�wÐÐ!BÐCØ�!ˆf�q˜!�fÐÐ?Ð@Ø�!ˆf�q˜!�fÐÐ@ÐAØ�!ˆf�q˜!�fÐÐ@ÐAØ�!ˆf�q˜!�fÐÐ@ÐAð	
óñ 7ó!ð 7ð ‡[�[×ÑØà�2ˆh˜˜R˜Ð!Ð#CÐDØ�Aˆh˜˜q˜	Ð"Ð$EÐFØ�!ˆf�q˜!�fÐÐ@ÐAØ�!ˆf�r˜2�hÐÐ!AÐBØ�"ˆg˜˜B�xÐ Ð"CÐDØ�"ˆg˜˜B�xÐ Ð"CÐDØ�1ˆg˜˜A�wÐÐ!BÐCØ�!ˆf�q˜!�fÐÐ?Ð@Ø�!ˆf�q˜!�fÐÐ@ÐAØ�!ˆf�q˜!�fÐÐ@ÐAØ�!ˆf�q˜!�fÐÐ@ÐAð	
óñ 7ó!ð 7ò;ð4 ‡[�[×ÑØà�!ˆf�q˜!�fÐ˜xÐ(ð	
óñ-óð-ð ‡[�[×ÑØà�!ˆf�q˜"�gÐ  b§f¡f Ð.Ø�!ˆf�r˜1�gÐ  b§f¡f Ð.ð	
óñ-óð-ð ‡[�[×ÑØà�!ˆf�q˜!�fÐÐ@ÐAØ�#ˆh˜˜a˜Ð!Ð#:Ð;Ø�2ˆh˜˜q˜	Ð"Ð$;Ð<ð	
óð ‡[�[×Ñ˜]¨Y¸Ð,?Ó@ñ
ó Aóö
r<   r  c                   óü  a € ] tR tRt o RtRt]P                  P                  R^^.^^..R3^^.^
^
..R3^^.^^..R3^
^.^
^..R3^^ .^^..R3^ ^.^^..R3^^.^^..R3^^.^^..R3^
^.^^%..R3.	4      R 4       t	]P                  P                  R^+^(.^
^'..R3^^.^^..R3^^.^
^
..R3^^.^^..R3^^.^^..R3^^ .^^..R3^ ^.^^..R3^ ^.^^..R3^^.^^..R3^^.^^..R3^
^.^^%..R3.4      R 4       t
]P                  P                  R^+^(.^
^'..R3^^.^^..R 3^^.^
^
..R!3^^.^^..R"3^^ .^^..R#3^ ^.^^..R$3^^.^^..R 3^^.^^..R%3.4      R 4       tR t]P                  P                  R^ ^.^ ^
..]P                  ]P                  33^^ .^
^ ..]P                  ]P                  33.4      R	 4       tR
 t]P                  P                  RR&4      R 4       tRtV tR# )'ÚTestBoschlooExacti@  z9Some tests to show that boschloo_exact() works correctly.r.  r  c                ó~   € \        VRR7      pVP                  VP                  rT\        WE.W P                  R7       R# )aA  The expected values have been generated by R, using a resolution
for the nuisance parameter of 1e-8 :
```R
library(Exact)
options(digits=10)
data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
a = exact.test(data, method="Boschloo", alternative="less",
               tsmethod="central", np.interval=TRUE, beta=1e-8)
```
rè   rÖ   r'   N©r   r\   r^   r   ÚATOLr  s   &&&   r9   Ú	test_lessÚTestBoschlooExact.test_lessE  s0   € ô2 ˜\°vÔ>ˆØŸM™M¨3¯:©:�6Ü˜Ð+¨X¿I¹I×Fr<   c                ó~   € \        VRR7      pVP                  VP                  rT\        WE.W P                  R7       R# )aD  The expected values have been generated by R, using a resolution
for the nuisance parameter of 1e-8 :
```R
library(Exact)
options(digits=10)
data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
a = exact.test(data, method="Boschloo", alternative="greater",
               tsmethod="central", np.interval=TRUE, beta=1e-8)
```
ré   rÖ   r'   Nr:  r  s   &&&   r9   Útest_greaterÚTestBoschlooExact.test_greaterb  s0   € ô6 ˜\°yÔAˆØŸM™M¨3¯:©:�6Ü˜Ð+¨X¿I¹I×Fr<   c                ó€   € \        VR^@R7      pVP                  VP                  rT\        WE.W P                  R7       R# )aF  The expected values have been generated by R, using a resolution
for the nuisance parameter of 1e-8 :
```R
library(Exact)
options(digits=10)
data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
a = exact.test(data, method="Boschloo", alternative="two.sided",
               tsmethod="central", np.interval=TRUE, beta=1e-8)
```
ræ   )r×   r‰   r'   Nr:  r  s   &&&   r9   Útest_two_sidedÚ TestBoschlooExact.test_two_sided�  s2   € ô0 ˜\°{ÀbÔIˆàŸM™M¨3¯:©:�6Ü˜Ð+¨X¿I¹I×Fr<   c                óŠ  € R p\        \        VR7      ;_uu_ 4        \        ^^.^^..^ R7       RRR4       Rp\        \        VR7      ;_uu_ 4        \        \        P                  ! ^4      P                  ^^4      4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        R^.^^..4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        ^^.^^..R4       RRR4       R#   + '       g   i     LÐ; i  + '       g   i     L�; i  + '       g   i     Ln; i  + '       g   i     R# ; i)	r  r«   r  Nr  r  zK`alternative` should be one of \('two-sided', 'less', 'greater'\), found .*r  rk   )rÚ   rÃ   r   rL   rM   rß  r  s   & r9   r!  ÚTestBoschlooExact.test_raisesž  sý   € ð Fð 	ô œ:¨Y×7Ö7Ü˜Q ˜F Q¨ FÐ+¨qÕ1÷ 8ð Eˆ	Üœ:¨Y×7Ö7Üœ2Ÿ9š9 Q›<×/Ñ/°°1Ó5Ô6÷ 8ð Aˆ	Üœ:¨Y×7Ö7Ü˜R ˜G a¨ VÐ,Ô-÷ 8ð
%ð 	ô œ:¨Y×7Ö7Ü˜Q ˜F Q¨ FÐ+¨]Ô;÷ 8Ñ7÷% 8×7ú÷
 8×7ú÷
 8×7ú÷ 8×7Ð7úr#  c                ó’   € \        V4      pVP                  VP                  rT\        WR^ ,          4       \        WB^,          4       R# r%  )r   r\   r^   r   r  s   &&&   r9   r*  Ú&TestBoschlooExact.test_row_or_col_zero¸  s5   € ô ˜\Ó*ˆØŸM™M¨3¯:©:�6Ü�V a�[Ô)Ü�Y¨¥Ö,r<   c                óä   € ^^.^^..p\        VRR7      P                  p\        VRR7      P                  p^\        W#4      ,          ^8”  g   Q h\        VRR7      P                  pVR8X  g   Q hR# )r?   rè   rÖ   ré   ræ   r�   N)r   r^   r^  )r3   ÚtblÚplÚpgÚpts   &    r9   Útest_two_sided_gt_1Ú%TestBoschlooExact.test_two_sided_gt_1Å  sn   € ð �1ˆv˜˜B�xÐ ˆÜ˜C¨VÔ4×;Ñ;ˆÜ˜C¨YÔ7×>Ñ>ˆØ”�R“�}˜qÔ Ð Ð Ü˜C¨[Ô9×@Ñ@ˆØ�SŒyÐŠyr<   r×   c                ó”   € ^^.^^..p\        W!R7      P                  p\        P                  ! W!R7      ^,          p\	        W44       R# )r@   rÖ   N)r   r\   r   Úfisher_exactr   )r3   r×   rI  Úboschloo_statÚfisher_ps   &&   r9   Útest_against_fisher_exactÚ+TestBoschlooExact.test_against_fisher_exactÏ  sC   € ð �1ˆv˜˜1�vÐˆÜ& sÔD×NÑNˆÜ×%Ò% cÔCÀAÕFˆÜ˜Ö0r<   rw   N)ç<vB\÷’?gèÁ–„/?„?)g¬“ŽÍéMï?gßÏA>î?)ç_¬VÃÑ¶?gÂñ¥…Ö­?)ç‘uÝ Ø%Å?gc'�íµ?)r?   r?   )rË   g      Ö?)çß+Âf°?gXc}Áv¡?)gZÑ‹D¸É?g‰¦¢gi]Ã?)çòk¾\Ø2?g–ìà0í,%?)gKïvî÷ï?gâN3î½ï?)rW  g‡'&5Õ·?)gÏw@_„ï?g™•7Ñøï?)gµ‹i¦{ï?g€ÁÉ‘)zî?)ç˜ïÖ…a˜?g³1×ëÛ|?)gYðì<;ªï?g¨ýÖN”Dï?)gê­e×ì?g™Gþ` ë?)rY  gôqQSé,5?)rU  gG’Þ?/?”?)rW  gKE`ÕÇ?)rV  gÓhr1Ö½?)rZ  grÒfbÛŒ?)rË   g      æ?)rX  gP:pRÁv±?)rè   ré   )rz   r{   r|   r}   r6  r;  r/   r~   r   r<  r?  rB  r!  rL   r]   r*  rM  rS  r€   r�   r‚   s   @r9   r8  r8  @  s•  ø‡ € ÙCà€Dà‡[�[×ÑØà�!ˆf�q˜!�fÐÐ8Ð9Ø�!ˆf�r˜2�hÐÐ!7Ð8Ø�"ˆg˜˜B�xÐ Ð":Ð;Ø�1ˆg˜˜A�wÐÐ!8Ð9Ø�!ˆf�q˜!�fÐ˜vÐ&Ø�!ˆf�q˜!�fÐ˜~Ð.Ø�!ˆf�q˜!�fÐÐ8Ð9Ø�"ˆg˜˜1�vÐÐ 8Ð9Ø�2ˆh˜˜R˜Ð!Ð#9Ð:ð
	
óñGóðGð ‡[�[×ÑØà�2ˆh˜˜R˜Ð!Ð#?Ð@Ø�!ˆf�q˜!�fÐÐ5Ð6Ø�!ˆf�r˜2�hÐÐ!8Ð9Ø�"ˆg˜˜B�xÐ Ð"8Ð9Ø�"ˆg˜˜B�xÐ Ð"7Ð8Ø�!ˆf�q˜!�fÐÐ8Ð9Ø�!ˆf�q˜!�fÐ˜vÐ&Ø�!ˆf�q˜!�fÐ˜vÐ&Ø�!ˆf�q˜!�fÐÐ5Ð6Ø�"ˆg˜˜1�vÐÐ 6Ð7Ø�2ˆh˜˜R˜Ð!Ð#9Ð:ð	
óñ Gó!ð Gð ‡[�[×ÑØà�2ˆh˜˜R˜Ð!Ð#?Ð@Ø�!ˆf�q˜!�fÐÐ7Ð8Ø�!ˆf�r˜2�hÐÐ!7Ð8Ø�"ˆg˜˜B�xÐ Ð"8Ð9Ø�!ˆf�q˜!�fÐÐ7Ð8Ø�!ˆf�q˜!�fÐ˜}Ð-Ø�!ˆf�q˜!�fÐÐ7Ð8Ø�"ˆg˜˜1�vÐÐ 8Ð9ð		
óñGóðGò <ð4 ‡[�[×ÑØà�!ˆf�q˜"�gÐ §¡¨¯©Ð 0Ð1Ø�!ˆf�r˜1�gÐ §¡¨¯©Ð 0Ð1ð	
óñ-óð-òð ‡[�[×Ñ˜]Ð,?Ó@ñ1ó Aö1r<   r8  c                   óØ  a € ] tR tRt o ]P
                  P                  R. ]P                  ! ^4      3]P                  ! ^4      ^.3.4      ]P
                  P                  RRR7      R 4       4       t
R tR t]P
                  P                  R	. RO4      R 4       t]P
                  P                  R. RO4      R 4       t]P
                  P                  R 4       tR tR tR tRtV tR
# )ÚTestCvm_2sampiÙ  rÆ   r¥   zlazy -> no axis_nan_policyr§   c                ód  a€ V3R  lV 4       p\        \        \        SR7      ;_uu_ 4        \        V!  p\	        VP
                  SP                  SP                  4      4       \	        VP                  SP                  SP                  4      4       RRR4       R#   + '       g   i     R# ; i)c              3   ó\   <"  € T F!  pSP                  V\        S4      R 7      x € K#  	  R# 5i)r&   N)r2   r   )Ú.0Úargr4   s   & €r9   Ú	<genexpr>Ú5TestCvm_2samp.test_too_small_input.<locals>.<genexpr>ß  s'   øé € ÐLÁtÀ�—
‘
˜3Ô&6°rÓ&:�
×;Ð;Ãtùs   ƒ),rY   N)	r   r   r   r   r   r\   r2   r]   r^   )r3   rÆ   r4   r`   s   &&f r9   Útest_too_small_inputÚ"TestCvm_2samp.test_too_small_inputÛ  sq   ø€ ô MÁtÓLˆÜÔ+Ô3HÈR×PÖPÜ&¨Ñ-ˆCÜ˜CŸM™M¨2¯:©:°b·f±fÓ+=Ô>Ü˜CŸJ™J¨¯
©
°2·6±6Ó(:Ô;÷ Q×P×PÒPús   ¬A(BÂB/	c                óÆ   € VP                  ^4      pRp\        P                  ! \        VR7      ;_uu_ 4        \	        W"R4       RRR4       R#   + '       g   i     R# ; i)rC   z/method must be either auto, exact or asymptoticr«   ÚxyzN)rM   r/   r   rÃ   r   )r3   r4   r6   Úmsgs   &&  r9   r­   Ú TestCvm_2samp.test_invalid_inputå  s>   € Ø�I‰I�a‹LˆØ?ˆÜ�]Š]œ:¨S×1Ö1Ü   uÔ-÷ 2×1×1Ò1ús   ¸AÁA 	c                ó  € . ROp. ROp\        W4      p\        \        P                  ! V4      \        P                  ! V4      4      p\        VP                  VP
                  3VP                  VP
                  34       R# )r@   N)r@   rA   rB   rF   rD   )r†  rÂ   ri   r»  )r   rL   rÆ  r   r\   r^   )r3   r5   r6   Úr1Úr2s   &    r9   Útest_list_inputÚTestCvm_2samp.test_list_inputë  sV   € ÚˆÚˆÜ! !Ó'ˆÜ!¤"§(¢(¨1£+¬r¯xªx¸«{Ó;ˆÜ�b—l‘l B§I¡IÐ.°·±¸r¿y¹yÐ0IÖJr<   r!   Nc                óÆ  € \        V4      '       d/   VP                  R 8  d   VR8X  d   \        P                  ! R4       Vf   \	        V4      M
\        W!4      pVP                  . R
OVR7      pVP                  . ROVR7      p\        W44      p\        VP                  VP                  RVR7      RR7       \        VP                  VP                  RVR7      R	R7       R# )r#   r$   r%   Nr&   gøSã¥›ÄÐ?r>   r'   g
×£p=
Ç?rÉ   )	gffffff@gÍÌÌÌÌÌ @r-   gffffff!@çš™™™™™"@gÍÌÌÌÌÌ#@g333333$@g333333%@gffffff&@)gÍÌÌÌÌÌ@gÍÌÌÌÌÌ@gš™™™™™@ç      @ç333333@gffffff @g333333"@gš™™™™™#@gš™™™™™%@gš™™™™™&@g      '@gš™™™™™(@g      )@gÍÌÌÌÌÌ*@g333333-@)r   r.   r/   r0   r   r1   r2   r   r   r\   r^   )r3   r!   r4   r5   r6   Úrs   &&&   r9   Útest_example_conoverÚ"TestCvm_2samp.test_example_conoverò  s¶   € ô �B�<Š<˜BŸN™N¨UÔ2°uÀ	Ô7IÜ�KŠKÐ;Ô<Ø(-ªÔ  Ô$¼7À2Ó;MˆØ�J‰JÒGÈuˆJÓUˆØ�J‰Jò BØINð ó Pˆä  Ó&ˆÜ˜Ÿ™ R§Z¡Z°¸U ZÓ%CÈ$ÕOÜ˜Ÿ™ "§*¡*¨S¸ *Ó">ÀT×Jr<   zstatistic, m, n, pvalc                ó2   € \        \        WV4      V4       R # r´   )r   r   )r3   r\   r  r‰   Úpvals   &&&&&r9   Útest_exact_pvalueÚTestCvm_2samp.test_exact_pvalue   s   € ô 	Ô*¨9¸Ó;¸TÖBr<   c                ó¼  € \         P                  P                  R 4      p\        P                  P                  RVR7      p\        P                  P                  RVR7      pVP                  V4      VP                  V4      rC\        W44      p^ VP                  u;8  d	   ^8  g   Q h Q h\        W4R,           4      p^ VP                  u;8  d	   ^8  g   Q h Q hR# )i  r  )re   rÙ  i » r¶   N)	rL   rl   rm   r
   ÚnormrÞ  r2   r   r^   )r3   r4   ro   r5   r6   rr  s   &&    r9   Útest_large_sampleÚTestCvm_2samp.test_large_sample  s·   € ô �i‰i×#Ñ# DÓ)ˆÜ×Ñ×"Ñ"¨¸cÐ"ÓBˆÜ×Ñ×"Ñ"¨¸SÐ"ÓAˆØ�z‰z˜!‹}˜bŸj™j¨›mˆ1Ü  Ó&ˆØ�1—8‘8Ö˜aÔÐÑÐÐÜ   c¥EÓ*ˆØ�1—8‘8Ö˜aÔÐÑÐÒr<   c                ó|  € \         P                  P                  ^ 4      pVP                  VP                  ^4      4      pVP                  VP                  ^4      4      p\	        W4RR7      p\	        W4RR7      p\        VP                  VP                  4       \        VP                  VP                  RR7       R# )r   rß   rØ   rÞ   rÉ   r'   N)	rL   rl   rÜ  r2   r   r   r\   r   r^   )r3   r4   ro   r5   r6   rj  rk  s   &&     r9   Útest_exact_vs_asymptoticÚ&TestCvm_2samp.test_exact_vs_asymptotic  s€   € Ü�i‰i×#Ñ# AÓ&ˆØ�J‰J�s—z‘z !“}Ó%ˆØ�J‰J�s—z‘z !“}Ó%ˆÜ! !¨wÔ7ˆÜ! !¨|Ô<ˆÜ˜Ÿ™ b§l¡lÔ3Ü˜Ÿ	™	 2§9¡9°4×8r<   c                óX  € VP                  R 4      pVP                  . RO4      p\        W#RR7      p\        W#RR7      p\        VP                  VP                  4       VP                  R4      p\        W#RR7      p\        W#RR7      p\        VP                  VP                  4       R# )rÃ  rß   rØ   rã   g      5@rÞ   N)rË   gÍÌÌÌÌÌ@g333333*@)rM   r2   r   r   r^   )r3   r4   r5   r6   rj  rk  s   &&    r9   Útest_method_autoÚTestCvm_2samp.test_method_auto!  s   € Ø�I‰I�c‹NˆØ�J‰JÒ'Ó(ˆÜ! !¨wÔ7ˆÜ! !¨vÔ6ˆÜ˜Ÿ	™	 2§9¡9Ô-à�I‰I�c‹NˆÜ! !¨|Ô<ˆÜ! !¨vÔ6ˆÜ˜Ÿ	™	 2§9¡9Ö-r<   c                óš  € VP                  ^4      p\        W"4      p\        VP                  VP	                  R4      4       \        VP
                  VP	                  R4      4       \        VR,          VR,          4      p\        VP                  VP	                  R4      4       \        VP
                  VP	                  R4      4       R# )é   rŽ   r�   :NrB   NN)rM   r   r   r\   r2   r^   )r3   r4   r5   r`   s   &&  r9   Útest_same_inputÚTestCvm_2samp.test_same_input-  s‡   € ð �I‰I�b‹MˆÜ" 1Ó(ˆÜ˜Ÿ™ r§z¡z°"£~Ô6Ü˜Ÿ
™
 B§J¡J¨r£NÔ3ä" 1 R¥5¨!¨B­%Ó0ˆÜ˜Ÿ™ r§z¡z°"£~Ô6Ü˜Ÿ
™
 B§J¡J¨r£NÖ3r<   rw   rx   ))iÆ  rC   rD   g¾cj`ï˜º?)ii  rF   rF   gtÑE]t±?)i@  rB   rD   g8�8�ƒ?)iä  rD   rF   g¶ëéXwS?)rz   r{   r|   r}   r/   r~   r   rL   rM   rÌ   rc  r­   rl  rs  rw  Úxslowr{  r~  r�  r…  r€   r�   r‚   s   @r9   r\  r\  Ù  sÿ   ø‡ € à‡[�[×Ñ˜V r¨2¯9ª9°Q«<Ð&8Ø')§y¢y°£|°a°SÐ&9ð&;ó <à‡[�[×!Ñ! +Ð6RÐ!ÓSñ<ó Tó<ð<ò.òKð ‡[�[×Ñ˜WÒ&BÓCñKó DðKð ‡[�[×ÑÐ4ò5ó6ñ
Có6ð
Cð ‡[�[×Ññ
 ó ð
 ò9ò
.÷4ð 4r<   r\  c                   óò  a € ] tR tRt o . RO. R O. R!O3t. R"O. R O. R!O3t. R#O. R$O. R!O3tRtRtRt	]
P                  P                  R]]R3]]R3]]	R33. R%OR	7      R
 4       tRtRt]
P                  P                  R]]R3]]R33RR.R	7      R 4       tR tR tR tR tR tR tR t]
P                  P                  RR&4      R 4       t]
P                  P                  R. R'O4      R 4       tR tRtV tR# )(ÚTestTukeyHSDi;  aK  
    Comparison LowerCL Difference UpperCL Significance
    2 - 3	0.6908830568	4.34	7.989116943	    1
    2 - 1	0.9508830568	4.6 	8.249116943 	1
    3 - 2	-7.989116943	-4.34	-0.6908830568	1
    3 - 1	-3.389116943	0.26	3.909116943	    0
    1 - 2	-8.249116943	-4.6	-0.9508830568	1
    1 - 3	-3.909116943	-0.26	3.389116943	    0
    aS  
    Comparison LowerCL Difference UpperCL Significance
    2 - 1	0.2679292645	3.645	7.022070736	    1
    2 - 3	0.5934764007	4.34	8.086523599	    1
    1 - 2	-7.022070736	-3.645	-0.2679292645	1
    1 - 3	-2.682070736	0.695	4.072070736	    0
    3 - 2	-8.086523599	-4.34	-0.5934764007	1
    3 - 1	-4.072070736	-0.695	2.682070736	    0
    aS  
    Comparison LowerCL Difference UpperCL Significance
    2 - 3	1.561605075	    4.34	7.118394925	    1
    2 - 1	2.740784879	    6.08	9.419215121	    1
    3 - 2	-7.118394925	-4.34	-1.561605075	1
    3 - 1	-1.964526566	1.74	5.444526566	    0
    1 - 2	-9.419215121	-6.08	-2.740784879	1
    1 - 3	-5.444526566	-1.74	1.964526566	    0
    zdata,res_expect_str,atolr)   g»½×Ùß|Û=úequal size sample©Úidsc                óP  € \         P                  ! VP                  RR4      P                  4       R,          \        R7      P                  R4      p\        P                  ! V!  pVP                  4       pV F«  w  rxršr¼\        V4      ^,
          \        V4      ^,
          r‡\        VP                  Wx3,          W“R7       \        VP                  Wx3,          W£R7       \        VP                  Wx3,          W³R7       \        VP                  Wx3,          R8*  V^8H  4       K­  	  R# )	aë  
SAS code used to generate results for each sample:
DATA ACHE;
INPUT BRAND RELIEF;
CARDS;
1 24.5
...
3 27.8
;
ods graphics on;   ODS RTF;ODS LISTING CLOSE;
   PROC ANOVA DATA=ACHE;
   CLASS BRAND;
   MODEL RELIEF=BRAND;
   MEANS BRAND/TUKEY CLDIFF;
   TITLE 'COMPARE RELIEF ACROSS MEDICINES  - ANOVA EXAMPLE';
   ods output  CLDiffs =tc;
proc print data=tc;
    format LowerCL 17.16 UpperCL 17.16 Difference 17.16;
    title "Output with many digits";
RUN;
QUIT;
ODS RTF close;
ODS LISTING;
ú - Ú ºrC   NNr&   r'   rÊ   N)rD   rD   ©rL   r2   ÚreplaceÚsplitÚfloatrß  r   Ú	tukey_hsdÚconfidence_intervalÚintr   Úlowr\   Úhighr^   )r3   ÚdataÚres_expect_strr(   Ú
res_expectÚ	res_tukeyÚconfrp   ÚjÚlr  ÚhÚsigs   &&&&         r9   Útest_compare_sasÚTestTukeyHSD.test_compare_sasf  sâ   € ôB —Z’Z × 6Ñ 6°u¸cÓ B× HÑ HÓ JÈ2Õ NÜ&+ô-ß-4©W°V«_ð 	ä—O’O TÑ*ˆ	Ø×,Ñ,Ó.ˆã",ÑˆA�!˜Ü�q“6˜A•:œs 1›v¨�zˆqÜ˜DŸH™H Q T�N¨AÕ9Ü˜I×/Ñ/°°Õ5°qÕDÜ˜DŸI™I a d�O¨QÕ:Ü˜Y×-Ñ-¨a¨dÕ3°sÑ:¸SÀA¹XÖFó #-r<   zÐ
        1	2	-8.2491590248597	-4.6	-0.9508409751403	0.0144483269098
        1	3	-3.9091590248597	-0.26	3.3891590248597	0.9803107240900
        2	3	0.6908409751403	4.34	7.9891590248597	0.0203311368795
        zÛ
        1	2	-7.02207069748501	-3.645	-0.26792930251500 0.03371498443080
        1	3	-2.68207069748500	0.695	4.07207069748500 0.85572267328807
        2	3	0.59347644287720	4.34	8.08652355712281 0.02259047020620
        rF  r.  zunequal size samplec                ó  € \         P                  ! VP                  4       \        R7      P	                  R4      p\
        P                  ! V!  pVP                  4       pV F¦  w  rxršr¼\        V4      ^,
          \        V4      ^,
          r‡\        VP                  Wx3,          W“R7       \        VP                  Wx3,          W£R7       \        VP                  Wx3,          W³R7       \        VP                  Wx3,          WÃR7       K¨  	  R# )a6  
vals = [24.5, 23.5,  26.4, 27.1, 29.9, 28.4, 34.2, 29.5, 32.2, 30.1,
 26.1, 28.3, 24.3, 26.2, 27.8]
names = {'zero', 'zero', 'zero', 'zero', 'zero', 'one', 'one', 'one',
 'one', 'one', 'two', 'two', 'two', 'two', 'two'}
[p,t,stats] = anova1(vals,names,"off");
[c,m,h,nms] = multcompare(stats, "CType","hsd");
r&   r'   N©rA   rD   )rL   r2   r“  r”  rß  r   r•  r–  r—  r   r˜  r\   r™  r^   )r3   rš  r›  r(   rœ  r�  rž  rp   rŸ  r   r  r¡  r8   s   &&&&         r9   Útest_compare_matlabÚ TestTukeyHSD.test_compare_matlabŸ  sÆ   € ô —Z’Z × 4Ñ 4Ó 6Ü&+ô-ß-4©W°V«_ð 	ä—O’O TÑ*ˆ	Ø×,Ñ,Ó.ˆã *ÑˆA�!˜Ü�q“6˜A•:œs 1›v¨�zˆqÜ˜DŸH™H Q T�N¨AÕ9Ü˜I×/Ñ/°°Õ5°qÕDÜ˜DŸI™I a d�O¨QÕ:Ü˜I×,Ñ,¨Q¨TÕ2°A×Aó !+r<   c                óh  € Rp\         P                  ! VP                  RR4      P                  4       R,          \        R7      P                  R4      p. RO. RO. RO3p\        P                  ! V!  pVP                  4       pV Fª  w  rgr‰r«\        V4      ^,
          \        V4      ^,
          rv\        VP                  Wg3,          V	RR7       \        VP                  Wg3,          VRR7       \        VP                  Wg3,          V
R	R7       \        VP                  Wg3,          VRR7       K¬  	  R
# )aÃ  
Testing against results and p-values from R:
from: https://www.rdocumentation.org/packages/stats/versions/3.6.2/
topics/TukeyHSD
> require(graphics)
> summary(fm1 <- aov(breaks ~ tension, data = warpbreaks))
> TukeyHSD(fm1, "tension", ordered = TRUE)
> plot(TukeyHSD(fm1, "tension"))
Tukey multiple comparisons of means
95% family-wise confidence level
factor levels have been ordered
Fit: aov(formula = breaks ~ tension, data = warpbreaks)
$tension
zÞ
                diff        lwr      upr     p adj
        2 - 3  4.722222 -4.8376022 14.28205 0.4630831
        1 - 3 14.722222  5.1623978 24.28205 0.0014315
        1 - 2 10.000000  0.4401756 19.55982 0.0384598
        rŽ  r�  r�  r&   r.  r'   rU  çñhãˆµøä>Nr¦  )é   rK   é6   r¹  éF   é4   é3   r«  éC   r¸  rº  é   é   r±  é   é)   é   é,   )r»  é   r±  r½  ri   r»  r¼  rK   é$   é*   r«  r²  é   é'   é   r·  r»  r±  )r¸  r·  é   r»  rE   é+   r¼  r„  r«  rµ  r·  r½  r½  r¹   r„  r„  rº  r¼  r‘  )r3   Ústr_resrœ  rš  r�  rž  rp   rŸ  r  r   r¡  r8   s   &           r9   Útest_compare_rÚTestTukeyHSD.test_compare_r¹  sý   € ðˆô —Z’Z §¡°°sÓ ;× AÑ AÓ CÀBÕ GÜ&+ô-ß-4©W°V«_ð 	ò5ò5ò5ð	6ˆô —O’O TÑ*ˆ	Ø×,Ñ,Ó.ˆã *ÑˆA�!˜Ü�q“6˜A•:œs 1›v¨�zˆqä˜DŸH™H Q T�N¨A°DÕ9Ü˜I×/Ñ/°°Õ5°q¸tÕDÜ˜DŸI™I a d�O¨Q°TÕ:Ü˜I×,Ñ,¨Q¨TÕ2°A¸D×Aó !+r<   c                ó²  € . ROp. ROp. ROp. ROp\         P                  ! WW44      pVP                  4       p\        P                  ! . RO. R	O. R
O. RO.4      p\        P                  ! . RO. RO. RO. RO.4      pR FU  w  rš\        VP                  Wš3,          WyV
3,          RR7       \        VP                  Wš3,          W‰V
3,          RR7       KW  	  R# )zX
Example sourced from:
https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm
rÉ   r'   N)çš™™™™™@gš™™™™™@ç333333@gffffff@rö   )gš™™™™™ @rq  g333333@gffffff"@rp  )g       @g      %@g333333 @rÃ  ro  )rÄ  gffffff@gffffff@gffffff@gÍÌÌÌÌÌ@)r   r   r   g      À)g�Âõ(\�Ò?r   gq=
×£pÀg¤p=
×£À?)g®Gázò?r   r   g
×£p=
ï?)r   r   r   r   )r   r   r   gáz®Gáþ?)gáz®Gá@r   g      ô?g=
×£p=@)g=
×£p=@r   r   gš™™™™™@)©r?   r   )r@   r   )r   rA   r#  rÌ  )r   r•  r–  rL   r2   r   r˜  r™  )r3   Úgroup1Úgroup2Úgroup3Úgroup4r`   rž  ÚlowerÚupperrp   rŸ  s   &          r9   Útest_engineering_stat_handbookÚ+TestTukeyHSD.test_engineering_stat_handbookâ  s¼   € ò
 +ˆÚ*ˆÚ+ˆÚ*ˆÜ�oŠo˜f¨fÓ=ˆØ×&Ñ&Ó(ˆÜ—
’
ÚÚ ÚÚð	ó ˆô
 —
’
ÚÚ!ÚÚð	ó ˆó ?‰FˆQÜ˜DŸH™H Q T�N¨E°Q°$­K¸dÕCÜ˜DŸI™I a d�O¨U°a°4­[¸t×Dó ?r<   c                óB  € \         P                  P                  R 4      pVP                  R4      p\        P                  ! V!  pVP                  4       p\        VP                  VP                  P                  ) 4       \        \         P                  ! VP                  4      VP                  R,          4       \        \         P                  ! VP                  4      VP                  R,          4       \        VP                  VP                  P                  ) 4       \        \         P                  ! VP                  4      ^ 4       \        VP                  VP                  P                  4       \        \         P                  ! VP                  4      ^4       R# )l   ã]ÏA N)rA   r˜   )r   r   )rL   rl   rm   r   r•  r–  r   r˜  r™  rÒ  Údiagonalr\   r^   )r3   ro   rš  r`   rž  s   &    r9   Útest_rand_symmÚTestTukeyHSD.test_rand_symmü  sõ   € ä�i‰i×#Ñ# JÓ/ˆØ�z‰z˜(Ó#ˆÜ�oŠo˜tÑ$ˆØ×&Ñ&Ó(ˆä�T—X‘X §	¡	§¡˜|Ô,ô 	”R—[’[ §¡Ó+¨T¯Y©Y°t­_Ô=Ü”R—[’[ §¡Ó*¨D¯H©H°T­NÔ;ä�S—]‘] S§]¡]§_¡_Ð$4Ô5Ü”R—[’[ §¡Ó/°Ô3ä�S—Z‘Z §¡§¡Ô.Ü”R—[’[ §¡Ó,¨aÖ0r<   c                óÊ   € \        \        R R7      ;_uu_ 4        \        P                  ! . RO^\        P
                  .. RO4       RRR4       R#   + '       g   i     R# ; i)z...must be finite.r«   NrÁ   )rD   rF   rA   )rÚ   rÃ   r   r•  rL   rn   r(  s   &r9   Útest_no_infÚTestTukeyHSD.test_no_inf  s8   € Üœ:Ð-A×BÖBÜ�OŠOšI¨¬2¯6©6 {²IÔ>÷ C×B×BÒBús   š-AÁA"	c                ó¶   € \        \        R R7      ;_uu_ 4        \        P                  ! ^^.^^..^^.. RO4       RRR4       R#   + '       g   i     R# ; i)z...must be one-dimensionalr«   N)rC   é   rD   ©rÚ   rÃ   r   r•  r(  s   &r9   Ú
test_is_1dÚTestTukeyHSD.test_is_1d  sA   € Üœ:Ð-I×JÖJÜ�OŠO˜a ˜V a¨ VÐ,¨q°!¨f²jÔA÷ K×J×JÒJús   š#AÁA	c                óª   € \        \        R R7      ;_uu_ 4        \        P                  ! . ^^.. RO4       RRR4       R#   + '       g   i     R# ; i)z...must be greater than oner«   N)rB   rC   rD   r×  r(  s   &r9   Útest_no_emptyÚTestTukeyHSD.test_no_empty  s4   € Üœ:Ð-J×KÖKÜ�OŠO˜B  A ª	Ô2÷ L×K×KÒKús   šAÁA	c           	     ó¶   € R p\        \        VR7      ;_uu_ 4        \        P                  ! . RO^^.^^.RR7       RRR4       R#   + '       g   i     R# ; i)z(Expected a boolean value for 'equal_var'r«   ÚFalse)Ú	equal_varNrÁ   )rÚ   Ú	TypeErrorr   r•  )r3   rg  s   & r9   Útest_equal_var_input_validationÚ,TestTukeyHSD.test_equal_var_input_validation  s=   € Ø8ˆÜœ9¨C×0Ö0Ü�OŠOšI¨¨1 v°°1¨vÀÕI÷ 1×0×0Ò0ús   œ!AÁA	Únargsc                ó®   € \        \        R R7      ;_uu_ 4        \        P                  ! . RO.V,          !   RRR4       R#   + '       g   i     R# ; i)z...more than 1 treatment.r«   N©rÖ  rF   rA   r×  )r3   rã  s   &&r9   Útest_not_enough_treatmentsÚ'TestTukeyHSD.test_not_enough_treatments   s3   € äœ:Ð-H×IÖIÜ�OŠOšz˜l¨UÕ2Ò4÷ J×I×IÒIús   šAÁA	Úclc                óÐ   € \        \        R R7      ;_uu_ 4        \        P                  ! . RO^^.^	^.4      pVP	                  V4       RRR4       R#   + '       g   i     R# ; i)zmust be between 0 and 1r«   Nrå  )rÚ   rÃ   r   r•  r–  )r3   rè  rr  s   && r9   Útest_conf_level_invalidÚ$TestTukeyHSD.test_conf_level_invalid%  sH   € äœ:Ð-F×GÖGÜ—’¢
¨Q°¨F°Q¸°FÓ;ˆAØ×!Ñ! "Ô%÷ H×G×GÒGús   š0AÁA%	c                ó6  € \         P                  ! V P                  R ,          !  p\         P                  ! V P                  R ,          !  p\	        VP
                  VP
                  R,          4       \	        VP
                  VP
                  R,          4       R# ):Nr@   NNré  rÅ  )r   r•  Údata_diff_sizeÚ	ttest_indr   r^   )r3   r�  Ú	res_ttests   &  r9   Útest_2_args_ttestÚTestTukeyHSD.test_2_args_ttest+  sj   € ä—O’O T×%8Ñ%8¸Õ%<Ñ=ˆ	Ü—O’O T×%8Ñ%8¸Õ%<Ñ=ˆ	Ü˜	×(Ñ(¨)×*:Ñ*:¸4Õ*@ÔAÜ˜	×(Ñ(¨)×*:Ñ*:¸4Õ*@ÖAr<   rw   N)rD  ç     €7@çffffff:@çš™™™™;@çfffffæ=@)çffffff<@çš™™™™A@ç     €=@çš™™™™@@çš™™™™>@)gš™™™™:@gÍÌÌÌÌL<@gÍÌÌÌÌL8@g333333:@gÍÌÌÌÌÌ;@)rD  rò  gHáz®G:@ró  rô  rõ  rú  rú  )rD  rò  ró  )
rö  r÷  rø  rù  rú  rö  r÷  rø  rù  rú  )rŠ  úunequal sample sizezextreme sample size differencesré  )rÅ  r   r?   r@   )rz   r{   r|   r}   Údata_same_sizerí  Úextreme_sizeÚsas_same_sizeÚsas_diff_sizeÚsas_extremer/   r~   r   r£  Úmatlab_sm_sizÚmatlab_diff_szr§  rÀ  rÌ  rÐ  rÓ  rØ  rÛ  rá  ræ  rê  rð  r€   r�   r‚   s   @r9   r‰  r‰  ;  sˆ  ø‡ € â4Ú4Ú4ð6€Nò HÚ4Ú4ð6€Nò 'òâ2ð4€Lð
€Mð€Mð€Kð ‡[�[×ÑÐ7Ø-¨}¸dÐCØ-¨}¸dÐCØ+¨[¸%Ð@ð ò"Eð ó Fñ#GóFð#GðJ€Mð€Nð ‡[�[×ÑÐ7Ø-¨}¸eÐDØ-¨~¸tÐDðFà"5Ø"7ð"9ð ó :ñ
Bó:ð
Bò*'BòREò41ò&?òBò3òJð
 ‡[�[×Ñ˜W fÓ-ñ5ó .ð5ð ‡[�[×Ñ˜T¢>Ó2ñ&ó 3ð&÷
Bð Br<   r‰  c                   óD  a € ] tR tRt o . RO. RO. RO3t. RO. RO. RO. RO3tRtRt]P                  P                  ]P                  P                  R]]3]]33RR.R7      R 4       4       tR	tR
t]P                  P                  R]]3]]33RR.R7      R 4       tRtV tR# )ÚTestGamesHowelli3  aK  
            Mean Diff      Lower Bound         Upper Bound         Sig
    0 - 1   8.25000000    -16.5492749527311    33.0492749527311    0.558733632413559
    0 - 2  -5.50000000    -63.6702454316458    52.6702454316458    0.941147750599221
    1 - 2  -13.7500000    -74.3174374251372    46.8174374251372    0.682983914946841
    a+  
             Mean Diff       Lower Bound        Upper Bound         Sig
    0 - 1	 28.16666667    -141.985416377670   198.318749711003	0.8727542747886180
    0 - 2	 4.466666667	-37.2830676783904   46.2164010117237	0.9752628408671710
    0 - 3	 16.26666667	-35.0933112382470   67.6266445715803	0.4262506151302880
    1 - 2	-23.70000000	-195.315617201249   147.915617201249	0.9148950609000590
    1 - 3	-11.90000000	-188.105478728519   164.305478728519	0.9861432250093960
    2 - 3	 11.80000000	-16.2894857524254	39.8894857524254    0.4755344436335670
    zdata, res_expect_strrŠ  rû  r‹  c                ó8  € \         P                  ! VP                  RR4      P                  4       R,          \        R7      P                  R^4      p\        P                  ! VRR/ pVP                  4       pV Fœ  w  rgr‰r«\        V4      \        V4      rv\        VP                  Wg3,          VRR7       \        VP                  Wg3,          VRR7       \        VP                  Wg3,          V	R	R7       \        VP                  Wg3,          V
R
R7       Kž  	  R# )zÆ
DATA LIST LIST /Group (F1.0) Value (F8.2).
BEGIN DATA
0 24
0 23
0 31
0 51
1 34
1 18
1 18
1 26
2 17
2 68
2 59
2 7
END DATA.

ONEWAY Value BY Group
    /MISSING ANALYSIS
    /POSTHOC=GH ALPHA(0.05).
rŽ  r�  :rF   NNr&   rß  Fg:Œ0âŽyE>r'   rU  rª  Nrk   )rL   r2   r’  r“  r”  rß  r   r•  r–  r—  r   r\   r^   r˜  r™  )r3   rš  r›  rœ  Ú	res_gamesrž  rp   rŸ  r  r   r¡  r8   s   &&&         r9   Útest_compare_spssÚ!TestGamesHowell.test_compare_spssO  sâ   € ô8 —Z’ZØ×"Ñ" 5¨#Ó.×4Ñ4Ó6°rÕ:Üôç ™  Q›ð 	ô —O’O TÐ;°UÑ;ˆ	Ø×,Ñ,Ó.ˆã *ÑˆA�!˜Ü�q“6œ3˜q›6ˆqÜ˜I×/Ñ/°°Õ5°q¸tÕDÜ˜I×,Ñ,¨Q¨TÕ2°A¸DÕAÜ˜DŸH™H Q T�N¨A°DÕ9Ü˜DŸI™I a d�O¨Q°T×:ó !+r<   zÙ
                  q value             Pr(>|q|)
    1 - 0 == 0   -1.5467805948856344  0.55873362851759
    2 - 0 == 0    0.4726721776628535  0.94114775035993
    2 - 1 == 0    1.246837541297872   0.68298393799782
    aw  
                 q value             Pr(>|q|)
    1 - 0 == 0  -1.0589317485313876  0.87275427357438
    2 - 0 == 0  -0.5716222106144833  0.97526284087419
    3 - 0 == 0  -2.6209678382077000  0.42625067714691
    2 - 1 == 0   0.8971899898179028  0.91489506061850
    3 - 1 == 0   0.4579447210555352  0.98614322544695
    3 - 2 == 0  -2.198800177874794   0.47553444364614
    c                óx  € \         P                  ! VP                  RR4      P                  RR4      P                  4       R,          \        R7      P                  R^4      p\        P                  ! VRR/ pV F<  w  rV rx\        V4      \        V4      rV\        VP                  We3,          VRR	7       K>  	  R
# )aÓ  
games-howell is provided by PMCMRplus package
https://search.r-project.org/CRAN/refmans/PMCMRplus/html/gamesHowellTest.html
> library("PMCMRplus")
> options(digits=16)
> table = data.frame(
    values = c(24., 23., 31., 51., 34., 18., 18., 26., 17., 68., 59.,  7.),
    groups = c("0", "0", "0", "0", "1", "1", "1", "1", "2", "2", "2", "2")
  )
> table$groups = as.factor(table$groups)
> fit <-aov(values ~ groups, table)
> res = gamesHowellTest(fit)
> summary(res)
rŽ  r�  z == :rA   NNr&   rß  Fr.  r'   Nrk   )rL   r2   r’  r“  r”  rß  r   r•  r—  r   r^   )	r3   rš  r›  rœ  r  rŸ  rp   Ú_r8   s	   &&&      r9   rÀ  ÚTestGamesHowell.test_compare_r‰  s�   € ô( —Z’ZØ×"Ñ" 5¨#Ó.ß‰W�V˜SÓ!§%¡%£'¨"õ.äô÷ !™  Q›ð 	ô —O’O TÐ;°UÑ;ˆ	ó (‰MˆA�!�QÜ�q“6œ3˜q›6ˆqÜ˜I×,Ñ,¨Q¨TÕ2°A¸D×Aó (r<   rw   N)g      8@r…  g      ?@ç     €I@)g      A@ç      2@r  g      :@)g      1@g      Q@g     €M@g      @)g      >@r…  r  )g     @TÀg     ÀQ@g      ;Àg     €O@)g      E@g      &@g      =@g      3@g      I@)r…  g      6@rÃ  r  g      "@)rz   r{   r|   r}   rü  rí  Úspss_same_sizeÚspss_diff_sizer/   r~   r‡  r   r  Úr_same_sizeÚr_diff_sizerÀ  r€   r�   r‚   s   @r9   r  r  3  sñ   ø‡ € â*Ú*Ú*ð,€Nò &Ú,Ú/Ú.ð0€Nð
€Nð€Nð ‡[�[×ÑØ‡[�[×ÑÐ3Ø,¨nÐ=Ø+¨^Ð<ð>à!4Ø!6ð!8ð ó 9ñ
!;ó9ó ð!;ðF€Kð€Kð ‡[�[×ÑÐ3Ø,¨kÐ:Ø+¨[Ð9ð;à!4Ø!6ð!8ð ó 9ñ
Bó9ö
Br<   r  c                   óö   a € ] tR tRt o ]P
                  P                  R. RO. RO34      R 4       t]P
                  P                  R. RO. RO. RO. RO. RO. RO. RO. RO34      R 4       tR t	R t
R tR	tV tR
# )ÚTestPoissonMeansTesti¬  zc1, n1, c2, n2, p_expectc                ód   € \         P                  ! WW44      p\        VP                  VR R7       R# rˆ   ©r   Úpoisson_means_testr   r^   )r3   Úc1Ún1Úc2Ún2Úp_expectr`   s   &&&&&& r9   Útest_paper_examplesÚ(TestPoissonMeansTest.test_paper_examples­  s&   € ô ×&Ò& r¨rÓ6ˆÜ˜Ÿ
™
 H°4×8r<   z c1, n1, c2, n2, p_expect, alt, dc           	     ój   € \         P                  ! WW4WgR 7      p\        VP                  VRRR7       R# ))r×   Údiffg�íµ ÷ÆÀ>r,  ©r(   rW  Nr  )	r3   r  r  r  r  r  ÚaltÚdr`   s	   &&&&&&&& r9   Útest_fortran_authorsÚ)TestPoissonMeansTest.test_fortran_authors¶  s*   € ô$ ×&Ò& r¨rÀ3ÔOˆÜ˜Ÿ
™
 H°4¸e×Dr<   c                ól   € R R r!R R rC\         P                  ! WW$4      p\        VP                  ^4       R# )r”   Nr  ©r3   Úcount1Úcount2Únobs1Únobs2r`   s   &     r9   Útest_different_resultsÚ+TestPoissonMeansTest.test_different_resultsË  s2   € ð  �Ø˜eˆuÜ×&Ò& v°fÓDˆÜ˜Ÿ
™
 AÖ&r<   c                ól   € ^ ^ r!^^rC\         P                  ! WW$4      p\        VP                  ^4       R# r%  r  r&  s   &     r9   Útest_less_than_zero_lambda_hat2Ú4TestPoissonMeansTest.test_less_than_zero_lambda_hat2Ô  s2   € ð ˜A�Ø˜!ˆuÜ×&Ò& v°fÓDˆÜ˜Ÿ
™
 AÖ&r<   c           
     ó
  € ^ ^ r!^^rCRp\        \        VR7      ;_uu_ 4        \        P                  ! RW2V4       RRR4       \        \        VR7      ;_uu_ 4        \        P                  ! WRV4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        P                  ! RW2V4       RRR4       \        \        VR7      ;_uu_ 4        \        P                  ! WRV4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        P                  ! VRW$4       RRR4       \        \        VR7      ;_uu_ 4        \        P                  ! WVR4       RRR4       Rp\        \        VR7      ;_uu_ 4        \        P                  ! WW$RR7       RRR4       R	p\        \        VR7      ;_uu_ 4        \        P                  ! ^^^^R
R7       RRR4       R#   + '       g   i     ELµ; i  + '       g   i     EL�; i  + '       g   i     ELg; i  + '       g   i     ELA; i  + '       g   i     EL; i  + '       g   i     Lò; i  + '       g   i     LÈ; i  + '       g   i     R# ; i)r   z`k1` and `k2` must be integers.r«   rÂ   Nz1`k1` and `k2` must be greater than or equal to 0.z%`n1` and `n2` must be greater than 0.z(diff must be greater than or equal to 0.)r  zAlternative must be one of ...ÚerrorrÖ   rk   )rÚ   rà  r   r  rÃ   )r3   r'  r(  r)  r*  rÅ   s   &     r9   rÛ   Ú*TestPoissonMeansTest.test_input_validationÜ  s¯  € Ø˜A�Ø˜!ˆuð 4ˆÜœ9¨G×4Ö4Ü×$Ò$ R¨¸Ô>÷ 5äœ9¨G×4Ö4Ü×$Ò$ V°B¸Ô>÷ 5ð FˆÜœ:¨W×5Ö5Ü×$Ò$ R¨¸Ô>÷ 6äœ:¨W×5Ö5Ü×$Ò$ V°B¸Ô>÷ 6ð :ˆÜœ:¨W×5Ö5Ü×$Ò$ V¨R°Ô?÷ 6äœ:¨W×5Ö5Ü×$Ò$ V°F¸BÔ?÷ 6ð =ˆÜœ:¨W×5Ö5Ü×$Ò$ V°FÈÕK÷ 6ð 3ˆÜœ:¨W×5Ö5Ü×$Ò$ Q¨¨1¨a¸WÕE÷ 6Ñ5÷5 5×4Ð4úç4×4Ð4ú÷
 6×5Ð5úç5×5Ð5ú÷
 6×5Ð5úç5×5ú÷
 6×5ú÷
 6×5Ð5ús_   ¢G'ÁG;ÂHÃH#ÄH7ÅIÆIÇI1Ç'G8	Ç;H	ÈH 	È#H4	È7I	ÉI	ÉI.	É1J	rw   N)r   r˜   rA   r˜   gþe÷äa¡¶?)r@   r˜   rD   r˜   gÞ	ŠcÆ?)rµ  rE   rµ  rE   gŽŸ{}ÿÿï?ræ   r   )rE   rE   rE   rE   goPFªÿÿï?ræ   r   )é2   r„  r?   r?   góæ°ae¹?ræ   rÊ   )rA   r˜   rµ  r,  gò/V›-=¿?ræ   r   )rA   ri   rB   rµ  g"Ü)‘ÅÝÙ?ré   r   )rB   rµ  rA   r˜   g_ù'Qm~€?ré   r   )rB   rµ  rA   rE   g|¨Š»Ó?rè   r   )r?   r?   r3  r„  gï0�ëÝ·?rè   r   )rz   r{   r|   r}   r/   r~   r   r  r#  r+  r.  rÛ   r€   r�   r‚   s   @r9   r  r  ¬  s”   ø‡ € Ø‡[�[×ÑÐ7â Ú ð:ó ñ
9óð
9ð ‡[�[×ÑÐ?ò
 	=Ú<Ú=Ú>Ú9Ú;ò 	6Ú6ðBó ñ"Eó#ð"Eò'ò'÷!Fð !Fr<   r  c                   óÈ   a € ] tR tRt o R tR t]P                  P                  R
. RO4      R 4       t	]P                  P                  R
. RO4      R 4       t
R tR tRtV tR	# )ÚTestBWSTesti   c                ó  € \         P                  P                  R 4      pVP                  RR7      w  r#Rp\        P                  ! \
        VR7      ;_uu_ 4        \        P                  ! W".W3.4       RRR4       Rp\        P                  ! \
        VR7      ;_uu_ 4        \        P                  ! \         P                  .V4       RRR4       Rp\        P                  ! \
        VR7      ;_uu_ 4        \        P                  ! V. 4       RRR4       Rp\        P                  ! \
        VR7      ;_uu_ 4        \        P                  ! W#RR	7       RRR4       R
p\        P                  ! \
        VR7      ;_uu_ 4        \        P                  ! W#^*R7       RRR4       R#   + '       g   i     EL<; i  + '       g   i     Lú; i  + '       g   i     LÇ; i  + '       g   i     L“; i  + '       g   i     R# ; i)ì   <oôvêT‘{ rd   z,`x` and `y` must be exactly one-dimensional.r«   Nz"`x` and `y` must not contain NaNs.z$`x` and `y` must be of nonzero size.zalternative` must be one of...rù  rÖ   z!method` must be an instance of...rØ   ©r@   rF   )	rL   rl   rm   r/   r   rÃ   r   Úbws_testr]   )r3   ro   r5   r6   rÅ   s   &    r9   Útest_bws_input_validationÚ%TestBWSTest.test_bws_input_validation  s>  € Ü�i‰i×#Ñ#Ð$7Ó8ˆà�z‰z˜vˆzÓ&‰ˆà@ˆÜ�]Š]œ:¨W×5Ö5Ü�NŠN˜A˜6 A 6Ô*÷ 6ð 7ˆÜ�]Š]œ:¨W×5Ö5Ü�NŠNœBŸF™F˜8 QÔ'÷ 6ð 9ˆÜ�]Š]œ:¨W×5Ö5Ü�NŠN˜1˜bÔ!÷ 6ð 3ˆÜ�]Š]œ:¨W×5Ö5Ü�NŠN˜1¨[Õ9÷ 6ð 6ˆÜ�]Š]œ:¨W×5Ö5Ü�NŠN˜1¨Õ+÷ 6Ñ5÷! 6×5Ð5ú÷ 6×5ú÷ 6×5ú÷ 6×5ú÷ 6×5Ð5ús<   ÁF'Â"'F;Ã7GÄ=G!ÆG4Æ'F8	Æ;G	ÇG	Ç!G1	Ç4H	c                ó¢   € . ROp. ROp\         P                  ! WRR7      p\        VP                  RRR7       \	        VP
                  R	4       R# )
r?   ræ   rÖ   gºI+‡@r>   r'   N)r?   r@   rA   rB   rD   rF   rG   )rC   rj   rE   rh   ri   r¹   rº  g¤f$/•Þg?)r   r9  r   r\   r   r^   rõ  s   &   r9   Ú test_against_published_referenceÚ,TestBWSTest.test_against_published_reference  s<   € ò "ˆÚ&ˆÜ�nŠn˜Q¨{Ô;ˆÜ˜Ÿ™ u°4Õ8Ü�S—Z‘Z Ö)r<   c                óþ   € \         P                  P                  R 4      pVP                  R	R7      w  rV\        P                  ! WVVR7      p\        VP                  VRR7       \        VP                  VRRR7       R# )
r7  rd   rÖ   ç‚vIhÂ%<=rV  rÉ   r¶   r   Nr8  ©rL   rl   rm   r   r9  r   r\   r^   ©r3   r×   r\   r^   ro   r5   r6   r`   s   &&&&    r9   Útest_against_RÚTestBWSTest.test_against_R&  s]   € ô �i‰i×#Ñ#Ð$7Ó8ˆØ�z‰z˜vˆzÓ&‰ˆÜ�nŠn˜Q¨{Ô;ˆÜ˜Ÿ™ y°uÕ=Ü˜Ÿ
™
 F°¸D×Ar<   c                ó  € \         P                  P                  R 4      pVP                  ^	R7      pVP                  ^R7      p\        P                  ! WVVR7      p\        VP                  VRR7       \        VP                  VRRR7       R# )	l   ‚.ÅÇs½Z rd   rÖ   r@  rV  rÉ   r¶   r   NrA  rB  s   &&&&    r9   Útest_against_R_imbalancedÚ%TestBWSTest.test_against_R_imbalanced7  sk   € ô �i‰i×#Ñ#Ð$7Ó8ˆØ�J‰J˜AˆJÓˆØ�J‰J˜AˆJÓˆÜ�nŠn˜Q¨{Ô;ˆÜ˜Ÿ™ y°uÕ=Ü˜Ÿ
™
 F°¸D×Ar<   c                ó$  € \         P                  P                  R 4      pVP                  RR7      w  r#\         P                  P                  R 4      p\        P                  ! ^
VR7      p\        P
                  ! W#VR7      p\        VP                  4      ^
8X  g   Q h\         P                  P                  R 4      p\        P                  ! ^
VR7      p\        P
                  ! W#VR7      p\        VP                  VP                  4       \         P                  P                  R4      p\        P                  ! ^
VR7      p\        P
                  ! W#VR7      p\         P                  ! VP                  VP                  4      '       d   Q hR# )ì   /°HøNÏ( rd   )Ún_resamplesro   rØ   l   ÝVC£	ãA N)r@   rE   )
rL   rl   rm   r   rc  r9  r	  Únull_distributionr   Úallclose)r3   ro   r5   r6   rÙ   r  r  r@  s   &       r9   Útest_methodÚTestBWSTest.test_methodI  s#  € ä�i‰i×#Ñ#Ð$7Ó8ˆØ�z‰z˜wˆzÓ'‰ˆä�i‰i×#Ñ#Ð$7Ó8ˆÜ×(Ò(°R¸SÔAˆÜ�~Š~˜a¨6Ô2ˆä�4×)Ñ)Ó*¨bÔ0Ð0Ð0ä�i‰i×#Ñ#Ð$7Ó8ˆÜ×(Ò(°R¸SÔAˆÜ�~Š~˜a¨6Ô2ˆä˜×.Ñ.°×0FÑ0FÔGä�i‰i×#Ñ#Ð$7Ó8ˆÜ×(Ò(°R¸SÔAˆÜ�~Š~˜a¨6Ô2ˆä—;’;˜t×5Ñ5°t×7MÑ7M×NÒNÐNÐNÑNr<   c                óê  € \         P                  P                  R 4      pVP                  ^R7      pV^,
          p\        P                  ! W#RR7      pVP
                  ^ 8”  g   Q h\        VP                  ^\        VP                  4      ,          4       \        P                  ! W#RR7      pVP
                  ^ 8”  g   Q h\        VP                  ^4       \        P                  ! W2RR7      pVP
                  ^ 8  g   Q h\        VP                  ^\        VP                  4      ,          4       \        P                  ! W2RR7      pVP
                  ^ 8  g   Q h\        VP                  ^4       R# )rI  rd   ré   rÖ   rè   N)
rL   rl   rm   r   r9  r\   r   r^   r	  rK  )r3   ro   r5   r6   r`   s   &    r9   Útest_directionsÚTestBWSTest.test_directions`  s  € ä�i‰i×#Ñ#Ð$7Ó8ˆØ�J‰J˜AˆJÓˆØ��Eˆä�nŠn˜Q¨yÔ9ˆØ�}‰}˜qÔ Ð Ð Ü�S—Z‘Z ¤S¨×)>Ñ)>Ó%?Õ!?Ô@ä�nŠn˜Q¨vÔ6ˆØ�}‰}˜qÔ Ð Ð Ü�S—Z‘Z Ô#ä�nŠn˜Q¨vÔ6ˆØ�}‰}˜qÔ Ð Ð Ü�S—Z‘Z ¤S¨×)>Ñ)>Ó%?Õ!?Ô@ä�nŠn˜Q¨yÔ9ˆØ�}‰}˜qÔ Ð Ð Ü�S—Z‘Z Ö#r<   rw   N)r×   r\   r^   ))ræ   g
»ù-ü?g4ˆñ³B/À?)rè   ç
»ù-ü¿g«î0&Àv­?)ré   rR  gÉñœý“(î?))ræ   góD 5Hò?g«ÒdüÔ•Ò?)rè   ç`�Ñ‡©áï?gÈ²µ×šXë?)ré   rS  gß4)¡”�Â?)rz   r{   r|   r}   r:  r=  r/   r~   r   rC  rF  rM  rP  r€   r�   r‚   s   @r9   r5  r5     s   ø‡ € ò,ò4*ð ‡[�[×ÑÐCòNóOñBó	OðBð ‡[�[×ÑÐCòNóOñBó	OðBòO÷.$ð $r<   r5  )8Ú	itertoolsr   ÚnumpyrL   r¬  r/   Únumpy.testingr   r   r   r   rÚ   Úscipyr   r	   Úscipy.statsr
   Úscipy.stats._hypotestsr   r   r   r   r   r   r   Úscipy.stats._mannwhitneyur   r   r   Úscipy._lib._testutilsr   Ú
scipy._libr   rà   Úscipy._lib._array_apir   r   r   r   Úscipy._lib._array_api_no_0dr   r   Úscipy.stats._axis_nan_policyr   r   r    r…   rÎ   r¦  r  r8  r\  r‰  r  r  r5  rw   r<   r9   Ú<module>r`     sJ  ðÝ ã Û Û ß @Ñ @Ý *ç  Ý %÷4÷ 4ñ 4÷ EÑ DÝ 2Ý -÷0ó 0ç Hß Rñ Ð'Ó(÷?2ð ?2ó )ð?2ñD �5×'Ñ'Ó(÷\Oð \Oó )ð\Oñ~ �5×%Ñ%Ó&÷	Cð 	Có 'ð	CôDl<Ð"ô l<÷^P
ñ P
÷fV1ñ V1ñr Ð'Ó(÷^4ð ^4ó )ð^4÷BuBñ uB÷psBñ sB÷rQFñ QF÷ht$ó t$r<   