+ ,i ^RIt^RIHt^RIHtHtHt^RIH t R.t Rt Rt Rt R t] !]R ^]^^R 7R ^R RRR/Rl4tR#)N)stats) _SimpleNormalSignificanceResult _get_pvalue)_axis_nan_policy_factory chatterjeexic VPR,p\P!VRR7p\P!WA4wrA\P!WRR7p\ P !VRRR7p\ P !V)RRR7p\P!\P!\P!VRR74RR7pV'd'^^V,V^,^, , , pMB^\P!W6, V,RR7,p ^W7,V , , pWV3#)axismax)methodr ) shapenpargsortbroadcast_arraystake_along_axisrrankdatasumabsdiff) xy y_continuousnjrlnum statisticdens &&& :/usr/lib/python3/dist-packages/scipy/stats/_correlation.py _xi_statisticr$s  A 12A  q $DA 1b)A qR0A r%b1A &&+,2 6CC16A:.. "&&!%12..# % ?cj\P!VPR,4pV'd2\P!R4\P!V4, #\P!^V^,4p\P !VRR7p\P !VRR7p^V^,, \P!^V,^V,, ^,V^,,RR7,p^V^,, \P!WcV, V,,^,RR7,p^V^,, \P!^V,^V,, ^,V,RR7,p ^V^,, \P!WV, ,RR7,p V^V,, V ^,,V ^,, p \P!V 4\P!V4, #)r r rg?)rfloat64rsqrtarangesortcumsumr) rrrriuvanbncndntau2s &&& r#_xi_stdr4*sa 1772;Awwu~ ** !QUA A !"A QTBFFAaC!A#IMQT1; ;B QTBFFAQ MA-B7 7B QTBFFAaC!A#IMQ.R8 8B QTBFFAQKr2 2B 2IA Q &D 774=2771: %%r%cVR9d \R4h\V\P4'g%VP 4pRpVR8wd \V4hW3#)Tz`y_continuous` must be boolean.z@`method` must be 'asymptotic' or a `PermutationMethod` instance. asymptotic>FT) ValueError isinstancerPermutationMethodlower)rrmessages&& r#_chatterjeexi_ivr<DsW=(:;; fe55 6 6T \ !W% %  r%c2VPVP3#)N)r!pvalue)res_s&&r#_unpackrATs ==#** $$r%T)paired n_samplesresult_to_tuple n_outputs too_smallr rFrr6c aa\SV4wopRpVR8Xd;\SVS4wrgp\WxS4p \4p \ Wi, WR7p Mm\ V\ P4'dN\ P!R RV3RVV3RlRVRR /VP4BR R /Bp V PV Pr\XX 4#) ah Compute the xi correlation and perform a test of independence The xi correlation coefficient is a measure of association between two variables; the value tends to be close to zero when the variables are independent and close to 1 when there is a strong association. Unlike other correlation coefficients, the xi correlation is effective even when the association is not monotonic. Parameters ---------- x, y : array-like The samples: corresponding observations of the independent and dependent variable. The (N-d) arrays must be broadcastable. axis : int, default: 0 Axis along which to perform the test. method : 'asymptotic' or `PermutationMethod` instance, optional Selects the method used to calculate the *p*-value. Default is 'asymptotic'. The following options are available. * ``'asymptotic'``: compares the standardized test statistic against the normal distribution. * `PermutationMethod` instance. In this case, the p-value is computed using `permutation_test` with the provided configuration options and other appropriate settings. y_continuous : bool, default: False Whether `y` is assumed to be drawn from a continuous distribution. If `y` is drawn from a continuous distribution, results are valid whether this is assumed or not, but enabling this assumption will result in faster computation and typically produce similar results. Returns ------- res : SignificanceResult An object containing attributes: statistic : float The xi correlation statistic. pvalue : float The associated *p*-value: the probability of a statistic at least as high as the observed value under the null hypothesis of independence. See Also -------- scipy.stats.pearsonr, scipy.stats.spearmanr, scipy.stats.kendalltau Notes ----- There is currently no special handling of ties in `x`; they are broken arbitrarily by the implementation. [1]_ notes that the statistic is not symmetric in `x` and `y` *by design*: "...we may want to understand if :math:`Y` is a function :math:`X`, and not just if one of the variables is a function of the other." See [1]_ Remark 1. References ---------- .. [1] Chatterjee, Sourav. "A new coefficient of correlation." Journal of the American Statistical Association 116.536 (2021): 2009-2022. :doi:`10.1080/01621459.2020.1758115`. Examples -------- Generate perfectly correlated data, and observe that the xi correlation is nearly 1.0. >>> import numpy as np >>> from scipy import stats >>> rng = np.random.default_rng(348932549825235) >>> x = rng.uniform(0, 10, size=100) >>> y = np.sin(x) >>> res = stats.chatterjeexi(x, y) >>> res.statistic np.float64(0.9012901290129013) The probability of observing such a high value of the statistic under the null hypothesis of independence is very low. >>> res.pvalue np.float64(2.2206974648177804e-46) As noise is introduced, the correlation coefficient decreases. >>> noise = rng.normal(scale=[[0.1], [0.5], [1]], size=(3, 100)) >>> res = stats.chatterjeexi(x, y + noise, axis=-1) >>> res.statistic array([0.79507951, 0.41824182, 0.16651665]) Because the distribution of `y` is continuous, it is valid to pass ``y_continuous=True``. The statistic is identical, and the p-value (not shown) is only slightly different. >>> stats.chatterjeexi(x, y + noise, y_continuous=True, axis=-1).statistic array([0.79507951, 0.41824182, 0.16651665]) greaterr6) alternativedatar!c,<\SVS4^,#)r)r$)rr rrs&&r#chatterjeexi..sq!\1RST1Ur%rIpermutation_typepairingsr r) r<r$r4rrr8rr9permutation_test_asdictr!r>r) rrr rrrIxirrstdnormr>r?s f&$d$ r#rrXsJ,L&AL& K  A|4qaL)RXtE FE33 4 4$$!U$7AEKNNDT  ]]CJJF b& ))r%)numpyrscipyrscipy.stats._stats_pyrrrscipy.stats._axis_nan_policyr__all__r$r4r<rArrPr%r#r[suPPA  8&4  %,TQ*1Q!Mx*qx*ux*\x*Mx*r%