(phHSrSSKJr SSKrSSKrSSKJrJr SSK J r SSK J r SSK Jr SS KJr SS KJr /S QrS rS r\"S/SQ/5rSSS.SjjrSrSrSrSSjrg)ax Contingency table functions (:mod:`scipy.stats.contingency`) ============================================================ Functions for creating and analyzing contingency tables. .. currentmodule:: scipy.stats.contingency .. autosummary:: :toctree: generated/ chi2_contingency relative_risk odds_ratio crosstab association expected_freq margins )reduceN)power_divergence _untabulate) relative_risk)crosstab) odds_ratio)_make_tuple_bunch)stats)margins expected_freqchi2_contingencyr associationrr c /n[[UR55nUHQn[R"[R XVs/sH oDU:wdM UPM sn5nUR U5 MS U$s snf)a~Return a list of the marginal sums of the array `a`. Parameters ---------- a : ndarray The array for which to compute the marginal sums. Returns ------- margsums : list of ndarrays A list of length `a.ndim`. `margsums[k]` is the result of summing `a` over all axes except `k`; it has the same number of dimensions as `a`, but the length of each axis except axis `k` will be 1. Examples -------- >>> import numpy as np >>> from scipy.stats.contingency import margins >>> a = np.arange(12).reshape(2, 6) >>> a array([[ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11]]) >>> m0, m1 = margins(a) >>> m0 array([[15], [51]]) >>> m1 array([[ 6, 8, 10, 12, 14, 16]]) >>> b = np.arange(24).reshape(2,3,4) >>> m0, m1, m2 = margins(b) >>> m0 array([[[ 66]], [[210]]]) >>> m1 array([[[ 60], [ 92], [124]]]) >>> m2 array([[[60, 66, 72, 78]]]) )listrangendimnpapply_over_axessumappend)amargsumsrangedkjmargs J/var/www/html/venv/lib/python3.13/site-packages/scipy/stats/contingency.pyr r 'sjXH %- F !!"&&!-JA6a-JK O.Ks A:A:c[R"U[RS9n[U5nURn[ [R U5UR5US- -- nU$)ac Compute the expected frequencies from a contingency table. Given an n-dimensional contingency table of observed frequencies, compute the expected frequencies for the table based on the marginal sums under the assumption that the groups associated with each dimension are independent. Parameters ---------- observed : array_like The table of observed frequencies. (While this function can handle a 1-D array, that case is trivial. Generally `observed` is at least 2-D.) Returns ------- expected : ndarray of float64 The expected frequencies, based on the marginal sums of the table. Same shape as `observed`. Examples -------- >>> import numpy as np >>> from scipy.stats.contingency import expected_freq >>> observed = np.array([[10, 10, 20],[20, 20, 20]]) >>> expected_freq(observed) array([[ 12., 12., 16.], [ 18., 18., 24.]]) )dtyper)rasarrayfloat64r rrmultiplyr)observedrdexpecteds rr r [sYFzz("**5Hx H  Abkk8,x||~!a%/HHH OChi2ContingencyResult) statisticpvaluedofr )methodc[R"U5n[R"US:5(a [S5eURS:Xa [S5e[ U5n[R"US:H5(a:[ [[R"US:H565Sn[SUS35eUb [XXU5$UR[UR5- UR-S- nUS:XaSnS nOwUS:XaSU(aLX@- n [R"U 5n [R"S [R"U 55n X U --n[!XURS- U- SUS 9upx[#XxXd5$) aChi-square test of independence of variables in a contingency table. This function computes the chi-square statistic and p-value for the hypothesis test of independence of the observed frequencies in the contingency table [1]_ `observed`. The expected frequencies are computed based on the marginal sums under the assumption of independence; see `scipy.stats.contingency.expected_freq`. The number of degrees of freedom is (expressed using numpy functions and attributes):: dof = observed.size - sum(observed.shape) + observed.ndim - 1 Parameters ---------- observed : array_like The contingency table. The table contains the observed frequencies (i.e. number of occurrences) in each category. In the two-dimensional case, the table is often described as an "R x C table". correction : bool, optional If True, *and* the degrees of freedom is 1, apply Yates' correction for continuity. The effect of the correction is to adjust each observed value by 0.5 towards the corresponding expected value. lambda_ : float or str, optional By default, the statistic computed in this test is Pearson's chi-squared statistic [2]_. `lambda_` allows a statistic from the Cressie-Read power divergence family [3]_ to be used instead. See `scipy.stats.power_divergence` for details. method : ResamplingMethod, optional Defines the method used to compute the p-value. Compatible only with `correction=False`, default `lambda_`, and two-way tables. If `method` is an instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is computed using `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the provided configuration options and other appropriate settings. Otherwise, the p-value is computed as documented in the notes. Note that if `method` is an instance of `MonteCarloMethod`, the ``rvs`` attribute must be left unspecified; Monte Carlo samples are always drawn using the ``rvs`` method of `scipy.stats.random_table`. .. versionadded:: 1.15.0 Returns ------- res : Chi2ContingencyResult An object containing attributes: statistic : float The test statistic. pvalue : float The p-value of the test. dof : int The degrees of freedom. NaN if `method` is not ``None``. expected_freq : ndarray, same shape as `observed` The expected frequencies, based on the marginal sums of the table. See Also -------- scipy.stats.contingency.expected_freq scipy.stats.fisher_exact scipy.stats.chisquare scipy.stats.power_divergence scipy.stats.barnard_exact scipy.stats.boschloo_exact :ref:`hypothesis_chi2_contingency` : Extended example Notes ----- An often quoted guideline for the validity of this calculation is that the test should be used only if the observed and expected frequencies in each cell are at least 5. This is a test for the independence of different categories of a population. The test is only meaningful when the dimension of `observed` is two or more. Applying the test to a one-dimensional table will always result in `expected` equal to `observed` and a chi-square statistic equal to 0. This function does not handle masked arrays, because the calculation does not make sense with missing values. Like `scipy.stats.chisquare`, this function computes a chi-square statistic; the convenience this function provides is to figure out the expected frequencies and degrees of freedom from the given contingency table. If these were already known, and if the Yates' correction was not required, one could use `scipy.stats.chisquare`. That is, if one calls:: res = chi2_contingency(obs, correction=False) then the following is true:: (res.statistic, res.pvalue) == stats.chisquare(obs.ravel(), f_exp=ex.ravel(), ddof=obs.size - 1 - dof) The `lambda_` argument was added in version 0.13.0 of scipy. References ---------- .. [1] "Contingency table", https://en.wikipedia.org/wiki/Contingency_table .. [2] "Pearson's chi-squared test", https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test .. [3] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984), pp. 440-464. Examples -------- A two-way example (2 x 3): >>> import numpy as np >>> from scipy.stats import chi2_contingency >>> obs = np.array([[10, 10, 20], [20, 20, 20]]) >>> res = chi2_contingency(obs) >>> res.statistic 2.7777777777777777 >>> res.pvalue 0.24935220877729619 >>> res.dof 2 >>> res.expected_freq array([[ 12., 12., 16.], [ 18., 18., 24.]]) Perform the test using the log-likelihood ratio (i.e. the "G-test") instead of Pearson's chi-squared statistic. >>> res = chi2_contingency(obs, lambda_="log-likelihood") >>> res.statistic 2.7688587616781319 >>> res.pvalue 0.25046668010954165 A four-way example (2 x 2 x 2 x 2): >>> obs = np.array( ... [[[[12, 17], ... [11, 16]], ... [[11, 12], ... [15, 16]]], ... [[[23, 15], ... [30, 22]], ... [[14, 17], ... [15, 16]]]]) >>> res = chi2_contingency(obs) >>> res.statistic 8.7584514426741897 >>> res.pvalue 0.64417725029295503 When the sum of the elements in a two-way table is small, the p-value produced by the default asymptotic approximation may be inaccurate. Consider passing a `PermutationMethod` or `MonteCarloMethod` as the `method` parameter with `correction=False`. >>> from scipy.stats import PermutationMethod >>> obs = np.asarray([[12, 3], ... [17, 16]]) >>> res = chi2_contingency(obs, correction=False) >>> ref = chi2_contingency(obs, correction=False, method=PermutationMethod()) >>> res.pvalue, ref.pvalue (0.0614122539870913, 0.1074) # may vary For a more detailed example, see :ref:`hypothesis_chi2_contingency`. rz-All values in `observed` must be nonnegative.zNo data; `observed` has size 0.zLThe internally computed table of expected frequencies has a zero element at .Nrgg?g?)ddofaxislambda_)rr!any ValueErrorsizer rzipnonzero_chi2_resampling_methodsrshapersignminimumabsrr() r$ correctionr1r,r&zeroposr+chi2pdiff direction magnitudes rrrsuPzz(#H vvhlHII}}:;;X&H vvh!msBJJx1}567:>>EYaIJ J'JQWXX --#hnn- - = AC ax  !8 &D I 3t 5Ii"77H"8(0 (9C(?d+24 !# 88r'cURS:wa Sn[U5eU(aSU<SU<S3n[U5eUbSU<SU<S3n[U5e[U[R5(a [ XU5nO>[U[R 5(a [XU5nOSU<S3n[U5e[URUR[RU5$) Nz7Use of `method` is only compatible with two-way tables.z `correction=z!` is not compatible with `method=z.`z `lambda_=z`method=zi` not recognized; if provided, `method` must be an instance of `PermutationMethod` or `MonteCarloMethod`.) rr3 isinstancer PermutationMethod_chi2_permutation_methodMonteCarloMethod_chi2_monte_carlo_methodr(r)r*rnan)r$r&r<r1r,messageress rr7r7cs}}K!!!j]"DVIRH!!gZA&"E!!&%1122&x6B FE22 3 3&x6Bvi LL!!  BFFH MMr'c^^[U5unmUU4Sjn[R"U4U4SSS.UR5D6$)Nc`>[UT5Sn[R"UT- S-T- 5$)NrrD)rrr)xtabler&ys rr)+_chi2_permutation_method..statistics1Aq!vvux'!+H455r'pairingsgreater)permutation_type alternative)rr permutation_test_asdict)r$r&r,rOr)rQs ` @rrGrG}sN x DAq6  ! !1$  MJ.7 M;A>>;K MMr'c^^ UR5nURSS5b Sn[U5e[RR URSS55n[ RRU5upV[ R"UR5UR5US9m U 4SjnTR5mU4Sjn[ R"UR5Xx4SS0UD6$) NrvszIf the `method` argument of `chi2_contingency` is an instance of `MonteCarloMethod`, its `rvs` attribute must be unspecified. Use the `MonteCarloMethod` `rng` argument to control the random state.rng)seedcJ>USnTRUS9RU5$)Nr)r4)rZreshape)r4 n_resamplesXs rrZ%_chi2_monte_carlo_method..rvss(1g uu+u&..t44r'c@>[R"UT- S-T- US9$)NrD)r0)rr)rPr0r&s rr)+_chi2_monte_carlo_method..statistics#vvux'!+H44@@r'rVrT) rXpopr3rrandom default_rngr contingencyr random_tableravelmonte_carlo_test) r$r&r,rKr[rowsumscolsumsrZr)r`s ` @rrIrIs ^^ F zz%*2!! ))   5$ 7 8C((00:G 7==?GMMO#FA5~~HA  ! !(.."2C C.7 C;A CCr'cH[R"U5n[R"UR[R5(d [ S5e[ UR5S:wa [ S5e[XBUS9nURUR5- nURupxUS:XaU[US- US- 5- n OCUS:Xa#U[R"US- US- -5- n OUS:Xa USU-- n O [ S 5e[R"U 5$) a6 Calculates degree of association between two nominal variables. The function provides the option for computing one of three measures of association between two nominal variables from the data given in a 2d contingency table: Tschuprow's T, Pearson's Contingency Coefficient and Cramer's V. Parameters ---------- observed : array-like The array of observed values method : {"cramer", "tschuprow", "pearson"} (default = "cramer") The association test statistic. correction : bool, optional Inherited from `scipy.stats.contingency.chi2_contingency()` lambda_ : float or str, optional Inherited from `scipy.stats.contingency.chi2_contingency()` Returns ------- statistic : float Value of the test statistic Notes ----- Cramer's V, Tschuprow's T and Pearson's Contingency Coefficient, all measure the degree to which two nominal or ordinal variables are related, or the level of their association. This differs from correlation, although many often mistakenly consider them equivalent. Correlation measures in what way two variables are related, whereas, association measures how related the variables are. As such, association does not subsume independent variables, and is rather a test of independence. A value of 1.0 indicates perfect association, and 0.0 means the variables have no association. Both the Cramer's V and Tschuprow's T are extensions of the phi coefficient. Moreover, due to the close relationship between the Cramer's V and Tschuprow's T the returned values can often be similar or even equivalent. They are likely to diverge more as the array shape diverges from a 2x2. References ---------- .. [1] "Tschuprow's T", https://en.wikipedia.org/wiki/Tschuprow's_T .. [2] Tschuprow, A. A. (1939) Principles of the Mathematical Theory of Correlation; translated by M. Kantorowitsch. W. Hodge & Co. .. [3] "Cramer's V", https://en.wikipedia.org/wiki/Cramer's_V .. [4] "Nominal Association: Phi and Cramer's V", http://www.people.vcu.edu/~pdattalo/702SuppRead/MeasAssoc/NominalAssoc.html .. [5] Gingrich, Paul, "Association Between Variables", http://uregina.ca/~gingrich/ch11a.pdf Examples -------- An example with a 4x2 contingency table: >>> import numpy as np >>> from scipy.stats.contingency import association >>> obs4x2 = np.array([[100, 150], [203, 322], [420, 700], [320, 210]]) Pearson's contingency coefficient >>> association(obs4x2, method="pearson") 0.18303298140595667 Cramer's V >>> association(obs4x2, method="cramer") 0.18617813077483678 Tschuprow's T >>> association(obs4x2, method="tschuprow") 0.14146478765062995 z$`observed` must be an integer array.rDzmethod only accepts 2d arrays)r<r1cramerr tschuprowpearsonzUInvalid argument value: 'method' argument must be 'cramer', 'tschuprow', or 'pearson')rr! issubdtyper integerr3lenr8rr)rminmathsqrt) r$r,r<r1arr chi2_statphi2n_rowsn_colsvalues rrrs \ **X C ==BJJ / /?@@ 399~899 )02I    *DYYNF s6A:vz22 ; tyy&1*!!<== 9 D!BC C 99U r')TN)rnFN)__doc__ functoolsrrunumpyr _stats_pyrr_relative_riskr _crosstabr _odds_ratior scipy._lib._bunchr scipyr __all__r r r(rr7rGrIrr'rrsv. 4)#/ 91h-`*3R O9O9dN4 MC6dr'