M/PhŬdZddlZddlZddlZddlmZddlm Z ddl m Z ddl m Z dZGdd ZGd d ZGd d eZGddeZGddZddZddZdS)a Methods for analyzing two-way contingency tables (i.e. frequency tables for observations that are cross-classified with respect to two categorical variables). The main classes are: * Table : implements methods that can be applied to any two-way contingency table. * SquareTable : implements methods that can be applied to a square two-way contingency table. * Table2x2 : implements methods that can be applied to a 2x2 contingency table. * StratifiedTable : implements methods that can be applied to a collection of 2x2 contingency tables. Also contains functions for conducting McNemar's test and Cochran's q test. Note that the inference procedures may depend on how the data were sampled. In general the observed units are independent and identically distributed. N)stats)iolib) sm_exceptions)cache_readonlyctt|tjs|S|j|jsbt t|jt|jz}|| ||d}| |j}|S)z Reindex a pandas DataFrame so that it becomes square, meaning that the row and column indices contain the same values, in the same order. The row and column index are extended to achieve this. r)indexcolumns fill_value) isinstancepd DataFramerequalsr listsetsortreindex)tableixs d/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/stats/contingency_tables.py_make_df_squarer's eR\ * *  ;  em , ,B #ek""S%7%77 8 8   Bq AA MM%- ( (E LceZdZdZdZdS)_BunchcdS)Nz1selfs r__repr__z_Bunch.__repr__?sBBrcld|jD}|td|D}g}dt |zdz}|D]6}||||j|7d|S)Ncg|]\}}|Srr).0k_s r z"_Bunch.__str__..Cs 2 2 2DAqa 2 2 2rc,g|]}t|Sr)len)r!r"s rr$z"_Bunch.__str__..Es$$$AQ$$$rz{:z} {} )__dict__itemsrmaxstrappendformatjoin)rkymtabfr"s r__str__z_Bunch.__str__Bs 2 2DM//11 2 2 2  $$$$$ % % 3q66MH $ 6 6A JJqxx4=#344 5 5 5 5yy~~rN)__name__ __module__ __qualname__rr3rrrrr=s5CCCrrc"eZdZdZddZdZeddZdZddZ e d Z e d Z e d Z e d Ze d Ze dZe dZe dZe dZe dZdS)Tablea0 A two-way contingency table. Parameters ---------- table : array_like A contingency table. shift_zeros : bool If True and any cell count is zero, add 0.5 to all values in the table. Attributes ---------- table_orig : array_like The original table is cached as `table_orig`. See Also -------- statsmodels.graphics.mosaicplot.mosaic scipy.stats.chi2_contingency Notes ----- The inference procedures used here are all based on a sampling model in which the units are independent and identically distributed, with each unit being classified with respect to two categorical variables. References ---------- Definitions of residuals: https://onlinecourses.science.psu.edu/stat504/node/86 Tc||_tj|tj|_|r2|jdkrd|j|jdk<dSdSdS)Ndtyper?) table_orignpasarrayfloat64rmin)rr shift_zeross r__init__zTable.__init__psgZRZ888  .DJNN,,11*-DJtzQ ' ' ' . .11rcvdt|jjz}|tj|jz }|S)Nz'A %dx%d contingency table with counts: )tuplershaper> array_str)rss rr3z Table.__str__xs7 7 4:# $ $% R\$* % %%rct|tjr4tj|jdddf|jdddf}n)tj|dddf|dddf}|||S)a Construct a Table object from data. Parameters ---------- data : array_like The raw data, from which a contingency table is constructed using the first two columns. shift_zeros : bool If True and any cell count is zero, add 0.5 to all values in the table. Returns ------- A Table instance. Nrr r r crosstabilocclsdatarBrs r from_datazTable.from_data~s& dBL ) ) 8K !!!Q$111a4AAEEKQQQT DAJ77Es5+&&&rcNtj|j}tjtj|jjdz }dtj ||z }t}||_ ||_ ||_ |S)a Assess independence for nominal factors. Assessment of independence between rows and columns using chi^2 testing. The rows and columns are treated as nominal (unordered) categorical variables. Returns ------- A bunch containing the following attributes: statistic : float The chi^2 test statistic. df : int The degrees of freedom of the reference distribution pvalue : float The p-value for the test. rJ)r>r? chi2_contribssumprodrrFrchi2cdfr statisticdfpvalue)rrXrYrZbs rtest_nominal_associationzTable.test_nominal_associations(Jt1226688 WRZ 011A5 6 6UZ^^Ir222 HH rNcd|$tj|jjd}|$tj|jjd}t ||jjdkrd}t |t ||jjdkrd}t |tj|tj|j|}|j}|jd}tj||}tj|dz|}|jd} tj|| } tj|dz| } || z|z } ||dz|z z | | dz|z z z|dz z } tj| }|| z |z }dtj tj | z}t}||_| |_||_||_||_|S)ar Assess independence between two ordinal variables. This is the 'linear by linear' association test, which uses weights or scores to target the test to have more power against ordered alternatives. Parameters ---------- row_scores : array_like An array of numeric row scores col_scores : array_like An array of numeric column scores Returns ------- A bunch with the following attributes: statistic : float The test statistic. null_mean : float The expected value of the test statistic under the null hypothesis. null_sd : float The standard deviation of the test statistic under the null hypothesis. zscore : float The Z-score for the test statistic. pvalue : float The p-value for the test. Notes ----- The scores define the trend to which the test is most sensitive. Using the default row and column scores gives the Cochran-Armitage trend test. NrrJzEThe length of `row_scores` must match the first dimension of `table`.zFThe length of `col_scores` must match the second dimension of `table`.)r>arangerrFr& ValueErrordotrTsqrtrnormrWabsrrX null_meannull_sdzscorerZ)r row_scores col_scoresmsgrXn_obsrtotumu2mctotvnv2ne_statv_statsd_statrgrZr[s rtest_ordinal_associationzTable.test_ordinal_associationsP  4:#3A#677J  4:#3A#677J z??dj.q1 1 1+CS// ! z??dj.q1 1 1+CS// !F:rvdj*'E'EFF    z~~a   VJ % %fZ]D))z~~a   VJ % %fZ]D))b5A %#A *=>%!)L'&//f$/UZ^^RVF^^O444 HH   rcj|j}|jd|z }|jd|z }t|jtjr>t j||jj}t j||jj}||fS)z Estimate marginal probability distributions for the rows and columns. Returns ------- row : ndarray Marginal row probabilities col : ndarray Marginal column probabilities rJr) rrTr r=r r Seriesrr )rnrowcols rmarginal_probabilitieszTable.marginal_probabilities s JNN  jnnQ!#jnnQ!# dor| 4 4 :)C!677C)C!899CCxrc|j\}}tj||}t|jt jr*t j||jj|jj}|S)z Returns fitted joint probabilities under independence. The returned table is outer(row, column), where row and column are the estimated marginal distributions of the rows and columns. ) r{r>outerr r=r r rr )rryrzitabs rindependence_probabilitiesz Table.independence_probabilities s`.SxS!! dor| 4 4 9<do&; $ 799D rcL|j}|j|z}|S)z Returns fitted cell counts under independence. The returned cell counts are estimates under a model where the rows and columns of the table are independent. )rrrT)rprobsfits r fittedvalueszTable.fittedvalues3s'/jnn& rcR|j}|j|z tj|z }|S)z Returns Pearson residuals. The Pearson residuals are calculated under a model where the rows and columns of the table are independent. )rrr>rb)rrresidss r resid_pearsonzTable.resid_pearson@s**s"bgcll2 rc|j\}}|jtjtjd|z d|z z }|S)zD Returns standardized residuals under independence. rJ)r{rr>rbr})rryrzsresidss rstandardized_residszTable.standardized_residsMs@ .S$rwrxCS/I/I'J'JJrc|jdzS)a Returns the contributions to the chi^2 statistic for independence. The returned table contains the contribution of each cell to the chi^2 test statistic for the null hypothesis that the rows and columns are independent. r^)rrs rrSzTable.chi2_contribsWs!1$$rch|j}|ddddf}|ddddf}|ddddf}|ddddf}tj|tj|ztj|z tj|z }tj|jjtj}|tjz}||ddddf<t|j tj r+tj ||j j |j j }|S)z Returns local log odds ratios. The local log odds ratios are the log odds ratios calculated for contiguous 2x2 sub-tables. rrJNrr )rcopyr>logemptyrFr@nanr r=r r rr rtaar[cdr1rslts rlocal_log_oddsratioszTable.local_log_oddsratioscsZ__   qtQrTzN qtQRRxL qrr1R4xL qrr122vJfQii"&))#bfQii/"&));x ("*55 QrT1R4Z dor| 4 4 A<DO,A(,(?AAAD rc4tj|jS)za Returns local odds ratios. See documentation for local_log_oddsratios. )r>exprrs rlocal_oddsratioszTable.local_oddsratios|svd/000rc|jdd}|ddddf}|ddddf|z }|ddddf|z }|d||z|zz }tj|tj|ztj|z tj|z }tj|jjtj}|tjz}||ddddf<t|j tj r+tj ||j j |j j }|S)aP Returns cumulative log odds ratios. The cumulative log odds ratios for a contingency table with ordered rows and columns are calculated by collapsing all cells to the left/right and above/below a given point, to obtain a 2x2 table from which a log odds ratio can be calculated. rrJrN)rrr)rcumsumr>rrrFr@rr r=r r rr rs rcumulative_log_oddsratioszTable.cumulative_log_oddsratioss;Z  q ! ! ( ( + + qtQrTzN qtRSSyMA  rssAbDyMA  vJ!a%!) $fQii"&))#bfQii/"&));x ("*55 QrT1R4Z dor| 4 4 A<DO,A(,(?AAAD rc4tj|jS)z Returns the cumulative odds ratios for a contingency table. See documentation for cumulative_log_oddsratio. )r>rrrs rcumulative_oddsratioszTable.cumulative_oddsratiossvd4555rT)NN)r4r5r6__doc__rCr3 classmethodrQr\rurr{rrrrrSrrrrrrrr8r8Ms  D.... '''['2:RRRRh^,^$  ^   ^ ^ % %^ %^011^1^:66^666rr8c<eZdZdZd fd Zd dZd dZdd ZxZS) SquareTablea Methods for analyzing a square contingency table. Parameters ---------- table : array_like A square contingency table, or DataFrame that is converted to a square form. shift_zeros : bool If True and any cell count is zero, add 0.5 to all values in the table. Notes ----- These methods should only be used when the rows and columns of the table have the same categories. If `table` is provided as a Pandas DataFrame, the row and column indices will be extended to create a square table, inserting zeros where a row or column is missing. Otherwise the table should be provided in a square form, with the (implicit) row and column categories appearing in the same order. Tct|}|j\}}||krtdt||dS)Nztable must be square)rrFr`superrC)rrrBk1k2 __class__s rrCzSquareTable.__init__sS&&B 88344 4  ,,,,,rbowkerc|dkrtd|jjd}t j|d}|jj|}|j|}||z dz||zdzz }||dz zdz }tj ||}t} || _ || _ || _| S)a Test for symmetry of a joint distribution. This procedure tests the null hypothesis that the joint distribution is symmetric around the main diagonal, that is .. math:: p_{i, j} = p_{j, i} for all i, j Returns ------- Bunch A bunch with attributes * statistic : float chisquare test statistic * p-value : float p-value of the test statistic based on chisquare distribution * df : int degrees of freedom of the chisquare distribution Notes ----- The implementation is based on the SAS documentation. R includes it in `mcnemar.test` if the table is not 2 by 2. However a more direct generalization of the McNemar test to larger tables is provided by the homogeneity test (TableSymmetry.homogeneity). The p-value is based on the chi-square distribution which requires that the sample size is not very small to be a good approximation of the true distribution. For 2x2 contingency tables the exact distribution can be obtained with `mcnemar` See Also -------- mcnemar homogeneity rz,method for symmetry testing must be 'bowker'rrJr^g#B ;g@)lowerr`rrFr> triu_indicesTrTrrVsfrrXrZrY) rmethodr"upp_idxtriltriurXrYrZr[s rsymmetryzSquareTable.symmetrysR <<>>X % %KLL L J Q /!Q''z|G$z'"TkA%u)<=BBDD !A#Y^y"-- HH rstuart_maxwellct|jjddkrtd|jjddkr%t}d|_d|_d|_|S|}|dvrtd|z|j}|j tj |z }|ddd}|ddd}|ddddf}||z }|jd}|dkrZ||j z tj ||z } ||zdtj|zz |dzz } tj| | nC|d kr=||j z } ||zdtj|zz } tj| |  |tj|tj| |z} nr#tjj$r[t)jd t,jt}tj|_tj|_||_|cYSwxYwdt2j| |z } t}| |_| |_||_|S) a( Compare row and column marginal distributions. Parameters ---------- method : str Either 'stuart_maxwell' or 'bhapkar', leading to two different estimates of the covariance matrix for the estimated difference between the row margins and the column margins. Returns ------- Bunch A bunch with attributes: * statistic : float The chi^2 test statistic * pvalue : float The p-value of the test statistic * df : int The degrees of freedom of the reference distribution Notes ----- For a 2x2 table this is equivalent to McNemar's test. More generally the procedure tests the null hypothesis that the marginal distribution of the row factor is equal to the marginal distribution of the column factor. For this to be meaningful, the two factors must have the same sample space (i.e. the same categories). rrJztable is empty)bhapkarrz%method '%s' for homogeneity not knownrrr^rz"Unable to invert covariance matrix)rrFr`rrXrZrYrrTastyper>r@rr}diag fill_diagonalralinalgsolve LinAlgErrorwarningswarnrSingularMatrixWarningrrrVrW) rrr[rkprryrzrrYvmatdvrXrZs r homogeneityzSquareTable.homogeneity sB : A  " "-.. . Z a A % %AAKAHADH 6 6 6DvMNN N    Z  rz * *U 2ffQii"offQii"o "ad ^ #IXa[ Y  "$Y<"(1a..0DsQrwr{{]*QT1B  T2 & & & & ' ' '"$Y'= ? ? ?A&AKvAHADHHH UZ^^Ir222 HH s 6HA,I/.I/皙?%.3fc|}gd}ddg}|}|}||jz||jzd|jzg||jz||jzd|jzgg}t j|||dd} | S)a Produce a summary of the analysis. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the interval. float_format : str Used to format numeric values in the table. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. ) StatisticP-valueDFSymmetry Homogeneity%dr data_alignstable_dec_above)rrrXrZrYr SimpleTable) ralpha float_formatfmtheadersstubssyhmrPr1s rsummaryzSquareTable.summaryfs000]+ ]]__     r|#S29_dRUlCr|#S29_dRUlCEgu#02444 rr)r)r)rr) r4r5r6rrCrrr __classcell__rs@rrrs.------;;;;zXXXXtrrceZdZdZdfd ZeddZedZedZ edZ dd Z dd Z ddZ ddZedZedZedZddZddZddZddZddZxZS)Table2x2a  Analyses that can be performed on a 2x2 contingency table. Parameters ---------- table : array_like A 2x2 contingency table shift_zeros : bool If true, 0.5 is added to all cells of the table if any cell is equal to zero. Notes ----- The inference procedures used here are all based on a sampling model in which the units are independent and identically distributed, with each unit being classified with respect to two categorical variables. Note that for the risk ratio, the analysis is not symmetric with respect to the rows and columns of the contingency table. The two rows define population subgroups, column 0 is the number of 'events', and column 1 is the number of 'non-events'. Tct|turtj|}|jdks"|jddks|jddkrt dt||dS)Nr^rrJz$Table2x2 takes a 2x2 table as input.) typerr>r?ndimrFr`rrC)rrrBrs rrCzTable2x2.__init__s} ;;$  Ju%%E J!OOQ1!4!4%+a.A:M:MCDD D  ,,,,,rct|tjr4tj|jdddf|jdddf}n)tj|dddf|dddf}|||S)a Construct a Table object from data. Parameters ---------- data : array_like The raw data, the first column defines the rows and the second column defines the columns. shift_zeros : bool If True, and if there are any zeros in the contingency table, add 0.5 to all four cells of the table. NrrJrKrNs rrQzTable2x2.from_datas dBL ) ) 8K !!!Q$111a4AAEEKQQQT DAJ77Es5+&&&rc|j}tjtj|tjdS)z= Returns the log odds ratio for a 2x2 table. )rJrrrJ)rflattenr>rarr_)rr2s r log_oddsratiozTable2x2.log_oddsratios8 J   vbfQii|!4555rcp|jd|jdz|jd|jdzz S)z9 Returns the odds ratio for a 2x2 table. )rr)rJrJrrJrJr)rrs r oddsratiozTable2x2.oddsratios:  4 4:d#33D!DJt$446 7rc^tjtjd|jz S)zD Returns the standard error for the log odds ratio. rJ)r>rbrTrrs rlog_oddsratio_sezTable2x2.log_oddsratio_ses$ wrva$*n--...rrJcP|tj|S)z P-value for a hypothesis test about the odds ratio. Parameters ---------- null : float The null value of the odds ratio. )log_oddsratio_pvaluer>rrnulls roddsratio_pvaluezTable2x2.oddsratio_pvalue ((666rrc|j|z |jz }dtjt j| z}|S)z P-value for a hypothesis test about the log odds ratio. Parameters ---------- null : float The null value of the log odds ratio. r^)rrrrcrWr>rdrrrgrZs rrzTable2x2.log_oddsratio_pvalue@$t+t/DDUZ^^RVF^^O444 rrnormalctj|dz  }|j}|j}|||zz }|||zz}||fS)a} A confidence level for the log odds ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. r^)rrcppfrr)rrrr2lorselcbucbs rlog_oddsratio_confintzTable2x2.log_oddsratio_confintsQZ^^EAI & & &   "AFlAFlCxrc|||\}}tj|tj|fS)a| A confidence interval for the odds ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. r)rr>rrrrrrs roddsratio_confintzTable2x2.oddsratio_confint;--eF-CCSvc{{BF3KK''rc||jdddf|jdz }|d|dz S)zy Returns the risk ratio for a 2x2 table. The risk ratio is calculated with respect to the rows. NrrJ)rrT)rps r riskratiozTable2x2.riskratios= Jqqq!t tz~~a00 0tad{rc4tj|jS)z4 Returns the log of the risk ratio. )r>rrrs r log_riskratiozTable2x2.log_riskratios vdn%%%rc|jd}|jdddf|z }tjd|z ||zz }tj|S)zJ Returns the standard error of the log of the risk ratio. rJNr)rrTr>rb)rrxrvas rlog_riskratio_sezTable2x2.log_riskratio_se'sY JNN1   Jqqq!t q  VQUqsO $ $wr{{rcP|tj|S)z p-value for a hypothesis test about the risk ratio. Parameters ---------- null : float The null value of the risk ratio. )log_riskratio_pvaluer>rrs rriskratio_pvaluezTable2x2.riskratio_pvalue2rrc|j|z |jz }dtjt j| z}|S)z p-value for a hypothesis test about the log risk ratio. Parameters ---------- null : float The null value of the log risk ratio. r^)r r rrcrWr>rdrs rrzTable2x2.log_riskratio_pvalue>rrctj|dz  }|j}|j}|||zz }|||zz}||fS)a A confidence interval for the log risk ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. r^)rrcrr r )rrrr2lrrrrrs rlog_riskratio_confintzTable2x2.log_riskratio_confintLsQZ^^EAI & & &   "AFlAFlCxrc|||\}}tj|tj|fS)a| A confidence interval for the risk ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. r)rr>rrs rriskratio_confintzTable2x2.riskratio_confint`rrrc ~fdgd}gd}|||\}}|||\}} |||\} } |||\} } fd|jd|||fDfd|j|j|| |fDfd|jd| | | fDfd|j |j | | | fDg}tj |||d d }|S) a Summarizes results for a 2x2 table analysis. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence intervals. float_format : str Used to format the numeric values in the table. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. c<t|tr|S|zSNr r+xrs rrzTable2x2.summary..fmt%!S!! !# #r)EstimateSELCBUCBzp-value)z Odds ratiozLog odds ratioz Risk ratiozLog risk ratioc&g|] }|Srrr!rrs rr$z$Table2x2.summary..-<<.3HHHAQHHHrc&g|] }|Srrr"s rr$z$Table2x2.summary..r#rc&g|] }|Srrr"s rr$z$Table2x2.summary..r%rrr)rrrrrrrrrrr r rr)rrrrrrlcb1ucb1lcb2ucb2lcb3ucb3lcb4ucb4rPr1rs ` @rrzTable2x2.summaryps  $ $ $ $ $ >==###++E6:: d//v>> d++E6:: d//v>> d<<<<$."dD"&"7"7"9"9";<<<HHHH$"4d6K"&d.C.C.E.E"GHHH<<<<$."dD"&"7"7"9"9";<<<HHHH$"4d6K"&d.C.C.E.E"GHHH Igu#02444 rr)rJ)rrrrrr)r4r5r6rrCrrQrrrrrrrrrr r rrrrrrrs@rrrs0------'''['(66^677^7//^/ 7 7 7 7    *(((( ^&&^&^ 7 7 7 7    ((((( ''''''''rrceZdZdZddZedZddZedZ edZ edZ ed Z dd Z dd ZddZddZdS)StratifiedTablea Analyses for a collection of 2x2 contingency tables. Such a collection may arise by stratifying a single 2x2 table with respect to another factor. This class implements the 'Cochran-Mantel-Haenszel' and 'Breslow-Day' procedures for analyzing collections of 2x2 contingency tables. Parameters ---------- tables : list or ndarray Either a list containing several 2x2 contingency tables, or a 2x2xk ndarray in which each slice along the third axis is a 2x2 contingency table. Notes ----- This results are based on a sampling model in which the units are independent both within and between strata. Fct|tjrG|j}t |dks|ddks |ddkrt d|dz}n[t d|Drd}t |tj|tj }|r|dk d d}tj |dk}t |dkr+| }|dddd|fxxd z cc<||_ i|_|ddddf|ddddfz|_|ddddf|ddddfz|_|ddddf|ddddfz|_|ddddf|ddddfz|_|ddddf|ddddfz|_|ddddf|ddddfz|_|ddddf|ddddfz|_|ddddf|ddddfz |_| d d|_dS) Nrr^rJz%If an ndarray, argument must be 2x2xn?cHg|]}tj|jdk S)r^r^)r>r?rF)r!rs rr$z,StratifiedTable.__init__..s(BBBaBJqMM'61BBBrz8If `tables` is a list, all of its elements should be 2x2r<)r r>ndarrayrFr&r`anydstackrr@rT flatnonzerorr_cache_apb_apc_bpd_cpd_ad_bc_apd_dma_n)rtablesrBsprr0zxrs rrCzStratifiedTable.__init__s fbj ) ) 9BB1 "Q%1**"Q%1** !HIIIRKEEBB6BBBCC $N mm#If%%,,RZ88E  '1*!!!$$((++BQ''B2ww{{ aaaBh3&  !Q'NU1a7^3 !Q'NU1a7^3 !Q'NU1a7^3 !Q'NU1a7^3 Aqqq>E!Q'N2Aqqq>E!Q'N2!Q'NU1a7^3 !Q'NU1a7^3 ))A,,""1%%rct|tjstjtj|jd|||g}|dd|f||j|<|dd|f||j|<|dd|f||j|<n ||||g}||j}g}|D]}||} tj |j | |f|j | |f} | jtj dk rd} t| |tj| ||S)ad Construct a StratifiedTable object from data. Parameters ---------- var1 : int or string The column index or name of `data` specifying the variable defining the rows of the contingency table. The variable must have only two distinct values. var2 : int or string The column index or name of `data` specifying the variable defining the columns of the contingency table. The variable must have only two distinct values. strata : int or string The column index or name of `data` specifying the variable defining the strata. data : array_like The raw data. A cross-table for analysis is constructed from the first two columns. Returns ------- StratifiedTable rrNr8zInvalid table dimensions)r r r r>r_rFr groupbygroupsrLlocrr:r`r,r?) rOvar1var2stratarPdata1gbrGgiir1rjs rrQzStratifiedTable.from_datasj6$ -- /LryA'?'?*.f)=???E)-aaagE%-% &)-aaagE%-% &+/6 ?E%-' ( ($f-.E ]]6 " " ) + +AAB+eiD159RX3FGGC RU4[(--// &0 oo% MM"*S// * * * *s6{{rctj|jddddf|j|jz|jz z }tj|}|r|dz}|dz}|j|jz|jz|jz}||jdz|jdz zz}tj|}||z}dtj |dz }t}||_ ||_|S)a Test that all tables have odds ratio equal to 1. This is the 'Mantel-Haenszel' test. Parameters ---------- correction : bool If True, use the continuity correction when calculating the test statistic. Returns ------- Bunch A bunch containing the chi^2 test statistic and p-value. rNr<r^rJ)r>rTrr>r?rFrdr@rArrVrWrrXrZ)r correctionrXdenomrZr[s rtest_null_oddszStratifiedTable.test_null_oddss$F4:aAAAg.9ty047:;<< F9%%    IqL  DI% 1DI= $'1*! ,-u U UZ^^Iq111 HH rctj|j|jz tj|j|jz z }|S)z The pooled odds ratio. The value is an estimate of a common odds ratio across all of the stratified tables. )r>rTrBrFrC)r odds_ratios roddsratio_pooledz StratifiedTable.oddsratio_pooled-s:VDHtw.//"&DG9K2L2LL rc4tj|jS)zu Returns the logarithm of the pooled odds ratio. See oddsratio_pooled for more information. )r>rr[rs rlogodds_pooledzStratifiedTable.logodds_pooled8svd+,,,rc|jddddf|jz}|jddddf|jz}tj||jz tj||jz z }|S)z4 Estimate of the pooled risk ratio. rNrJ)rrAr>r>rTrF)racdcabrrs rriskratio_pooledz StratifiedTable.riskratio_pooledAsm jAqqq!DI-jAqqq!DI- VC$'M " "RVC$'M%:%: : rcZtj|j|jz }tj|j|jz }tj|j|jz|jdzz |dzz }|j|jz|jdzz }|d|j|jz z |jz|jz z }tj|}|||zz}||z }|tjd|j|jz z |jz|jz |dzz z }|dz}tj|}|S)a> Estimated standard error of the pooled log odds ratio References ---------- J. Robins, N. Breslow, S. Greenland. "Estimators of the Mantel-Haenszel Variance Consistent in Both Sparse Data and Large-Strata Limiting Models." Biometrics 42, no. 2 (1986): 311-23. r^rJ)r>rTrBrFrCrDrb)radnsbcnslor_vamidlor_ses rlogodds_pooled_sez!StratifiedTable.logodds_pooled_seMs&vdh())vdh()) DH,twz9::T1WDi$("TWaZ/ DI''483dg==fSkk t # "&!di$'11"$(G,--/3Qw7 7!  rrrctj|j}|j}tj|dz  }|||zz }|||zz}||fS)a A confidence interval for the pooled log odds ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. Returns ------- lcb : float The lower confidence limit. ucb : float The upper confidence limit. r^)r>rr[rirrcr)rrrrrhr2rrs rlogodds_pooled_confintz&StratifiedTable.logodds_pooled_confintgs]*fT*++' Z^^EAI & & &AJAJCxrc|||\}}tj|}tj|}||fS)a A confidence interval for the pooled odds ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. Returns ------- lcb : float The lower confidence limit. ucb : float The upper confidence limit. r)rkr>rrs roddsratio_pooled_confintz(StratifiedTable.oddsratio_pooled_confintsC*..uV.DDSfSkkfSkkCxrc|j}|j}d|z }||j|jzz|jz}| |jz|jz}t j|dzd|z|zz }| |zd|zz }d|z d|j|z z zd|j|z z zd|j|zz z} d| z } t j|ddddf|z dz| z } |rU|ddddf|z } | dz} | t j| z} | | z} dtj | |j ddz z } t}| |_ | |_|S)a Test that all odds ratios are identical. This is the 'Breslow-Day' testing procedure. Parameters ---------- adjust : bool Use the 'Tarone' adjustment to achieve the chi^2 asymptotic distribution. Returns ------- A bunch containing the following attributes: statistic : float The chi^2 test statistic. p-value : float The p-value for the test. rJr^rN)rr[r>r?rEr>rbrTrrVrWrFrrXrZ) radjustrrrr[rdre11v11rXadjrZs rtest_equal_oddszStratifiedTable.test_equal_oddss,   ! E TY& '$) 3 BNTY &WQTAaCE\ " "rBw1Q33wdi#o..di#o1FFDIO$%#gFE!Q'NS014s:;;  1aaa.$$&&2Cq&C 26#;; C  IUZ^^Iu{1~/ABBB HH rrcfd|||\}}|||\}}gd}gd} fd|j||fDfd|j||fDfd|jddfDgd g} t j| || d d } gd }d dg} |} |} fd| j | j dfDfd| j | j dfDg} t j| || d }| |gd }gd} |j d d}d|j jdzddgdt|zddgdt!|zddgdt#j|zddgdt|zdddgg} t j| || d }| || S)a A summary of all the main results. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence intervals. float_format : str Used for formatting numeric values in the summary. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. c<t|tr|S|zSrrrs rrz$StratifiedTable.summary..fmtrr)rr)rrr )z Pooled oddszPooled log oddszPooled risk ratiorc&g|] }|Srrr"s rr$z+StratifiedTable.summary..!IIIAQIIIrc&g|] }|Srrr"s rr$z+StratifiedTable.summary..ryrc&g|] }|Srrr"s rr$z+StratifiedTable.summary..s!AAAAQAAArr)rrrrr)rrrz Test of OR=1zTest constant ORc&g|] }|Srrr"s rr$z+StratifiedTable.summary..!EEEAQEEErc&g|] }|Srrr"s rr$z+StratifiedTable.summary..r}r)r)zNumber of tableszMin nzMax nzAvg nzTotal nrrr^z%.0f)rmrkr[r]rbrrrXrurXrZextendrrTrFrAr*r>mean)rrrrco_lcbco_ucbclo_lcbclo_ucbrrrPtab1rslt1rslt2tab2sstab3rs ` @rrzStratifiedTable.summarys  $ $ $ $ $ 667((667((,,,KKKIIII$"7!HIIIIIII$"5w!HIIIAAAA$"7R!@AAA  w313555/..!34##%%$$&&EEEE%/5<!DEEEEEEE%/5<!DEEEG w3GGG D,,JJJ Z^^A   " "1 % % (++R4BR(BR("'"++%r2.BR, .  w3GGG D rN)Fr0r1)r4r5r6rrCrrQrXrr[r]rbrirkrmrurrrrr3r3s!*%&%&%&%&N--[-^$$$$L^--^-  ^ ^2>44444l666666rr3Tc`t|}tj|tj}|d|d}}|rytj||}t ||z}|||zkrt dtj ||ddz}tj|d}nWt |}tj ||z |z dzd||zzz }d} tj || }t} || _|| _| S) a McNemar test of homogeneity. Parameters ---------- table : array_like A square contingency table. exact : bool If exact is true, then the binomial distribution will be used. If exact is false, then the chisquare distribution will be used, which is the approximation to the distribution of the test statistic for large sample sizes. correction : bool If true, then a continuity correction is used for the chisquare distribution (if exact is false.) Returns ------- A bunch with attributes: statistic : float or int, array The test statistic is the chisquare statistic if exact is false. If the exact binomial distribution is used, then this contains the min(n1, n2), where n1, n2 are cases that are zero in one sample but one in the other sample. pvalue : float or array p-value of the null hypothesis of equal marginal distributions. Notes ----- This is a special case of Cochran's Q test, and of the homogeneity test. The results when the chisquare distribution is used are identical, except for continuity correction. r:rrz7exact can only be used with tables containing integers.r<r^rJr6)rr>r?r@minimumintr`rbinomrWrdrVrrrXrZ) rexactrVn1n2rXint_sumrZcorrrYr[s rmcnemarrs!H E " "E JuBJ / / /E 4[%+B .Jr2&& b2g,, rBw  I GS99A=FA&&:VBG__t+a/2b>B y"--AAKAH Hrctj|tj}tj|}|j\}}||dkdt }||dkdt }|}|}||ksJ|dz |tj|dzz|dzz z||ztj|dzz z } |dz } tj | | } |r%t} | | _ | | _ | | _ | S| | | fS)a Cochran's Q test for identical binomial proportions. Parameters ---------- x : array_like, 2d (N, k) data with N cases and k variables return_object : bool Return values as bunch instead of as individual values. Returns ------- Returns a bunch containing the following attributes, or the individual values according to the value of `return_object`. statistic : float test statistic pvalue : float pvalue from the chisquare distribution Notes ----- Cochran's Q is a k-sample extension of the McNemar test. If there are only two groups, then Cochran's Q test and the McNemar test are equivalent. The procedure tests that the probability of success is the same for every group. The alternative hypothesis is that at least two groups have a different probability of success. In Wikipedia terminology, rows are blocks and columns are treatments. The number of rows N, should be large for the chisquare distribution to be a good approximation. The Null hypothesis of the test is that all treatments have the same effect. References ---------- https://en.wikipedia.org/wiki/Cochran_test SAS Manual for NPAR TESTS r:rrJrr^)r>r?r@uniquerFrTfloatrrVrrrXrYrZ) r return_objectgruniNr"count_row_successcount_col_success count_row_ss count_col_ssq_statrYrZr[s r cochrans_qrNsKX 1BJ'''A IaLLE 7DAqeBi,,Q66eBi,,Q66$((**L$((**L < ' ' ' 'sq26"3Q"6777,/IJ\!BF+pandasr scipyr statsmodelsrstatsmodels.toolsrstatsmodels.tools.decoratorsrrrr8rrr3rrrrrrs6++++++777777,         _6_6_6_6_6_6_6_6D QQQQQ%QQQhTTTTT{TTTnrrrrrrrrj < < < < ~IIIIIIr