U Qv fB8@sTddlZddlZddlmZddlmZddlm Z ddgZ d d dZ d d dZ dS)N)f)options)_postprocess_dataframecronbach_alphaintraclass_corrpairwiseffffff?cs^ttjstd|dks ttdd|||fDrHj|||dj\}}|dksbtd|dksrtdd }tfd djDst| r|d krj d d dj dd} ||ddt | | } d|} |d} | |d} dd| t| d| | }dd| td| d| | }| t ||gdfS)aGCronbach's alpha reliability measure. Parameters ---------- data : :py:class:`pandas.DataFrame` Wide or long-format dataframe. items : str Column in ``data`` with the items names (long-format only). scores : str Column in ``data`` with the scores (long-format only). subject : str Column in ``data`` with the subject identifier (long-format only). nan_policy : bool If `'listwise'`, remove the entire rows that contain missing values (= listwise deletion). If `'pairwise'` (default), only pairwise missing values are removed when computing the covariance matrix. For more details, please refer to the :py:meth:`pandas.DataFrame.cov` method. ci : float Confidence interval (.95 = 95%) Returns ------- alpha : float Cronbach's alpha Notes ----- This function works with both wide and long format dataframe. If you pass a long-format dataframe, you must also pass the ``items``, ``scores`` and ``subj`` columns (in which case the data will be converted into wide format using the :py:meth:`pandas.DataFrame.pivot` method). Internal consistency is usually measured with Cronbach's alpha [1]_, a statistic calculated from the pairwise correlations between items. Internal consistency ranges between negative infinity and one. Coefficient alpha will be negative whenever there is greater within-subject variability than between-subject variability. Cronbach's :math:`\alpha` is defined as .. math:: \alpha ={k \over k-1}\left(1-{\sum_{{i=1}}^{k}\sigma_{{y_{i}}}^{2} \over\sigma_{x}^{2}}\right) where :math:`k` refers to the number of items, :math:`\sigma_{x}^{2}` is the variance of the observed total scores, and :math:`\sigma_{{y_{i}}}^{2}` the variance of component :math:`i` for the current sample of subjects. Another formula for Cronbach's :math:`\alpha` is .. math:: \alpha = \frac{k \times \bar c}{\bar v + (k - 1) \times \bar c} where :math:`\bar c` refers to the average of all covariances between items and :math:`\bar v` to the average variance of each item. 95% confidence intervals are calculated using Feldt's method [2]_: .. math:: c_L = 1 - (1 - \alpha) \cdot F_{(0.025, n-1, (n-1)(k-1))} c_U = 1 - (1 - \alpha) \cdot F_{(0.975, n-1, (n-1)(k-1))} where :math:`n` is the number of subjects and :math:`k` the number of items. Results have been tested against the `psych `_ R package. References ---------- .. [1] http://www.real-statistics.com/reliability/cronbachs-alpha/ .. [2] Feldt, Leonard S., Woodruff, David J., & Salih, Fathi A. (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11(1):93-103. Examples -------- Binary wide-format dataframe (with missing values) >>> import pingouin as pg >>> data = pg.read_dataset('cronbach_wide_missing') >>> # In R: psych:alpha(data, use="pairwise") >>> pg.cronbach_alpha(data=data) (0.732660835214447, array([0.435, 0.909])) After listwise deletion of missing values (remove the entire rows) >>> # In R: psych:alpha(data, use="complete.obs") >>> pg.cronbach_alpha(data=data, nan_policy='listwise') (0.8016949152542373, array([0.581, 0.933])) After imputing the missing values with the median of each column >>> pg.cronbach_alpha(data=data.fillna(data.median())) (0.7380191693290734, array([0.447, 0.911])) Likert-type long-format dataframe >>> data = pg.read_dataset('cronbach_alpha') >>> pg.cronbach_alpha(data=data, items='Items', scores='Scores', ... subject='Subj') (0.5917188485995826, array([0.195, 0.84 ])) data must be a dataframe.)rlistwisecSsg|] }|dk qSN.0vr r 8/tmp/pip-unpacked-wheel-2te3nxqf/pingouin/reliability.py sz"cronbach_alpha..)indexvaluescolumnsz At least two items are required.z*At least two raters/subjects are required.zAll columns must be numeric.csg|]}|jjdkqS)bfiu)dtypekind)rcdatar rrsr ranyZaxishowT)Z numeric_only) isinstancepd DataFrameAssertionErrorallZpivotshaperisnardropnaZcovnptracesumrZisfround)ritemsZscoressubject nan_policycinkerrCZcronbachalphadf1df2lowerupperr rrr s&r    & "raisec/ s>ddlm}ttjs tdtdd|||fDs`_ R package: - **ICC1**: Each target is rated by a different rater and the raters are selected at random. This is a one-way ANOVA fixed effects model. - **ICC2**: A random sample of :math:`k` raters rate each target. The measure is one of absolute agreement in the ratings. ICC1 is sensitive to differences in means between raters and is a measure of absolute agreement. - **ICC3**: A fixed set of :math:`k` raters rate each target. There is no generalization to a larger population of raters. ICC2 and ICC3 remove mean differences between raters, but are sensitive to interactions. The difference between ICC2 and ICC3 is whether raters are seen as fixed or random effects. Then, for each of these cases, the reliability can either be estimated for a single rating or for the average of :math:`k` ratings. The 1 rating case is equivalent to the average intercorrelation, while the :math:`k` rating case is equivalent to the Spearman Brown adjusted reliability. **ICC1k**, **ICC2k**, **ICC3K** reflect the means of :math:`k` raters. This function has been tested against the ICC function of the R psych package. Note however that contrarily to the R implementation, the current implementation does not use linear mixed effect but regular ANOVA, which means that it only works with complete-case data (no missing values). References ---------- .. [1] http://www.real-statistics.com/reliability/intraclass-correlation/ .. [2] Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: uses in assessing rater reliability. Psychological bulletin, 86(2), 420. Examples -------- ICCs of wine quality assessed by 4 judges. >>> import pingouin as pg >>> data = pg.read_dataset('icc') >>> icc = pg.intraclass_corr(data=data, targets='Wine', raters='Judge', ... ratings='Scores').round(3) >>> icc.set_index("Type") Description ICC F df1 df2 pval CI95% Type ICC1 Single raters absolute 0.728 11.680 7 24 0.0 [0.43, 0.93] ICC2 Single random raters 0.728 11.787 7 21 0.0 [0.43, 0.93] ICC3 Single fixed raters 0.729 11.787 7 21 0.0 [0.43, 0.93] ICC1k Average raters absolute 0.914 11.680 7 24 0.0 [0.75, 0.98] ICC2k Average random raters 0.914 11.787 7 21 0.0 [0.75, 0.98] ICC3k Average fixed raters 0.915 11.787 7 21 0.0 [0.75, 0.98] r)anovar cSsg|] }|dk qSr r r r r rrsz#intraclass_corr..csg|]}|jkqSr )rr rr rrs)omitr:T)rrrZobservedr<rrzwEither missing values are present in data or data are unbalanced. Please remove them manually or use nan_policy='omit'.)Zid_varsZ value_namerzRatings must be numeric.ignore)invalidNr,r)rZdvZbetweenZss_type)rMS)rSS)rr@)rDF)rrA)rr?)rr?rZICC1ZICC2ZICC3ZICC1kZICC2kZICC3kzSingle raters absolutezSingle random raterszSingle fixed raterszAverage raters absolutezAverage random raterszAverage fixed raters)Type DescriptionZICCFr6r7Zpvalg?zCI95%)Zpingouinr;r!r"r#r$r%Z pivot_tabler'rr( ValueErrorZ reset_indexZmeltrrZnuniquer)ZerrstatercopyupdateatrZsfZppfarrayr)/rtargetsZratersZratingsr/r;Z nan_presentr2r1Z old_optionsZaovZmsbZmswZmsjZmseZicc1Zicc2Zicc3Zicc1kZicc2kZicc3kZf1kr6Zdf1kdZp1kZf2kZf3kZdf2kdZp2kstatsr5Zf1lZf1ul1u1Zf3lZf3ul3u3fjZvnZvdrZf2uZf2ll2u2r rrrsd      (  (     0<88   4 )NNNNrr)NNNNr:) Znumpyr)Zpandasr"Z scipy.statsrZpingouin.configrZpingouin.utilsr__all__rrr r r rs