Statistics stats
This section collects various statistical tests and tools.
Some can be used independently of any models, some are intended as extension to the
models and model results.
API Warning: The functions and objects in this category are spread out in
various modules and might still be moved around. We expect that in future the
statistical tests will return class instances with more informative reporting
instead of only the raw numbers.
Sandwich Robust Covariances
The following functions calculate covariance matrices and standard errors for
the parameter estimates that are robust to heteroscedasticity and
autocorrelation in the errors. Similar to the methods that are available
for the LinearModelResults, these methods are designed for use with OLS.
The following are standalone versions of the heteroscedasticity robust
standard errors attached to LinearModelResults
Goodness of Fit Tests and Measures
some tests for goodness of fit for univariate distributions
powerdiscrepancy(observed, expected[, ...]) |
Calculates power discrepancy, a class of goodness-of-fit tests as a measure of discrepancy between observed and expected data. |
gof_chisquare_discrete(distfn, arg, rvs, ...) |
perform chisquare test for random sample of a discrete distribution |
gof_binning_discrete(rvs, distfn, arg[, nsupp]) |
get bins for chisquare type gof tests for a discrete distribution |
chisquare_effectsize(probs0, probs1[, ...]) |
effect size for a chisquare goodness-of-fit test |
normal_ad(x[, axis]) |
Anderson-Darling test for normal distribution unknown mean and variance |
kstest_normal(x[, pvalmethod]) |
lilliefors test for normality, |
lilliefors(x[, pvalmethod]) |
lilliefors test for normality, |
Non-Parametric Tests
mcnemar(x[, y, exact, correction]) |
McNemar test |
symmetry_bowker(table) |
Test for symmetry of a (k, k) square contingency table |
median_test_ksample(x, groups) |
chisquare test for equality of median/location |
runstest_1samp(x[, cutoff, correction]) |
use runs test on binary discretized data above/below cutoff |
runstest_2samp(x[, y, groups, correction]) |
Wald-Wolfowitz runstest for two samples |
cochrans_q(x) |
Cochran’s Q test for identical effect of k treatments |
Runs(x) |
class for runs in a binary sequence |
Interrater Reliability and Agreement
The main function that statsmodels has currently available for interrater
agreement measures and tests is Cohen’s Kappa. Fleiss’ Kappa is currently
only implemented as a measures but without associated results statistics.
cohens_kappa(table[, weights, ...]) |
Compute Cohen’s kappa with variance and equal-zero test |
fleiss_kappa(table) |
Fleiss’ kappa multi-rater agreement measure |
to_table(data[, bins]) |
convert raw data with shape (subject, rater) to (rater1, rater2) |
aggregate_raters(data[, n_cat]) |
convert raw data with shape (subject, rater) to (subject, cat_counts) |
Multiple Tests and Multiple Comparison Procedures
multipletests is a function for p-value correction, which also includes p-value
correction based on fdr in fdrcorrection.
tukeyhsd performs simulatenous testing for the comparison of (independent) means.
These three functions are verified.
GroupsStats and MultiComparison are convenience classes to multiple comparisons similar
to one way ANOVA, but still in developement
multipletests(pvals[, alpha, method, ...]) |
test results and p-value correction for multiple tests |
fdrcorrection0(pvals[, alpha, method, is_sorted]) |
pvalue correction for false discovery rate |
GroupsStats(x[, useranks, uni, intlab]) |
statistics by groups (another version) |
MultiComparison(data, groups[, group_order]) |
Tests for multiple comparisons |
TukeyHSDResults(mc_object, results_table, q_crit) |
Results from Tukey HSD test, with additional plot methods |
pairwise_tukeyhsd(endog, groups[, alpha]) |
calculate all pairwise comparisons with TukeyHSD confidence intervals |
local_fdr(zscores[, null_proportion, ...]) |
Calculate local FDR values for a list of Z-scores. |
fdrcorrection_twostage(pvals[, alpha, ...]) |
(iterated) two stage linear step-up procedure with estimation of number of true |
NullDistribution(zscores[, null_lb, ...]) |
Estimate a Gaussian distribution for the null Z-scores. |
The following functions are not (yet) public
varcorrection_pairs_unbalanced(nobs_all[, ...]) |
correction factor for variance with unequal sample sizes for all pairs |
varcorrection_pairs_unequal(var_all, ...) |
return joint variance from samples with unequal variances and unequal |
varcorrection_unbalanced(nobs_all[, srange]) |
correction factor for variance with unequal sample sizes |
varcorrection_unequal(var_all, nobs_all, df_all) |
return joint variance from samples with unequal variances and unequal |
StepDown(vals, nobs_all, var_all[, df]) |
a class for step down methods |
catstack(args) |
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ccols |
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compare_ordered(vals, alpha) |
simple ordered sequential comparison of means |
distance_st_range(mean_all, nobs_all, var_all) |
pairwise distance matrix, outsourced from tukeyhsd |
ecdf(x) |
no frills empirical cdf used in fdrcorrection |
get_tukeyQcrit(k, df[, alpha]) |
return critical values for Tukey’s HSD (Q) |
homogeneous_subsets(vals, dcrit) |
recursively check all pairs of vals for minimum distance |
maxzero(x) |
find all up zero crossings and return the index of the highest |
maxzerodown(x) |
find all up zero crossings and return the index of the highest |
mcfdr([nrepl, nobs, ntests, ntrue, mu, ...]) |
MonteCarlo to test fdrcorrection |
qcrit |
str(object=’‘) -> str |
randmvn(rho[, size, standardize]) |
create random draws from equi-correlated multivariate normal distribution |
rankdata(x) |
rankdata, equivalent to scipy.stats.rankdata |
rejectionline(n[, alpha]) |
reference line for rejection in multiple tests |
set_partition(ssli) |
extract a partition from a list of tuples |
set_remove_subs(ssli) |
remove sets that are subsets of another set from a list of tuples |
tiecorrect(xranks) |
should be equivalent of scipy.stats.tiecorrect |
Basic Statistics and t-Tests with frequency weights
Besides basic statistics, like mean, variance, covariance and correlation for
data with case weights, the classes here provide one and two sample tests
for means. The t-tests have more options than those in scipy.stats, but are
more restrictive in the shape of the arrays. Confidence intervals for means
are provided based on the same assumptions as the t-tests.
Additionally, tests for equivalence of means are available for one sample and
for two, either paired or independent, samples. These tests are based on TOST,
two one-sided tests, which have as null hypothesis that the means are not
“close” to each other.
DescrStatsW(data[, weights, ddof]) |
descriptive statistics and tests with weights for case weights |
CompareMeans(d1, d2) |
class for two sample comparison |
ttest_ind(x1, x2[, alternative, usevar, ...]) |
ttest independent sample |
ttost_ind(x1, x2, low, upp[, usevar, ...]) |
test of (non-)equivalence for two independent samples |
ttost_paired(x1, x2, low, upp[, transform, ...]) |
test of (non-)equivalence for two dependent, paired sample |
ztest(x1[, x2, value, alternative, usevar, ddof]) |
test for mean based on normal distribution, one or two samples |
ztost(x1, low, upp[, x2, usevar, ddof]) |
Equivalence test based on normal distribution |
zconfint(x1[, x2, value, alpha, ...]) |
confidence interval based on normal distribution z-test |
weightstats also contains tests and confidence intervals based on summary
data
_tconfint_generic(mean, std_mean, dof, ...) |
generic t-confint to save typing |
_tstat_generic(value1, value2, std_diff, ...) |
generic ttest to save typing |
_zconfint_generic(mean, std_mean, alpha, ...) |
generic normal-confint to save typing |
_zstat_generic(value1, value2, std_diff, ...) |
generic (normal) z-test to save typing |
_zstat_generic2(value, std_diff, alternative) |
generic (normal) z-test to save typing |
Power and Sample Size Calculations
The power module currently implements power and sample size calculations
for the t-tests, normal based test, F-tests and Chisquare goodness of fit test.
The implementation is class based, but the module also provides
three shortcut functions, tt_solve_power, tt_ind_solve_power and
zt_ind_solve_power to solve for any one of the parameters of the power
equations.
TTestIndPower(**kwds) |
Statistical Power calculations for t-test for two independent sample |
TTestPower(**kwds) |
Statistical Power calculations for one sample or paired sample t-test |
GofChisquarePower(**kwds) |
Statistical Power calculations for one sample chisquare test |
NormalIndPower([ddof]) |
Statistical Power calculations for z-test for two independent samples. |
FTestAnovaPower(**kwds) |
Statistical Power calculations F-test for one factor balanced ANOVA |
FTestPower(**kwds) |
Statistical Power calculations for generic F-test |
tt_solve_power |
solve for any one parameter of the power of a one sample t-test |
tt_ind_solve_power |
solve for any one parameter of the power of a two sample t-test |
zt_ind_solve_power |
solve for any one parameter of the power of a two sample z-test |
Proportion
Also available are hypothesis test, confidence intervals and effect size for
proportions that can be used with NormalIndPower.
proportion_confint(count, nobs[, alpha, method]) |
confidence interval for a binomial proportion |
proportion_effectsize(prop1, prop2[, method]) |
effect size for a test comparing two proportions |
binom_test(count, nobs[, prop, alternative]) |
Perform a test that the probability of success is p. |
binom_test_reject_interval(value, nobs[, ...]) |
rejection region for binomial test for one sample proportion |
binom_tost(count, nobs, low, upp) |
exact TOST test for one proportion using binomial distribution |
binom_tost_reject_interval(low, upp, nobs[, ...]) |
rejection region for binomial TOST |
multinomial_proportions_confint(counts[, ...]) |
Confidence intervals for multinomial proportions. |
proportions_ztest(count, nobs[, value, ...]) |
Test for proportions based on normal (z) test |
proportions_ztost(count, nobs, low, upp[, ...]) |
Equivalence test based on normal distribution |
proportions_chisquare(count, nobs[, value]) |
test for proportions based on chisquare test |
proportions_chisquare_allpairs(count, nobs) |
chisquare test of proportions for all pairs of k samples |
proportions_chisquare_pairscontrol(count, nobs) |
chisquare test of proportions for pairs of k samples compared to control |
proportion_effectsize(prop1, prop2[, method]) |
effect size for a test comparing two proportions |
power_binom_tost(low, upp, nobs[, p_alt, alpha]) |
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power_ztost_prop(low, upp, nobs, p_alt[, ...]) |
Power of proportions equivalence test based on normal distribution |
samplesize_confint_proportion(proportion, ...) |
find sample size to get desired confidence interval length |
Moment Helpers
When there are missing values, then it is possible that a correlation or
covariance matrix is not positive semi-definite. The following three
functions can be used to find a correlation or covariance matrix that is
positive definite and close to the original matrix.
corr_clipped(corr[, threshold]) |
Find a near correlation matrix that is positive semi-definite |
corr_nearest(corr[, threshold, n_fact]) |
Find the nearest correlation matrix that is positive semi-definite. |
corr_nearest_factor(corr, rank[, ctol, ...]) |
Find the nearest correlation matrix with factor structure to a given square matrix. |
corr_thresholded(data[, minabs, max_elt]) |
Construct a sparse matrix containing the thresholded row-wise correlation matrix from a data array. |
cov_nearest(cov[, method, threshold, ...]) |
Find the nearest covariance matrix that is postive (semi-) definite |
cov_nearest_factor_homog(cov, rank) |
Approximate an arbitrary square matrix with a factor-structured matrix of the form k*I + XX’. |
FactoredPSDMatrix(diag, root) |
Representation of a positive semidefinite matrix in factored form. |
These are utility functions to convert between central and non-central moments, skew,
kurtosis and cummulants.
cum2mc(kappa) |
convert non-central moments to cumulants |
mc2mnc(mc) |
convert central to non-central moments, uses recursive formula |
mc2mvsk(args) |
convert central moments to mean, variance, skew, kurtosis |
mnc2cum(mnc) |
convert non-central moments to cumulants |
mnc2mc(mnc[, wmean]) |
convert non-central to central moments, uses recursive formula |
mnc2mvsk(args) |
convert central moments to mean, variance, skew, kurtosis |
mvsk2mc(args) |
convert mean, variance, skew, kurtosis to central moments |
mvsk2mnc(args) |
convert mean, variance, skew, kurtosis to non-central moments |
cov2corr(cov[, return_std]) |
convert covariance matrix to correlation matrix |
corr2cov(corr, std) |
convert correlation matrix to covariance matrix given standard deviation |
se_cov(cov) |
get standard deviation from covariance matrix |
