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315 lines
11 KiB
Python
315 lines
11 KiB
Python
# Titan Robotics Team 2022: StatisticalTest submodule
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# Written by Arthur Lu
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# Notes:
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# this should be imported as a python module using 'from tra_analysis import StatisticalTest'
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# setup:
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__version__ = "1.0.3"
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__changelog__ = """changelog:
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1.0.3:
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- optimized imports
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1.0.2:
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- added tukey_multicomparison
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- fixed styling
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1.0.1:
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- fixed typo in __all__
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1.0.0:
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- ported analysis.StatisticalTest() here
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- removed classness
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"""
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__author__ = (
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"Arthur Lu <learthurgo@gmail.com>",
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"James Pan <zpan@imsa.edu>",
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)
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__all__ = [
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'ttest_onesample',
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'ttest_independent',
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'ttest_statistic',
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'ttest_related',
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'ks_fitness',
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'chisquare',
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'powerdivergence'
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'ks_twosample',
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'es_twosample',
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'mw_rank',
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'mw_tiecorrection',
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'rankdata',
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'wilcoxon_ranksum',
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'wilcoxon_signedrank',
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'kw_htest',
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'friedman_chisquare',
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'bm_wtest',
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'combine_pvalues',
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'jb_fitness',
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'ab_equality',
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'bartlett_variance',
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'levene_variance',
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'sw_normality',
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'shapiro',
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'ad_onesample',
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'ad_ksample',
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'binomial',
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'fk_variance',
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'mood_mediantest',
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'mood_equalscale',
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'skewtest',
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'kurtosistest',
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'normaltest',
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'tukey_multicomparison'
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]
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import numpy as np
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import scipy
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def ttest_onesample(a, popmean, axis = 0, nan_policy = 'propagate'):
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results = scipy.stats.ttest_1samp(a, popmean, axis = axis, nan_policy = nan_policy)
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return {"t-value": results[0], "p-value": results[1]}
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def ttest_independent(a, b, equal = True, nan_policy = 'propagate'):
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results = scipy.stats.ttest_ind(a, b, equal_var = equal, nan_policy = nan_policy)
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return {"t-value": results[0], "p-value": results[1]}
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def ttest_statistic(o1, o2, equal = True):
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results = scipy.stats.ttest_ind_from_stats(o1["mean"], o1["std"], o1["nobs"], o2["mean"], o2["std"], o2["nobs"], equal_var = equal)
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return {"t-value": results[0], "p-value": results[1]}
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def ttest_related(a, b, axis = 0, nan_policy='propagate'):
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results = scipy.stats.ttest_rel(a, b, axis = axis, nan_policy = nan_policy)
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return {"t-value": results[0], "p-value": results[1]}
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def ks_fitness(rvs, cdf, args = (), N = 20, alternative = 'two-sided', mode = 'approx'):
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results = scipy.stats.kstest(rvs, cdf, args = args, N = N, alternative = alternative, mode = mode)
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return {"ks-value": results[0], "p-value": results[1]}
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def chisquare(f_obs, f_exp = None, ddof = None, axis = 0):
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results = scipy.stats.chisquare(f_obs, f_exp = f_exp, ddof = ddof, axis = axis)
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return {"chisquared-value": results[0], "p-value": results[1]}
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def powerdivergence(f_obs, f_exp = None, ddof = None, axis = 0, lambda_ = None):
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results = scipy.stats.power_divergence(f_obs, f_exp = f_exp, ddof = ddof, axis = axis, lambda_ = lambda_)
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return {"powerdivergence-value": results[0], "p-value": results[1]}
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def ks_twosample(x, y, alternative = 'two_sided', mode = 'auto'):
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results = scipy.stats.ks_2samp(x, y, alternative = alternative, mode = mode)
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return {"ks-value": results[0], "p-value": results[1]}
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def es_twosample(x, y, t = (0.4, 0.8)):
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results = scipy.stats.epps_singleton_2samp(x, y, t = t)
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return {"es-value": results[0], "p-value": results[1]}
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def mw_rank(x, y, use_continuity = True, alternative = None):
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results = scipy.stats.mannwhitneyu(x, y, use_continuity = use_continuity, alternative = alternative)
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return {"u-value": results[0], "p-value": results[1]}
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def mw_tiecorrection(rank_values):
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results = scipy.stats.tiecorrect(rank_values)
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return {"correction-factor": results}
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def rankdata(a, method = 'average'):
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results = scipy.stats.rankdata(a, method = method)
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return results
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def wilcoxon_ranksum(a, b): # this seems to be superceded by Mann Whitney Wilcoxon U Test
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results = scipy.stats.ranksums(a, b)
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return {"u-value": results[0], "p-value": results[1]}
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def wilcoxon_signedrank(x, y = None, zero_method = 'wilcox', correction = False, alternative = 'two-sided'):
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results = scipy.stats.wilcoxon(x, y = y, zero_method = zero_method, correction = correction, alternative = alternative)
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return {"t-value": results[0], "p-value": results[1]}
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def kw_htest(*args, nan_policy = 'propagate'):
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results = scipy.stats.kruskal(*args, nan_policy = nan_policy)
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return {"h-value": results[0], "p-value": results[1]}
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def friedman_chisquare(*args):
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results = scipy.stats.friedmanchisquare(*args)
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return {"chisquared-value": results[0], "p-value": results[1]}
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def bm_wtest(x, y, alternative = 'two-sided', distribution = 't', nan_policy = 'propagate'):
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results = scipy.stats.brunnermunzel(x, y, alternative = alternative, distribution = distribution, nan_policy = nan_policy)
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return {"w-value": results[0], "p-value": results[1]}
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def combine_pvalues(pvalues, method = 'fisher', weights = None):
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results = scipy.stats.combine_pvalues(pvalues, method = method, weights = weights)
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return {"combined-statistic": results[0], "p-value": results[1]}
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def jb_fitness(x):
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results = scipy.stats.jarque_bera(x)
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return {"jb-value": results[0], "p-value": results[1]}
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def ab_equality(x, y):
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results = scipy.stats.ansari(x, y)
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return {"ab-value": results[0], "p-value": results[1]}
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def bartlett_variance(*args):
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results = scipy.stats.bartlett(*args)
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return {"t-value": results[0], "p-value": results[1]}
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def levene_variance(*args, center = 'median', proportiontocut = 0.05):
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results = scipy.stats.levene(*args, center = center, proportiontocut = proportiontocut)
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return {"w-value": results[0], "p-value": results[1]}
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def sw_normality(x):
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results = scipy.stats.shapiro(x)
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return {"w-value": results[0], "p-value": results[1]}
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def shapiro(x):
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return "destroyed by facts and logic"
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def ad_onesample(x, dist = 'norm'):
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results = scipy.stats.anderson(x, dist = dist)
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return {"d-value": results[0], "critical-values": results[1], "significance-value": results[2]}
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def ad_ksample(samples, midrank = True):
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results = scipy.stats.anderson_ksamp(samples, midrank = midrank)
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return {"d-value": results[0], "critical-values": results[1], "significance-value": results[2]}
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def binomial(x, n = None, p = 0.5, alternative = 'two-sided'):
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results = scipy.stats.binom_test(x, n = n, p = p, alternative = alternative)
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return {"p-value": results}
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def fk_variance(*args, center = 'median', proportiontocut = 0.05):
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results = scipy.stats.fligner(*args, center = center, proportiontocut = proportiontocut)
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return {"h-value": results[0], "p-value": results[1]} # unknown if the statistic is an h value
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def mood_mediantest(*args, ties = 'below', correction = True, lambda_ = 1, nan_policy = 'propagate'):
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results = scipy.stats.median_test(*args, ties = ties, correction = correction, lambda_ = lambda_, nan_policy = nan_policy)
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return {"chisquared-value": results[0], "p-value": results[1], "m-value": results[2], "table": results[3]}
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def mood_equalscale(x, y, axis = 0):
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results = scipy.stats.mood(x, y, axis = axis)
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return {"z-score": results[0], "p-value": results[1]}
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def skewtest(a, axis = 0, nan_policy = 'propogate'):
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results = scipy.stats.skewtest(a, axis = axis, nan_policy = nan_policy)
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return {"z-score": results[0], "p-value": results[1]}
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def kurtosistest(a, axis = 0, nan_policy = 'propogate'):
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results = scipy.stats.kurtosistest(a, axis = axis, nan_policy = nan_policy)
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return {"z-score": results[0], "p-value": results[1]}
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def normaltest(a, axis = 0, nan_policy = 'propogate'):
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results = scipy.stats.normaltest(a, axis = axis, nan_policy = nan_policy)
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return {"z-score": results[0], "p-value": results[1]}
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def get_tukeyQcrit(k, df, alpha=0.05):
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'''
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From statsmodels.sandbox.stats.multicomp
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return critical values for Tukey's HSD (Q)
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Parameters
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----------
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k : int in {2, ..., 10}
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number of tests
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df : int
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degrees of freedom of error term
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alpha : {0.05, 0.01}
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type 1 error, 1-confidence level
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not enough error checking for limitations
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'''
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# qtable from statsmodels.sandbox.stats.multicomp
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qcrit = '''
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2 3 4 5 6 7 8 9 10
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5 3.64 5.70 4.60 6.98 5.22 7.80 5.67 8.42 6.03 8.91 6.33 9.32 6.58 9.67 6.80 9.97 6.99 10.24
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6 3.46 5.24 4.34 6.33 4.90 7.03 5.30 7.56 5.63 7.97 5.90 8.32 6.12 8.61 6.32 8.87 6.49 9.10
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7 3.34 4.95 4.16 5.92 4.68 6.54 5.06 7.01 5.36 7.37 5.61 7.68 5.82 7.94 6.00 8.17 6.16 8.37
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8 3.26 4.75 4.04 5.64 4.53 6.20 4.89 6.62 5.17 6.96 5.40 7.24 5.60 7.47 5.77 7.68 5.92 7.86
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9 3.20 4.60 3.95 5.43 4.41 5.96 4.76 6.35 5.02 6.66 5.24 6.91 5.43 7.13 5.59 7.33 5.74 7.49
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10 3.15 4.48 3.88 5.27 4.33 5.77 4.65 6.14 4.91 6.43 5.12 6.67 5.30 6.87 5.46 7.05 5.60 7.21
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11 3.11 4.39 3.82 5.15 4.26 5.62 4.57 5.97 4.82 6.25 5.03 6.48 5.20 6.67 5.35 6.84 5.49 6.99
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12 3.08 4.32 3.77 5.05 4.20 5.50 4.51 5.84 4.75 6.10 4.95 6.32 5.12 6.51 5.27 6.67 5.39 6.81
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13 3.06 4.26 3.73 4.96 4.15 5.40 4.45 5.73 4.69 5.98 4.88 6.19 5.05 6.37 5.19 6.53 5.32 6.67
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14 3.03 4.21 3.70 4.89 4.11 5.32 4.41 5.63 4.64 5.88 4.83 6.08 4.99 6.26 5.13 6.41 5.25 6.54
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15 3.01 4.17 3.67 4.84 4.08 5.25 4.37 5.56 4.59 5.80 4.78 5.99 4.94 6.16 5.08 6.31 5.20 6.44
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16 3.00 4.13 3.65 4.79 4.05 5.19 4.33 5.49 4.56 5.72 4.74 5.92 4.90 6.08 5.03 6.22 5.15 6.35
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17 2.98 4.10 3.63 4.74 4.02 5.14 4.30 5.43 4.52 5.66 4.70 5.85 4.86 6.01 4.99 6.15 5.11 6.27
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18 2.97 4.07 3.61 4.70 4.00 5.09 4.28 5.38 4.49 5.60 4.67 5.79 4.82 5.94 4.96 6.08 5.07 6.20
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19 2.96 4.05 3.59 4.67 3.98 5.05 4.25 5.33 4.47 5.55 4.65 5.73 4.79 5.89 4.92 6.02 5.04 6.14
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20 2.95 4.02 3.58 4.64 3.96 5.02 4.23 5.29 4.45 5.51 4.62 5.69 4.77 5.84 4.90 5.97 5.01 6.09
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24 2.92 3.96 3.53 4.55 3.90 4.91 4.17 5.17 4.37 5.37 4.54 5.54 4.68 5.69 4.81 5.81 4.92 5.92
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30 2.89 3.89 3.49 4.45 3.85 4.80 4.10 5.05 4.30 5.24 4.46 5.40 4.60 5.54 4.72 5.65 4.82 5.76
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40 2.86 3.82 3.44 4.37 3.79 4.70 4.04 4.93 4.23 5.11 4.39 5.26 4.52 5.39 4.63 5.50 4.73 5.60
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60 2.83 3.76 3.40 4.28 3.74 4.59 3.98 4.82 4.16 4.99 4.31 5.13 4.44 5.25 4.55 5.36 4.65 5.45
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120 2.80 3.70 3.36 4.20 3.68 4.50 3.92 4.71 4.10 4.87 4.24 5.01 4.36 5.12 4.47 5.21 4.56 5.30
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infinity 2.77 3.64 3.31 4.12 3.63 4.40 3.86 4.60 4.03 4.76 4.17 4.88 4.29 4.99 4.39 5.08 4.47 5.16
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'''
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res = [line.split() for line in qcrit.replace('infinity','9999').split('\n')]
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c=np.array(res[2:-1]).astype(float)
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#c[c==9999] = np.inf
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ccols = np.arange(2,11)
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crows = c[:,0]
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cv005 = c[:, 1::2]
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cv001 = c[:, 2::2]
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if alpha == 0.05:
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intp = scipy.interpolate.interp1d(crows, cv005[:,k-2])
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elif alpha == 0.01:
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intp = scipy.interpolate.interp1d(crows, cv001[:,k-2])
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else:
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raise ValueError('only implemented for alpha equal to 0.01 and 0.05')
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return intp(df)
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def tukey_multicomparison(groups, alpha=0.05):
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#formulas according to https://astatsa.com/OneWay_Anova_with_TukeyHSD/
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k = len(groups)
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df = 0
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means = []
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MSE = 0
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for group in groups:
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df+= len(group)
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mean = sum(group)/len(group)
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means.append(mean)
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MSE += sum([(i-mean)**2 for i in group])
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df -= k
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MSE /= df
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q_dict = {}
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crit_q = get_tukeyQcrit(k, df, alpha)
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for i in range(k-1):
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for j in range(i+1, k):
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numerator = abs(means[i] - means[j])
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denominator = np.sqrt( MSE / ( 2/(1/len(groups[i]) + 1/len(groups[j])) ))
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q = numerator/denominator
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q_dict["group "+ str(i+1) + " and group " + str(j+1)] = [q, q>crit_q]
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return q_dict |