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TOST test of equivalence for paired samples
'''Test of Equivalence and Non-Inferiority
currently only TOST for paired sample
Application for example bioequivalence
Author: Josef Perktold
License: BSD-3
'''
import numpy as np
from scipy import stats
def tost_paired(y, x, low, upp, transform=None):
'''test of (non-)equivalence for paired sample
TOST: two one-sided t tests
null hypothesis x - y < low or x - y > upp
alternative hypothesis: low < x - y < upp
If the pvalue is smaller than a threshold, then we reject the hypothesis
that there is difference between the two samples larger than the one
given by low and upp.
Parameters
----------
y, x : array_like
two paired samples
low, upp : float
equivalence interval low < x - y < upp
transform : None or function
If None (default), then the data is not transformed. Given a function
sample data and thresholds are transformed. If transform is log the
the equivalence interval is in ratio: low < x / y < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test
Notes
-----
tested on only one example
uses stats.ttest_1samp which doesn't have a real one-sided option
'''
if transform:
y = transform(y)
x = transform(x)
low = transform(low)
upp = transform(upp)
t1, pv1 = stats.ttest_1samp(x - y, low)
t2, pv2 = stats.ttest_1samp(x - y, upp)
return max(pv1, pv2)/2., (t1, pv1 / 2.), (t2, pv2 / 2.)
if __name__ == '__main__':
#example from http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_ttest_sect013.htm
raw = np.array('''\
103.4 90.11 59.92 77.71 68.17 77.71 94.54 97.51
69.48 58.21 72.17 101.3 74.37 79.84 84.44 96.06
96.74 89.30 94.26 97.22 48.52 61.62 95.68 85.80'''.split(), float)
x, y = raw.reshape(-1,2).T
print tost_paired(y, x, 0.8, 1.25, transform=np.log)
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