statsmodels.stats.proportion.tost_proportions_2indep

statsmodels.stats.proportion.tost_proportions_2indep(count1, nobs1, count2, nobs2, low, upp, method=None, compare='diff', correction=True)[source]

Equivalence test based on two one-sided test_proportions_2indep

This assumes that we have two independent binomial samples.

The Null and alternative hypothesis for equivalence testing are

for compare = ‘diff’

  • H0: prop1 - prop2 <= low or upp <= prop1 - prop2

  • H1: low < prop1 - prop2 < upp

for compare = ‘ratio’

  • H0: prop1 / prop2 <= low or upp <= prop1 / prop2

  • H1: low < prop1 / prop2 < upp

for compare = ‘odds-ratio’

  • H0: or <= low or upp <= or

  • H1: low < or < upp

where odds-ratio or = prop1 / (1 - prop1) / (prop2 / (1 - prop2))

Parameters
count1, nobs1 :

count and sample size for first sample

count2, nobs2 :

count and sample size for the second sample

low, upp :

equivalence margin for diff, risk ratio or odds ratio

methodstr

method for computing confidence interval. If method is None, then a default method is used. The default might change as more methods are added.

diff:

  • ‘wald’,

  • ‘agresti-caffo’

  • ‘score’ if correction is True, then this uses the degrees of freedom correction nobs / (nobs - 1) as in Miettinen Nurminen 1985.

ratio:

  • ‘log’: wald test using log transformation

  • ‘log-adjusted’: wald test using log transformation,

    adds 0.5 to counts

  • ‘score’ if correction is True, then this uses the degrees of freedom correction nobs / (nobs - 1) as in Miettinen Nurminen 1985.

odds-ratio:

  • ‘logit’: wald test using logit transformation

  • ‘logit-adjusted’:wald test using logit transformation,

    adds 0.5 to counts

  • ‘logit-smoothed’:wald test using logit transformation, biases

    cell counts towards independence by adding two observations in total.

  • ‘score’ if correction is True, then this uses the degrees of freedom

    correction nobs / (nobs - 1) as in Miettinen Nurminen 1985

comparestr in [‘diff’, ‘ratio’ ‘odds-ratio’]

If compare is diff, then the confidence interval is for diff = p1 - p2. If compare is ratio, then the confidence interval is for the risk ratio defined by ratio = p1 / p2. If compare is odds-ratio, then the confidence interval is for the odds-ratio defined by or = p1 / (1 - p1) / (p2 / (1 - p2).

correctionbool

If correction is True (default), then the Miettinen and Nurminen small sample correction to the variance nobs / (nobs - 1) is used. Applies only if method=’score’.

Returns
pvaluefloat

p-value is the max of the pvalues of the two one-sided tests

t1test results

results instance for one-sided hypothesis at the lower margin

t1test results

results instance for one-sided hypothesis at the upper margin

Notes

Status: experimental, API and defaults might still change.