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 – count and sample size for first sample

  • nobs1 – count and sample size for first sample

  • count2 – count and sample size for the second sample

  • nobs2 – count and sample size for the second sample

  • low – equivalence margin for diff, risk ratio or odds ratio

  • upp – equivalence margin for diff, risk ratio or odds ratio

  • method (string) –

    method for computing the hypothesis test. 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

  • compare (string in ['diff', 'ratio' 'odds-ratio']) – If compare is diff, then the hypothesis test is for diff = p1 - p2. If compare is ratio, then the hypothesis test is for the risk ratio defined by ratio = p1 / p2. If compare is odds-ratio, then the hypothesis test is for the odds-ratio defined by or = p1 / (1 - p1) / (p2 / (1 - p2).

  • correction (bool) – 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:

  • pvalue (float) – p-value is the max of the pvalues of the two one-sided tests

  • t1 (test results) – results instance for one-sided hypothesis at the lower margin

  • t1 (test results) – results instance for one-sided hypothesis at the upper margin

See also

test_proportions_2indep, confint_proportions_2indep

Notes

Status: experimental, API and defaults might still change.

The TOST equivalence test delegates to test_proportions_2indep and has the same method and comparison options.