statsmodels.stats.nonparametric.rank_compare_2ordinal(count1, count2, ddof=1, use_t=True)[source]

Stochastically larger probability for 2 independent ordinal samples.

This is a special case of rank_compare_2indep when the data are given as counts of two independent ordinal, i.e. ordered multinomial, samples.

The statistic of interest is the probability that a random draw from the population of the first sample has a larger value than a random draw from the population of the second sample, specifically

p = P(x1 > x2) + 0.5 * P(x1 = x2)


Counts of the first sample, categories are assumed to be ordered.


Counts of the second sample, number of categories and ordering needs to be the same as for sample 1.


Degrees of freedom correction for variance estimation. The default ddof=1 corresponds to rank_compare_2indep.


If use_t is true, the t distribution with Welch-Satterthwaite type degrees of freedom is used for p-value and confidence interval. If use_t is false, then the normal distribution is used.


This includes methods for hypothesis tests and confidence intervals for the probability that sample 1 is stochastically larger than sample 2.


The implementation is based on the appendix of Munzel and Hauschke (2003) with the addition of ddof so that the results match the general function rank_compare_2indep.