code: def rank_compare_2ordinal(count1, count2, ddof=1, use_t=True):
      """
      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)
  
      Parameters
      ----------
      count1 : array_like
          Counts of the first sample, categories are assumed to be ordered.
      count2 : array_like
          Counts of the second sample, number of categories and ordering needs
          to be the same as for sample 1.
      ddof : scalar
          Degrees of freedom correction for variance estimation. The default
          ddof=1 corresponds to `rank_compare_2indep`.
      use_t : bool
          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.
  
      Returns
      -------
      res : RankCompareResult
          This includes methods for hypothesis tests and confidence intervals
          for the probability that sample 1 is stochastically larger than
          sample 2.
  
      See Also
      --------
      rank_compare_2indep
      RankCompareResult
  
      Notes
      -----
      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`.
  
      """
  
      count1 = np.asarray(count1)
      count2 = np.asarray(count2)
      nobs1, nobs2 = count1.sum(), count2.sum()
      freq1 = count1 / nobs1
      freq2 = count2 / nobs2
      cdf1 = np.concatenate(([0], freq1)).cumsum(axis=0)
      cdf2 = np.concatenate(([0], freq2)).cumsum(axis=0)
  
      # mid rank cdf
      cdfm1 = (cdf1[1:] + cdf1[:-1]) / 2
      cdfm2 = (cdf2[1:] + cdf2[:-1]) / 2
      prob1 = (cdfm2 * freq1).sum()
      prob2 = (cdfm1 * freq2).sum()
  
      var1 = (cdfm2**2 * freq1).sum() - prob1**2
      var2 = (cdfm1**2 * freq2).sum() - prob2**2
  
      var_prob = var1 / (nobs1 - ddof) + var2 / (nobs2 - ddof)
      nobs = nobs1 + nobs2
      var = nobs * var_prob
      vn1 = var1 * nobs2 * nobs1 / (nobs1 - ddof)
      vn2 = var2 * nobs1 * nobs2 / (nobs2 - ddof)
      df = (vn1 + vn2) ** 2 / (
          vn1**2 / (nobs1 - 1) + vn2**2 / (nobs2 - 1)
      )
      res = RankCompareResult(
          statistic=None,
          pvalue=None,
          s1=None,
          s2=None,
          var1=var1,
          var2=var2,
          var=var,
          var_prob=var_prob,
          nobs1=nobs1,
          nobs2=nobs2,
          nobs=nobs,
          mean1=None,
          mean2=None,
          prob1=prob1,
          prob2=prob2,
          somersd1=prob1 * 2 - 1,
          somersd2=prob2 * 2 - 1,
          df=df,
          use_t=use_t,
      )
  
      return res
  
file_path: statsmodels/statsmodels/stats/nonparametric.py
imports: import numpy
  from scipy import stats
  from scipy.stats import rankdata
  from statsmodels.stats.base import HolderTuple
  from statsmodels.stats.weightstats import _tconfint_generic, _tstat_generic, _zconfint_generic, _zstat_generic
label_desc: Use image node_id 3 for calling a global function with example usage: rank_compare_2ordinal(count1, count2, ddof, use_t) and returns: res