code: def test_rank_compare_vectorized():
      np.random.seed(987126)
      x1 = np.random.randint(0, 20, (50, 3))
      x2 = np.random.randint(5, 25, (50, 3))
      res = rank_compare_2indep(x1, x2)
      tst = res.test_prob_superior(0.5)
      tost = res.tost_prob_superior(0.4, 0.6)
  
      # smoke test for summary
      res.summary()
  
      for i in range(3):
          res_i = rank_compare_2indep(x1[:, i], x2[:, i])
          assert_allclose(res.statistic[i], res_i.statistic, rtol=1e-14)
          assert_allclose(res.pvalue[i], res_i.pvalue, rtol=1e-14)
          assert_allclose(res.prob1[i], res_i.prob1, rtol=1e-14)
  
          tst_i = res_i.test_prob_superior(0.5)
          assert_allclose(tst.statistic[i], tst_i.statistic, rtol=1e-14)
          assert_allclose(tst.pvalue[i], tst_i.pvalue, rtol=1e-14)
  
          tost_i = res_i.tost_prob_superior(0.4, 0.6)
          assert_allclose(
              tost.statistic[i], tost_i.statistic, rtol=1e-14
          )
          assert_allclose(tost.pvalue[i], tost_i.pvalue, rtol=1e-14)
  
imports: from statsmodels.compat.python import lzip
  import numpy
  from numpy.testing import assert_allclose, assert_almost_equal, assert_approx_equal, assert_
  from scipy import stats
  import pytest
  from statsmodels.stats.contingency_tables import mcnemar, cochrans_q, SquareTable
  from statsmodels.sandbox.stats.runs import Runs, runstest_1samp, runstest_2samp
  from statsmodels.sandbox.stats.runs import mcnemar
  from statsmodels.stats.nonparametric import rank_compare_2indep, rank_compare_2ordinal, prob_larger_continuous, cohensd2problarger
  from statsmodels.tools.testing import Holder
label_desc: Use image node_id 15 for calling a global function with example usage: test_rank_compare_vectorized() without return types