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Tests of Hypotheses

  • In this course most of the hypotheses we consider involve two samples. Hypothesis testing is typically done using the Wilcoxon statistic. The CC's that may be used for this purpose are given below. Again, as in the case of CI's, the first one needs an extra effort of computing the p-value whereas the second one gives the p-value based on 1000 resamples directly.
  • Two-Sample bootstrap Wilcoxon statistic (Sorted)
  • As an example consider the following data.
        Y : 12   15   10   9   13
        X : 7    5    14   6   8   10
    Suppose we are testing H0 : X = Y versus HA : X < Y. The data and appropriate output based on 1000 resamples is
    So the p-value of the test is 0.025.