If\(\style{font-family:Times New Roman;}{\Delta_{\text{o}}\neq0}\), then the value\(\style{font-family:Times New Roman;}{\Delta_{\text{o}}}\)is subtracted from each observation in sample 1. This will:
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“shift” sample 1, effectively making\(\style{font-family:Times New Roman;}{{\overset˜\mu}_1={\overset˜\mu}_2}\)ifH0is true.
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correct for non-normality of both populations.
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effectively do nothing, because subtracting\(\style{font-family:Times New Roman;}{\Delta_{\text{o}}}\)from the values will not change the median.
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help smooth out discontinuities that occur when attempting to perform the test on discrete data.
