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Topic 1-Sample Sign vs. 1-Sample Wilcoxon

1-Sample Sign vs. 1-Sample Wilcoxon

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    Can someone explain the difference between 1-Sample Sign Test and 1-Sample Wilcoxon to me? Minitab says that this is the equivalent of 1-Sample t test with the exception that the normality is not assumed here. Minitab has the example file called EXH_STAT.MTW. I tried both these methods but got very different results (look at the p-value). Would someone help me understand this? Thank you.
    Results for: EXH_STAT.MTW
    Sign Test for Median: PriceIndex
    Sign test of median = 115.0 versus  not =  115.0
                   N  Below  Equal  Above         P     Median
    PriceInd      29     12      0     17    0.4583      144.0
    Wilcoxon Signed Rank Test: PriceIndex
    Test of median = 115.0 versus median not = 115.0
                    N for   Wilcoxon           Estimated
                 N   Test  Statistic        P     Median
    PriceInd    29     29      315.5    0.035      165.0


    Mini explains that the Wilcoxon assumes random samples from a continuous symmetric population.  The Sign test does not have that assumption.  If you generate some random numbers using Mini and compare the two tests for a normal distribution (symmetrical) you will see the p-values are pretty close.  But if you generate, for example, an exponential distribution (skewed) you will see results like in the example.  One p-value says accept and one says reject.  Hope that helps.

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