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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