Estimating p-value for Wilcoxon Signed-Rank Test

[Ford]

I'm trying to estimate the p-value range for a Wilcoxon Signed-Rank Test using a "www.dekasinthevents.org/images/wtable.jpg"[/URL]. For example:

Ho: M1 = M2
Ha: M1 < M2
alpha = 0.05
n = 17

I calculated W = 62 and the rejection region W <= 41. So I would reject Ho.

But I'm also required to know how to come to a conclusion using the estimated p-value that's supposed to come from the [PLAIN]"www.dekasinthevents.org/images/wtable.jpg"[/URL]. In a t-test using a t-table I would look at the t-table at the row with the right degrees of freedom and see where my test statistic would fall in. When I try to do this with a Wilcoxon test and a W-alpha table it gives me conclusion that contradicts the one I get from the test itself.

Any ideas on how to estimate the p-value properly from the W-alpha table? Thanks.

 

[EnumaElish]

How do you know that the rejection region is W <= 41? "41" is nowhere on the table on row "n=17".

 

[tacman]

Estimating the p-value for a Wilcoxon Signed-Rank Test using a W-alpha table is a bit different from using a t-table for a t-test. The W-alpha table gives you the critical values for W, which is the sum of the ranks of the smaller group. In this case, your calculated W is 62, which falls in the rejection region of W <= 41. This means that your W value is larger than the critical value of 41, so you would reject the null hypothesis.

To estimate the p-value from the W-alpha table, you would need to find the probability associated with your calculated W value. In your case, the p-value would be the probability of getting a W value of 62 or larger, given that the null hypothesis is true. This can be calculated by finding the area under the curve of the distribution of W values, starting from your calculated W value and going towards the larger end of the distribution. This area would represent the probability of getting a W value of 62 or larger, and this is your estimated p-value.

In order to find this probability from the W-alpha table, you would need to look at the row that corresponds to your sample size (n=17) and find the column that has a critical value closest to your calculated W value (in this case, it would be 61). The value in this cell would represent the probability of getting a W value of 61 or smaller. To get the probability of getting a W value of 62 or larger, you would need to subtract this value from 1. This would give you an estimated p-value of 0.055, which is larger than your alpha level of 0.05.

It is important to note that the estimated p-value from the W-alpha table is just an approximation and may not be completely accurate. It is always best to use the actual statistical software or calculator to calculate the p-value for more precise results. However, the estimated p-value from the W-alpha table can still give you a good idea of the significance of your results. In this case, although the estimated p-value is larger than the alpha level, it is still quite close and indicates that your results may be marginally significant.