Wilcoxon rank sum test

Hi I performed a Wilcoxon rank-sum test with two samples x and y with sample size n_x=55 and n_y=20. mean(x)=552.2632, std(x)=1210 and mean(y)=427.4472, std(y)=485 I have used matlab for this. [p,h,stats] = ranksum(x,y)

Results are p = 0.2678; h = 0; stats = zval: 1.1082 ranksum: 853

What is the interpretation of this result? what does p value signify here? Thanking you in advance.

Answer 1

[Guðmundur]

Most authors refer to statistically significant as P < 0.05

and statistically highly significant as P < 0.001 (less than one in a thousand chance of being wrong).

h = 1 indicates a rejection of the null hypothesis, and h = 0 indicates a failure to reject the null hypothesis at the 5% significance level.

If you combine vectors x & y then sum up the ranks(location of numbers in combined sorted vector) of the first vector you get the ranksum (https://onlinecourses.science.psu.edu/stat464/node/36)

Im guessing z-val tells you wether the likelyness of the vectors are statistically different. see for example : http://www.stratasearch.com/col_c_zratio.html

[Jos (10584)]

The statement " less than one in a thousand chance of being wrong" is wrong for sure.

Answer 2

[Jos (10584)]

The p-value is derived from comparing a test-statistic (in this case a z-value obtained by summing ranks) to a theoretical distribution. The p-value is an estimation of the chance of observing the data given the null-hypothesis being true. If this value is below a certain criterion (alpha, needed to set before you do the stats, not afterwards) you can decide to reject this null-hypothesis.

You have to understand that the p-value tells you absolutely nothing about the chance of any alternative hypothesis being true! Moreover, if your null-hypothesis is already unlikely in the first place, you have learned little by collecting the data and doing a test ...

Answer 3

[Abhijit Chakraborty]

Thank you Guðmundur, Jos and Star for your kind help.

From my result (as mentioned above) can I say, the p value indicates that I can’t reject the null hypothesis?

[Star Strider]

Correct.