The following table provides the critical values for two-tailed tests. For a one-tailed test, double the alpha value and use the table. See Wilcoxon Signed-Ranks Test for details about the test.

### Real Statistics Resources

### Current Section

- Statistics Tables
- Wilcoxon Rank-Sum Table
- Mann-Whitney Table
- Wilcoxon Signed-Ranks Table
- Runs Test Table
- Kolmogorov-Smirnov Table
- Shapiro-Wilk Tables
- Studentized Range q Table
- Spearman’s Rho Table
- Kendall’s Tau Table
- Durbin-Watson Table
- Lilliefors Test Table
- Pearson’s Correlation Table
- Dunnett’s Table
- Augmented Dickey-Fuller Table
- Interpolation

- Statistics Tables

need help solving this question “A machine which fills orange squash bottles should be set to deliver 725 ml,A sample of 50 bottles is checked and the mean quantity is found to be 721 ml and the sample standard deviation 13 ml.does this differ signficantly from 725 ml at 1% level of significance?”

Yes, you can do this using the one-sample t test. See the following webpage:

http://www.real-statistics.com/students-t-distribution/one-sample-t-test/

Charles

Can we generate z-score from Wilcoxon Signed Rank Test for small sample data? Currently I’m using SPSS as my statistical tools.

Sorry, but I don’t know whether SPSS provides a z-score for

smallsamples. The typical approach is to use the z-score for large samples (20 or so elements). I am sure this is provided by SPSS. It is also included in the Real Statistics Wilcoxon Signed Rank Test data analysis tool and SRank function.Charles

Hi

If I have a sample size of 1645 can you advise if this test can be used and if so what the critical value would be for a data set of this size? If this is not the appropriate test can you please advise what would be?

Many Thanks

Hi Victoria,

You can use this test with a sample of 1645, but you don’t need to use a table of critical values. Instead you should use the normal approximation as described in Wilcoxon Signed-Ranks Test.

Charles

In the case that with my large sample, it is not in fact normally distributed (I know this because I have run several normality tests and a histogram to prove), how to I proceed to interpret the Wilcoxon test statistic? Mine is very large, 9903.Thank you

Mai,

You can use Wilcoxon Signed-Ranks test even with data that is not normally distributed. See the following webpage for details

Wilcoxon Signed-Ranks Test

Charles

Mai,

Normality is not a requirement for the Wilcoxon signed ranks test.

The requirement instead is that the distribution of paired differences be relatively symmetric. See the following webpage for more details:

http://www.real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/

Charles

Hi..I am trying to used Wilcoxon signed rank test on a very large dataset. The sample size is around 30000. Does the test work on large sample size like this?

The test does work on such a large sample (using the normal approximation). I believe that the version provided by the Real Statistics Resource Pack does work on this size data set. I have tested it on large data sets, but I can’t recall what the largest size was. The easiest way to confirm that it works is to try it.

Charles

I downloaded the service pack. Thank you! But how do I format Column F so it contains the adjusted rankings of the non-zero values in column E?

Lucia,

This is explained on the webpage http://www.real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/. You need to use Excel’s RANK.AVG function.

Charles

Hi Sir.

May I know if Wilcoxon Test may be applied if you only have n=5. If not what may be an alternative test?

Thank you.

Robert,

The Wilcoxon Signed-Ranks Test can be applied with n = 5, but don’t expect much from the test since the sample size is so small. Only with a high value for alpha and extremely lopsided data will you find out anything. With so little data, there isn’t much that is meaningful that you can do. You can try the sign test.

Charles

Is there a formula or approximation for extrapolating to higher values of N?

Just apply the normal approximation as described on the webpage http://www.real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/

Charles

“For a 1-tail test, double the alpha value and use the table.”

Correct me if I’m wrong, but for a one tailed test shouldn’t I cut the alpha in half and use this chart?

Mike,

The table contains the critical values for the two-tailed test. For the one-tailed test you definitely need to double the value of alpha and use that column in the table.

Charles

Hi, Mike! I was asking myself the same question. Here I share another table and information about the test and you can decide for yourself. Good luck!

http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Nonparametric/BS704_Nonparametric6.html

Please how do I simulate for the most powerful willcoxom signed rank test using R software