Non-Symmetric 1-sample median test

[#1]

I am attempting to complete a non-parametric test on skewed data that is non-symmetric. I am using the test means option in the distribution window but the Wilcoxon Signed test requires symmetry and this skewed data is non-symmetric. Is there an option to so a 1-sample sign test instead of the Wilcoxon test?

[#2 · Accepted solution]

It is fairly easy to create the sign test.

Create a new column that is a conditional formula. Specify the value 1 if the original data is greater than your target, 0 otherwise (note that I am assuming there are no values equal to the target. If that occurs, most texts recommend removing that observation from the data).

This formula column should have a Nominal modeling type. Now make a distribution of that column. From the red popup, choose Test Probabilities. Typically the hypothesized probabilities are 0.5. You will have two different tests. The Likelihood Ratio test will match most of the "by hand" calculations that are mentioned in text books. Typically, both tests will agree on the conclusion.

[#3]

Thank you for this!

[#4]

Hi Dan,

I am also dealing with that problem nowadays.

I try to apply suggested solution below, but i can not find The Likelihood Ratio test to test whether the mean of a sample having non symmetric dist is equal to the target.  

Besides, how can we test symmetry of my distribution?

Kind regards

[#5]

If you followed the steps you should have two statistical tests. Could you please provide a screen capture of what you do see? Have you changed the column to have a nominal modeling type?

Testing for symmetry has several possible approaches. You could make a distribution of the continuous data and look at the Skewness measure under the Summary Statistics. A value reasonably close to zero would indicate the data likely come from a symmetric distribution. If you wanted to get a rough idea of the uncertainty in the skewness statistic, a rough rule of thumb is that the standard error for skewness is SQRT(6/n). This approach is usually sufficient for meeting the assumptions for the Wilcoxon test.

If you wish to perform a more precise test, you would need to build it using something like what is outlined in this journal article: 

Randles, Fligner, Policello and Wolfe (1980)
An Asymptotically Distribution-Free Test for Symmetry Versus Asymmetry
Journal of the American Statistical Association
Vol. 75, No. 369, Mar., pp. 168-172

[#6]

Thank you very much Dan.

I forget to change the type nominal. Now it works.

By the way, i find a ANOM with transfered rank test to use compare means for groups does not come form normal and symetric dist. but i try to understand how it works, because there is limited info in help and it gives ref. to nelson but i can not reach it. If you have basic knowledge i am happy to hear that.

Kind regards.