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My purpose is to compare my data with the general population data derived from a published report. I can only extract mean, median, 5th, 95th and 97.5th percentiles from it. Also, My data is non-normally distributed. Can I use one-sample Wilcoxon signed rank test? But this test only compares the median and I am doubt whether is accurate. Thanks!

ttnphns
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user392974
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  • What sort of comparison are you interested in? – Galen Jul 23 '23 at 19:31
  • Please consider using free and open-source alternatives to SPSS. There are lots of high-quality options to choose from these days. – Galen Jul 23 '23 at 19:33

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The one-sample Wilcoxon test has the H0 that the distribution in the population is symmetric about the suggested value (test value). If the H0 is violated, that is either because (1) the distribution is symmetric about a different value or (2) the distribution is not symmetric per se.

If we assume the distribution is symmetric shape in the population, only then the test is the test of the median (and also of the mean, since median and mean coincide in a symmetric population). [Further, if the distribution is normal in the population, you may use one-sample t-test instead of Wilcoxon.]

So, is the distribution in your population symmetric shape or not? If not, the test is useless. [If you do not believe me, create a variable with very asymmetric distribution and test it against its own observed median value; the Wilcoxon test will be significant!]

If your population is definitely asymmetric shape, use more general (though less powerful) one-sample Median test instead. The one-sample Median test is not found in SPSS as a special option, but it is fully equivalent to the Sign test between var1 = your variable (sample) vs var2 = constant variable equal to the test value. So may use that.

ttnphns
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Yes, the typically recommended test in this situation would be the one sample Wilcoxon signed-rank test.

In SPSS, you can enter your population median into the "hypothesized median" box within Non-parametric tests...One sample settings window.

However, some sources suggest that with large samples, t-test would be OK to use even with non-normal data. Top response to this question deals with this topic quite comprehensively.

Sointu
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