I am looking to see if the means obtained in previous clinical testing is significantly different to the means obtained by remote testing. I was planning on using a One sample T-test however the remote data has violated normality assumptions.

I do not have access to anything other than the mean for the previously collected clinically data therefore cannot conduct many of the other non-parametric tests suggested online.

  • $\begingroup$ if the samples does not come from a normal distribution, you have the central limit theorem that states that the mean is distributed as a normal distribution, and so you can use the t-test to test your mean $\endgroup$ Mar 1, 2022 at 23:11

1 Answer 1


If the data do not provide normality, independent sample t-test non-parametric methods are used for comparisons.

Non-parametric methods are Wilcoxon rank sum test and Mann-Whitney U test according to dependent and independent variable differences.

Because it is non-parametric, the Wilcoxon method is based on the median, not the mean. (mu parameter)

Therefore, you need samples from the data for analysis.

  • $\begingroup$ Hi, Thank you! Unfortunately, we cannot retrieve the original comparison data as the researchers have deleted it! Do you happen to know if there is anything that is used to compare the two mean data values without having to use the medians? $\endgroup$
    – Gemma Mcarthur
    Mar 2, 2022 at 8:59
  • $\begingroup$ You can apply a t-test from population comparison tests with only the mean data. However, t test can be applied if normality can be achieved after shapiro or smirnov normality tests. For this reason, as far as I know, there is no comparison test that can be applied for data whose normality cannot be accepted and only the average is known. Sorry for not being able to help. $\endgroup$
    – Esad
    Mar 2, 2022 at 9:47
  • $\begingroup$ Hi! No problem thank you so much for clarifying! $\endgroup$
    – Gemma Mcarthur
    Mar 2, 2022 at 12:46
  • $\begingroup$ I don't see that the first sentence follows. For example, you could use a generalized linear model with a binary predictor to make various comparisons. In any case, with many kinds of non-normal distributions, the implication is that means may not be the best summaries any way. $\endgroup$
    – Nick Cox
    Mar 2, 2022 at 14:58
  • $\begingroup$ –1 Neither the sign rank, nor the rank sum test are tests for mean difference or median difference without additional and quite strict assumptions. $\endgroup$
    – Alexis
    Mar 4, 2022 at 2:06

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