I am analysing Western blot data. In the experiment, I am looking at the expression level of a certain protein of interest in the brains of wild-type and knockout mice. I have seen online that many biological measurements, especially from animals such as mice, are assumed to follow a normal distribution (and thus hypothesis tests such as t-tests and ANOVA can be applied). I have used a t-test to analyse my data, however, I was wondering why is it that measurements from mice are assumed to follow a normal distribution? Any insights are appreciated.

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    $\begingroup$ Does this answer your question? Do biological phenomena follow Gaussian statistics? $\endgroup$
    – Luigi
    Commented Aug 2, 2021 at 13:48
  • $\begingroup$ Many biologists (and reviewers) seem to lack a fundamental understanding of statistical testing. For me, it usually comes down to normality testing, and sample size. If I'm working with particularly small sample sizes, I'll often stick with non-parametric testing regardless of normality (and I don't think it's uncommon to see non-parametric tests in such reports). Second, I always test for normality prior to reporting a parametric test with normality assumptions. Along with any data transformations, normality testing should be reported in a paper's methods, but may not always be. $\endgroup$
    – MikeyC
    Commented Aug 2, 2021 at 19:02

1 Answer 1


The normal distribution is often used as a "default" distribution because it is in fact quite common in measurements overall. And indeed, whenever there are a bunch of small additive errors in a measurement, the central limit theorem leads us to expect that the distribution will approximate a normal distribution. This is not a safe assumption to make, however, because there are also many cases where the error is not dominated by small additive factors.

Indeed, gene expression is one of the phenomena that are definitely not normally distributed at the single-cell level! Instead, strong genetic expression should be expected to show a log-normal distribution, due to the multiplicative factors in the chemical rates involved. Low levels of expression tend to have a Gamma distribution instead. If there is feedback regulating the expression levels, of course, all bets are off, and even more so if you are considering a population-level measure rather than measures at the single cell level.

What typically will still have a normal distribution, however, is the error induced by an instrument as part of the measurement process (not the biological part of the assay, just the physical, e.g., measuring the intensity of a light shined through a sample). So if you assume a normal distribution, you are essentially placing a bet that the variation in your measurement process is higher than the biological variation. From my experiences with animal studies, I would say that this is rarely a safe bet to place.


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