I discussed this issue several years ago in a short conference presentation. You can view the slides here:

Presentation Silly or pointless things people do when analyzing data: 3. ...

I hope this helps.

Some key considerations

1. ANOVA and Normality assumption

ANOVA assumes that residuals (not necessarily raw data) are normally distributed and that variances across groups are homogeneous. If the sample size is large (typically n>30n > 30n>30 per group), the Central Limit Theorem suggests that the test may still perform adequately despite some deviations from normality. However, with smaller sample sizes or strong departures from normality, this assumption should be addressed.

2. To transform or not?

Transforming data (e.g., log, square root, or other transformations) to achieve normality can help meet assumptions of parametric tests, but it also changes the interpretation of results. For instance:

• A log transformation converts differences into multiplicative changes.
• A square root transformation affects variability in proportion to magnitude.

Before transforming, assess whether the transformed data genuinely meet the assumptions and whether the interpretation remains meaningful for your research question.

3. When to use non-Parametric tests

Non-parametric tests (e.g., Mann-Whitney U, Kruskal-Wallis) are robust to deviations from normality but generally have less statistical power compared to parametric tests when assumptions are met. They’re a good choice if:

• Normality cannot be achieved, even after transformation.
• The data include outliers that cannot be addressed otherwise.

4. Your specific scenario

Given your data (11 sampling expeditions, 2 sites, 10 samples per site), the following suggestions apply:

• Check the residuals of your ANOVA model to determine if the normality assumption is violated, rather than relying solely on histograms of raw data.
• Use Levene’s test or Bartlett’s test to assess homogeneity of variances.
• Consider generalized linear models (GLMs) or mixed-effects models if your data exhibit hierarchical structure (e.g., repeated measures across expeditions).

5. Large sample sizes (>50)

With larger sample sizes, parametric tests like ANOVA are typically robust to moderate deviations from normality. However, it is still good practice to check the residuals to confirm that the assumptions hold.

6. Impact on analysis quality

Proceeding with ANOVA without addressing violations of assumptions could lead to biased or incorrect conclusions. Transforming or using non-parametric alternatives ensures that your analysis aligns with the data’s structure and improves the validity of your findings.

In summary, transforming data or using non-parametric tests is context-dependent. Given your dataset’s characteristics, I recommend checking residuals, considering transformations if necessary, or exploring alternative models that accommodate non-normal data.

Hello Precious Uahomo. I agree with much of what you wrote, but I do not agree with your advice about using statistical tests of homogeneity of variance. As Box (1953) said, "in the commonly occurring case in which the group sizes are equal, or not very different, the analysis of variance test is affected surprisingly little by variance inequalities." One rule of thumb (e.g., in David Howell's Statistical Methods for Psychology) is that when the sample sizes are the same (or nearly so), ANOVA is robust to variance heterogeneity so long as the largest variance is no more than 4 times the smallest variance. (And some others have argued that this rule of thumb is conservative.)

Re testing for homogeneity of variance, Box (famously) added:

"To make the preliminary test on variances is rather like putting to sea in a rowing boat to find out whether conditions are sufficiently calm for an ocean liner to leave port!"

Another thing that I don't think either of us has mentioned (explicitly, at least) is that good statistical software these days will have "robust" options that can be used when it is felt that the variances are too heterogeneous. E.g., the UNIANOVA command in SPSS added a ROBUST sub-command several versions ago; and Stata users can estimate the model via the -regress- command and include a vce() option--e.g., vce(robust). I'm sure SAS, R, and other software people might be using have similar options.

Cheers,

Bruce

If you have a response variable with a non-normal error, using a Generalized Linear Model is the answer. For example when you are counting (e.g. number of animals of a certain species), your response variable (counts) must be non-normal, because it has a lower boundary (of zero). In such a case it is common (albeit not yet in your field as it seems) to use Poisson or negative binomial regression.

Transforming the response variable and non-parametric statistics are outdated and have the disadvantage that you can no longer make quantitative statements.

See https://schmettow.github.io/New_Stats/glm.html