In general, the t-Test (and equivalently ANOVA) are relatively robust with regard to non-normality, especially with large sample sizes. So, if you have a small sample, I would use non-parametric tests, but otherwise the data as linear.

Despite the robustness of the t-tests etc for departures from normality of larger datasets, I would suggest you use non-parametric tests in this case (Wilcoxon/Mann-Whitney, Kruskal-Wallis).

The reason is that you have some evidence that some of the data is not normal. This opens the the question as to why are you using a normal based test for non-normal data, especially if you tested the data for normality hoping to use t-tests or ANOVA but have now found that the data may not be normal but then use the normal tests anyway.

Using non-parametric removes this question and one potential source of debate about your analysis.

This link maybe useful. https://www.researchgate.net/publication/256303889_Statistical_guidelines_for_Apis_mellifera_research

David L Morgan , I was unclear what you meant by "the data as linear." For example, for the t-test what variable are you saying should be linearly (or not linearly) related?

I should have said "interval."

Raymond Carragher, rank-based tests are not a panacea. See the following, for example.

Article The Wilcoxon-Mann-Whitney test under scrutiny

Zimmerman, D. W. (2003). A warning about the large-sample Wilcoxon-Mann-Whitney test. Understanding Statistics, 2(4), 267-280.

Zimmerman, D. W. (2000). Statistical significance levels of nonparametric tests biased by heterogeneous variances of treatment groups. The Journal of general psychology, 127(4), 354-364.

Georgia Saiani Mendes, can you report n, Mean & SD for each group? And can you explain why you want to do normality tests? If you are doing them as a precursor to t-tests or ANOVA, this is generally a bad idea, because the normality test is underpowered when n is low and (vastly) overpowered when n is large. HTH.

If the sample size is large enough, and both tests show same results then you can choose parametric test if most of your data are normally distributed or choose non parametric test if most data are not. But if both tests show different results, the best way is to log transform the data .