It is always a good idea to check the assumptions of normality and homoscedasticity in the residuals of statistical models. I suggest using a graphical approach rather than a specific test. A plot of residuals versus expected and a q-q plot work well.
The reason is that they are necessary assumptions for a mathematical proof that the statistical method works as advertised. If the assumptions are ignored, then there is a chance that the results from the statistical tests are misleading.
The source of the data is essential for you and people reading about your research. It makes no difference to the statistics. The values 12, 17.8 and 15 have a mean of 14.93 no matter if the values are the length of three laboratory fish, the weight of ears of corn, or the stock prices of three companies.
I like to add that the of normality and homoscedasticity in the residuals are the two basic assumptions made in most of the statistical methods of analysis of data. Accordingly in order to be confident on the accuracy of the findings of data analysis, it is necessary to examine whether the assumptions of normality and homoscedasticity in the residuals are valid for the data set used in analysis.
I do agree with Jacó Joaquim Mattos's comment that it is a good questio. I like to add one more comment that it is a genuine question also. Moreover, this question is essential to be treated as a question/problem for research. I think there is necessity of research for obtaining the answer to this question.