I'm a PhD student in molecular biology and I'm doing an experiment where I'm investigating the differences in protein levels (measured as mean intensities of the IHC images produced using a particular antibody, number of images per cell line, n =5) between four different cell lines. I am planning on doing a one-way ANOVA to determine whether there are any statistically significant differences between the cell lines. I know that one of the assumptions of ANOVA is that the experimental errors are normally distributed. I have used the Shapiro Wilks Test and determined that the data is normally distributed within each cell line. However, when I combined all 4 cell lines to produce a large dataset, the data was not normally distributed. I was wondering if I could proceed with my ANOVA in this case or should I do a non-parametric test, in other words, does ANOVA assume the normality within each particular group or the normality of all data points (coming from all 4 cell lines in my case) combined?

Best Wishes,

pito22