The independent variable is promotion, and it is assigned to 3 groups. The dependent variable is sales revenue. I have 172 observations of sales revenue for promotion group 1, 188 for group 2 and 188 for group 3.
With this dataset, I want to know which promotion is more effective at increasing sales revenue.
I first thought of doing ANOVA with Tukey test to answer the question.
To see whether to do ANOVA I checked the normality assumption with qqplot and the plot seems to tell me that residuals are a bit bimodally distributed and Shapiro-Wilk's null hypothesis is rejected as well (Is the sample size is too big for shapiro-wilk test?).
I want to know if I can continue to do ANOVA with the data. If not, what statistical analysis is best for this case? Also, when the sample size is only 22 with the same qqplot result (say, null hypothesis of Sapiro-Wilk is not rejected) , can I do ANOVA?
Thanks!