I have 4 (different sized) groups, each group having more than 20 values. Now I have made the following hypothesis:
The mean between these groups is the same and I have tested it with ANOVA getting a p-value of 0.12, i.e. I cannot reject the hypothesis.
Does that mean the mean between these groups is the same? Or else how can I test the null hypothesis that the mean between the groups is not the same, so that I can reject these null hypothesis to prove that the mean is the same?