I have survey responses from people from 10 countries (sample range from 10 to 71 response per country) and I am trying to see if there are significant differences between the people of each country and the total sample size.
I conducted 2 tests via Excel Analysis Pack (I don't have a more advanced program on my office computer and I don't have admin privilege, and I couldn't get my data to load in R):
ANOVA: Single factor I conducted an ANOVA across all 10 countries, and my p value was 0.225, with F < F Critical. I took the result to mean that there were no significant differences between the groups, although I would have thought there is because the means of some of the group varies quite a lot.
T-test (two sample assuming unequal variances) I then conducted t-tests between the sample of one country vs all the responses in all the countries. I conducted this 10 times, one for each country. After that, I realized that 3 of my countries showed significant differences (t-stat > t-critical for two tail) from the total sample size.
May I know why my ANOVA turned up negative significant difference although the individual t-tests showed that there were some differences? Am I doing my analysis wrong?