I am analysing 3 tests applied to the same sample of students. I correlated the results and then ran an ANOVA to check for statistical significance and a post-hoc test to see where the difference originated. The ANOVA results do not confirm the correlation results. For example with the correlation I found tests 2 and 3 shared variance presented a value of 50%; with ANOVA I found a significant difference between the mean score for reading section 2 (M= 30.24 ,SD= 15.5) and reading section 3 (M=34.77, SD=13.8). Why is this so? Should I omit the correlation part?
ANOVA and correlation in this context do completely different things.
ANOVA tests whether there is a difference in the mean scores on the three tests. Correlation tests whether there is a linear relationship between pairs of tests.