I am new to statistics and have to do some analysing for a beginner project. However, I am so confused right now and have nobody that I can ask.
About the project experiment: We conducted a between-subjects-design with repeated measures. There were three conditions (A, B, C), 9 blocks each. Each participant was assigned to one of these conditions.
My hypothesis: My hypothesis is that the participants will be best in C, worse in B and the worst in A (C>B>A). Also, I hypothesize that the correctness will improve with increasing block-number.
My data: So I have a dataframe:
head(dat) participant condition block correctness 1 A 1 0.87 2 B 2 0.74
My question now is:
Does it make any sense to do an ANOVA or should I do another analysis?
What test should I use after the ANOVA?
(->three pairwise t-tests in order to compare A-B, B-C, A-C,
-> a Tukey HSD, or
-> other ANOVAs where I do pairwise conditions)?
I already conducted an ANOVA:
summary(aov(correctness ~ condition * block + Error(participant/block), dat)) Error: participant Df Sum Sq Mean Sq F value Pr(>F) condition 2 0.295 0.14761 1.711 0.186 Residuals 100 8.629 0.08629 Error: participant:block Df Sum Sq Mean Sq F value Pr(>F) block 8 4.619 0.5774 44.350 <2e-16 *** condition:block 16 0.312 0.0195 1.496 0.0942 . Residuals 800 10.416 0.0130
So, I conclude that there is a main effect of block: Block number influences correctness. Also, the correctness does not seem to differ in the conditions.
However, I also conducted pairwise t-tests, and they say that, f.e., Condition A and B differ significantly from each other.
I don't get why the ANOVA says that the conditions do not differ but the t-tests states otherwise? Also, I am really not sure whether I used the right test and which test I should conduct as post-hoc tests?