I am using ANOVA with repeated measures to test significance between males and females results of an experiment during which participants had to evaluate 7 stimuli in 2 conditions (EXP1 and EXP2).
The problem is that even if from results it is clear that there are significant differences between males and females, I don´t get significance in the ANOVA results. Definitively there is an error, because results cannot be non-significant. Indeed looking at the means for each stimulus, it is possible to notice that males gave always higher evaluations than females.
To prove this I discarded for a moment the effect of the repeated measures, and I performed an ANOVA separately on both the two conditions (EXP1 and EXP2) during which the evaluations were given. What I get is significant differences between males and female, in both EXP1 and EXP2.
Now, why when I perform the ANOVA with repeated measures I don´t get the same behavior?
The structure of my table is the following: subject, stimulus, condition, sex, response. The design is the following:
- sex is a between-subjects factor (with two levels)
- stimulus is a within-subjects factor (with 3 assumed levels)
- condition is a within-subjects factor (with 2 levels)
- all factors are fully crossed
subject stimulus condition sex response subject1 gravel EXP1 M 59.8060 subject2 gravel EXP1 M 49.9880 subject3 gravel EXP1 M 73.7420 subject4 gravel EXP1 M 45.5190 subject5 gravel EXP1 M 51.6770 subject6 gravel EXP1 M 42.1760 subject7 gravel EXP1 M 56.1110 subject8 gravel EXP1 M 54.9500 subject9 gravel EXP1 M 62.6920 subject10 gravel EXP1 M 50.7270 subject1 gravel EXP2 M 70.9270 subject2 gravel EXP2 M 61.3200 subject3 gravel EXP2 M 70.2930 subject4 gravel EXP2 M 49.9880 subject5 gravel EXP2 M 69.1670 subject6 gravel EXP2 M 62.2700 subject7 gravel EXP2 M 70.9270 subject8 gravel EXP2 M 63.6770 subject9 gravel EXP2 M 72.4400 subject10 gravel EXP2 M 58.8560 subject11 gravel EXP1 F 46.5750 subject12 gravel EXP1 F 58.1520 subject13 gravel EXP1 F 57.4490 subject14 gravel EXP1 F 59.8770 subject15 gravel EXP1 F 55.5480 subject16 gravel EXP1 F 46.2230 subject17 gravel EXP1 F 63.3260 subject18 gravel EXP1 F 60.6860 subject19 gravel EXP1 F 59.4900 subject20 gravel EXP1 F 52.6630 subject11 gravel EXP2 F 55.7240 subject12 gravel EXP2 F 66.4220 subject13 gravel EXP2 F 65.9300 subject14 gravel EXP2 F 61.8120 subject15 gravel EXP2 F 62.5160 subject16 gravel EXP2 F 65.5780 subject17 gravel EXP2 F 59.5600 subject18 gravel EXP2 F 63.8180 subject19 gravel EXP2 F 61.4250 ..... ..... ..... .....
As you can notice each subject repeated the evaluation in 2 conditions (EXP1 and EXP2).
What I am interested in is to know if there are significant differences between the evaluations of the males and the females (both at global level and for each stimulus).
This is the command I used to perform the ANOVA with repeated measures:
aov1 = aov(response ~ sex*stimulus*condition + Error(subject/(stimulus*condition)), data=scrd) summary(aov1)
Doing so I don´t get significance for the differences between males and females.
Instead if I perform the ANOVA on the two subtables of EXP 1 and 2 I get significant differences.
table_EXP1 <- subset(scrd, condition == "EXP1") table_EXP2 <- subset(scrd, condition == "EXP2") fit_table_EXP1 <- lm(response ~ stimulus*sex, data=table_EXP1) anova(fit_table_EXP1) fit_table_EXP2 <- lm(response ~ stimulus*sex, data=table_EXP2) anova(fit_table_EXP2)
How can this be possible? Is it a contradiction?