I'm working with a dataset that was collected to test the following [adapted] research question: Does listening to music (categorical x; 2 conditions: pre_music - post_music) affect test scores (y; continuous variable), and is that relationship modified by IQ level (z; continuous variable)?
A reprex dataset:
dat <- data.table(participant_id = rep(1:30, each = 2), music_condition = rep(c("pre", "post"), 30), test_score = rnorm(60, 50, 15), iq = rep(rnorm(30, 100, 15), each = 2))
iq was measured only once at the beginning of the experiment and is therefore repeated twice per each participant because the value does not change between conditions.
My first instinct was to make a model,
m1 wherein the effects of
test_score were tested (or, equivalently, get the p-value from a paired t-test):
lmer(test_score ~ music_condition + (1 | participant_id), data = dat) %>% summary()
No significant effect.
Then, to answer the second question about IQ moderating the aforementioned relation, my thought was to fit a second model,
m2, with music_condition*iq interaction:
lmer(test_score ~ music_condition*iq + (1 | participant_id), data = dat) %>% summary()
No moderating effect of IQ.
My question: is it preferred to report the p-value from
m1 to address the first research question, and the p-value from
m2 to address the second research question? Or should I use both p-values (music_conditionpre and music_conditionpre:iq) from
m2? Also, in the context of my research question, what does the
iq fixed effects represent in
m2 and shouldn’t it be exactly 1 because it does not change at all between conditions?