# Meaning of significant interaction in repeated measures ANOVA - larval survival

#### Raphaelle

##### New Member
Hello,

My research looks at the effects of ocean acidification on the larval development of crab larvae. I experimentally subjected crab larvae to three pH levels in seawater tanks (low, intermediate and ambient), each replicated in three tanks. To measure survival, I counted the number of surviving larvae at days 0, 1, 2, 4, 6, 10 and 14 of my experiment in each seawater tank. So for each pH treatment, I have three replicate survival counts for each time point. My goal is to determine whether pH had an effect on survival of crab larvae during my experiment.

I conducted a repeated-measures ANOVA with time as the repeated measure and pH as a fixed factor to analyse the data. I used the following code in R:

library(lme4)
library(lmerTest)
Crab.survival\$pH=as.factor(Crab.survival\$pH)
Crab.survival\$Time=as.factor(Crab.survival\$Time)
Crab.survival\$pHTank=paste(Crab.survival\$pH,Crab.survival\$Tank)
crab.rm=lmer(Survival~pH*Time + (1|Tank),data=Crab.survival)
summary(crab.rm)
anova(crab.rm,ddf="Satterthwaite")

Here is the ANOVA result:
Df Sum Sq Mean Sq F value Denom Pr(>F)
pH 2 57 28.6 2.5416 5.999 0.15866
Time 6 73764 12294.1 1094.1038 35.999 < 2e-16 ***
pH:Time 12 365 30.4 2.7080 35.999 0.01035 *

I have no significant pH effect but a significant pH:time interaction. So I wanted to make individual comparisons to see if there was a significant effect of pH on any given day and was instructed to use the following code:

difflsmeans(crab.rm, test.effs="pH:Time",ddf="Satterthwaite")

The output from this code gave me t-values and p-values for each individual comparison. I then used the following code to determine my critical Q value:

qtukey(p, nmeans, df)

I then calculated the individual q value for each individual comparison using:

q*=sqrt(2)*t, compared each value to the critical Q value and looked for values that exceeded the critical Q value.

I found that for some comparisons the q value exceeded the critical Q. However, none of the comparisons of pH treatments WITHIN a time point had a q value that exceeded the critical Q (although some had a significant p value).

So my question is: given that the pH main effect was non-significant and that the pH:time interaction was significant but that none of the individual comparisons that compared pH treatments WITHIN one time point were significant (significant p-value but none of the q value exceeded the critical Q), DOES pH AFFECT SURVIVAL OF MY CRAB LARVAE?

Any help would be appreciated. Thank you!

Raphaelle