# Help Understanding Repeated Measures Anova

#### Clairemarie63

##### New Member
Hi,
I am having trouble understanding a paper I read. The paper used both univariate repeated measures analysis of variance for within subjects effects and repeated measures of analysis of variance for between subject effects. The research paper I have read is looking at the effects of incubation temperature and egg size on hatchling size and growth in turtles. These turtles lay different size eggs and the researcher is proposing that the larger eggs incubated at a higher temperature grow faster (over 3 years) than large eggs incubated at a lower temperature. Therefore there are two temperatures. Basically they collected eggs from four females and randomly assigned eggs from each of the females to one of the 2 temperatures.
-From what I understand the researcher eventually needs to determine if clutch of origin had any effect because these are not actually individual replicates because they came from the same mother? Is this correct thinking? If so one would need to used an Ancova to do so?

Now when the author plots (ln of egg mass) on the x axis and (ln of mass at 3 years) on the y axis, he finds a significant effect for those placed in the higher temperature (r^2=0.59, p<0.01), but not for those placed in a lower temperature (p=0.12). I understand that this means that 59% of the time ln egg mass has an effect of the ln of the mass at age 3 (in high temperature), and that this number is a good correlation (considering this is nature?).

However, the author puts one table the following:
Results of the univariate repeated measures analysis of variance for within subject effects. The dependent variable is the residual of natural log-transformed hatchling mass and juvenille mass. With the following sources:
1. Age Class
2. Age Class*Temperature
3. Age Class*Clutch
4. Age Class*Temperature*Clutch
5. Error
He gives degrees of freedom, type III S, mean square, F value, and P values for each.
My question is if the p value is significant (or not), what does this mean for each source given?

I have a question also about the between subject effects in which the table looks similiar, but maybe I will wait to hear about this one before I ask.
Thanks,
Claire

#### JohnM

##### TS Contributor
Claire,

-From what I understand the researcher eventually needs to determine if clutch of origin had any effect because these are not actually individual replicates because they came from the same mother? Is this correct thinking? If so one would need to used an Ancova to do so?

Yes, your reasoning makes sense here.

======================

I understand that this means that 59% of the time ln egg mass has an effect of the ln of the mass at age 3 (in high temperature), and that this number is a good correlation (considering this is nature?).

No, an r^2 of .59 means that 59% of the variance in the y-variable is explained by the variance in the x-variable.

======================

My question is if the p value is significant (or not), what does this mean for each source given?

It means that the source is a significant (or not) source of variation (significantly different from 0 or "no" variation).

In other words, the F-statistic, which is a ratio of between groups variance to the within-groups or "inherent" variance, is significantly greater than 1.0, and therefore the means are different.

This link is a good source of info on repeated-measures ANOVA:
http://davidmlane.com/hyperstat/within-subjects.html

#### Clairemarie63

##### New Member
Thanks for the reply. I took a look at this website you gave me and it said " It is also assumed that each subject is sampled independently from each other subject." Will the fact that only four mothers were used for this experiment involving over twenty individuals make this repeated measured anova of within-subjects variable invalid?

Also I am still confused about how to read the results. Say for instance Age Class was significant in this test and so was Age Class*Temperature, but Age Class*Clutch was not. How exactly would I say this in words? Could you say that Age class has an effect on the independent variable, age class and temperature combined have an effect on the independent variable, but age class and clutch combined do not have an effect on the independent variable?

Claire

#### JohnM

##### TS Contributor
Invalid may be a bit strong, but it certainly does raise questions about projecting or generalizing these results to the population at large.

When an interaction is significant, it means that the effect of one variable is dependent on the level of another variable.

An analogy I like to use is the interaction of wind and temperature. If it's a warm day, a large difference in wind speed will not make you feel colder. But if it's a cold day, a large difference in wind speed will have profound effects on how cold you feel. So, the wind effect is dependent on the temperature.

When you describe these in words, you shouldn't say anything about Age Class alone if it has a significant interaction with another variable - you need to focus the write-up on the higest-order interactions that are significant.