Use of linear mixed models for within subjects repeated measures experiment

#1
Hello,

I am trying to argue that I used the correct statistical test for a paper that is currently in review. I have formulated a counter-argument, but I'm not an expert so I wanted to make sure I am correct.

In my experiment, I measured how long it took for subjects to complete a task. The experiment has a single within-subjects factor (call it Task) with 3 levels. Each subject completed 8 trials in each condition (a total of 24 trials).

I analyzed my data in long format in SPSS. The table has these headers:Subject, Task, Trial, Time
I used a linear mixed model to look for an overall effect on Time due to Task. I selected Subject as the "Subjects" variable, and Task and Trial as the "Repeated" variables.
Specifying the model, I chose Time as the dependent variable, and Subject and Task as the factors. I specified Task to be a fixed effect and Subject to be a random effect (note that I did not use the "Subject Groupings" part of this model).

A reviewer of the paper said that I should not have "compared the times across all trials in each condition, as this violated data independence." They suggested that I should have averaged the data for each subject so that each subject contributed a single data point.

Am I correct in responding that by using a mixed effects ANOVA with Subject as a random effect, I account for the dependencies among each subject's repeated measurements?

Thank you!
 

spunky

Doesn't actually exist
#2
A reviewer of the paper said that I should not have "compared the times across all trials in each condition, as this violated data independence." They suggested that I should have averaged the data for each subject so that each subject contributed a single data point.
OK... i do remember from some time back that the syntax of SPSS in mixed-models menu thingy has to be modified slightly to actually get accurate estimates (i'm not sure whether this has been corrected in more recent versions) but, that issue aside, you're right and the reviewer's wrong. slap him/her with the first section of Chpt 14 from Cohen et. al.'s bible of everything regression (that blue book with the long, long title "applied multiple regression/correlation...somethin... something) and tell him/her to go google "ecological fallacy" and sit on a class of multilevel/hierarchical linear/mixed-effects/random-coefficients regression
 
#3
Haha, that is good to hear. I probably won't be doing any slapping, unfortunately, as we do need to make the reviewers happy...

The SPSS menu thing for linear mixed models is confusing, yes, and I'm not sure if I used it correctly. I tried to find good documentation of this, but I couldn't really understand the relationships between the "Subjects" and "Repeated" variables as well as the difference between a regular random effect, which is where I put Subject, and the "Subject Groupings" in the random effects configurations screen.

I was using the latest version of SPSS. I'm pretty sure that regardless of any minor differences those different configuration options would have played, the effects I was looking at were so big the p value would have always come out as "0.000" anyway.