# Data standardization in a repeated measures multilevel model

We have conducted a repeated measures experiment in which we have registered the response time (RT) of each subject in 21 trials in each of 2 conditions. I have some questions related to the best analysis we can conduct... First, to reduce individual variability between subjects, we have standardize "within subjects", by substracting the mean of 42 trials of the subject to each trial, and the dividing the results by the SD of the subject.

Our objective is to compare both conditions, but collapsing data of both conditions and comparing means is not an option... We think that a better solution is to carry out a multilevel repeated measures analysis (in SPSS), but we have many questions:

1. Is the standardization of data a problem for the analysis? Because after standarsization the mean of 42 trials of each subject is 0, and SD=1...

2. I guess that Condition and Trial are Fixed factors, and subjects are the random factors... is it correct?

3. Since each trial is expected to be correlated with previous and following, and this correlation with other trials is expected to be weaker as they are further in time, I think that the covarianze type for repeated measures is Autorregressive... is it correct??

I hope someone could help me, I think I really need it... :S

• I just wonder if you found any proper answer for the standardization problem. I have the same question now. I can imagine that for doing a repeated measure ANOVA this is better to do the standardization. But as I understood, multilevel analysis controls for between subject variation and within-subject between-observation variation separately. in this case I am in doubt about using the standardization or not. In case you got a proper answer know, this will be very helpful. Best, Hassan
– user40598
Feb 20, 2014 at 9:20

## 1 Answer

Jeff Rouder has done a lot of work on similar issues where he applied Bayesian hierarchical models for response time data. Analyzing these data with the out-of-the-box multilevel model is difficult to fully justify: such data tend to be skewed, with a clear left cut-off (reaction time), so as assumption of normality that you have to make with the standard multilevel software is dubious.

I would also imagine that standardization within subjects kills important information, as the mean and variance within a subject may be linked, which could help identifying the actual distributions you could use to model your RT data.

• Ok, I understand... I'll check Jeff Rouder site. But, just to be curious, do you think the kind of standardizarion that I have done is incompatible with a multilevel model per se; o just in this particular case (RT data)? Imagine that, with other kind of data (e.g. psychophysiological) after the standardization we obtain a normal distribution; do you think that, in that case, there would be any problem to fit a multuilevel model? Thank you for your answer! May 30, 2012 at 7:19
• It will still mask important information about the potential differences in scales and means if you do this by group. If you do this for the data set as a whole, you will underestimate the standard errors on your standardized coefficients, because you had suppressed some natural variability in your data. So I would advise against that unless ABSOLUTELY EVERYBODY IN YOUR LITERATURE does this, and there is no other way they know about. Jun 5, 2012 at 14:02
• Thank you, StasK, for your answer (I'm a newcomer and don't have enough reputation to mark your response as useful, otherwise I would). I've seen many papers using this kind of standardized scores in statistical analysis in my field, but not with multilevel models. So I think I'll follow your advice... Thank you! Jun 5, 2012 at 16:06