You have to keep the metric similar or your model will be estimating the wrong mean for the transformed time points. 

Why not use a log link rather than a data transformation? This will model the arithmetic mean (useful) rather than the geometric mean (hard to explain).

Thanks, that's helpful - I'm not familiar with log-link functions (or whether SPSS utilizes log link), but will look into it.

Are you sure that you need normality for each measurement point?

From what you wrote it seem you would like to run a linear mixed effect model.

The assumptions, for a linear mixed effects models are:

• The explanatory variables are related linearly to the response.

• The errors have constant variance.

• The errors are independent.

• The errors are Normally distributed.

So it is the residuals (errors) that have to be normally distributed and not the variables themselves.

You can get residuals from the "save" option within the analysis menu you use in SPSS. But I strongly encourage you to use some other software, such as R or stata. For example, the lme4 package within R is a very strong specialized package for dealing with such mixed models. It is fairly easy to check whether the assumptions hold true in R.

See this thread for example:

http://stats.stackexchange.com/questions/77891/checking-assumptions-lmer-lme-mixed-models-in-r

If you end up having to transform, by all means, transform the whole variable, not just some data points. Just be aware, that some transformations involve standardization, which might mask some of the differences you are looking for. Simple log transformation is fine though, its straightforward.

Thanks, that certainly makes a difference - I'll take a look at the lme4 package.