I would suggest that you look at the course notes of a real expert, Prof. Marie Davidian, here:

https://www4.stat.ncsu.edu/~davidian/st732/notes.html

Best, David Booth

I think Winer (Statistical Principles in Experimental Design, on p. 613) gives an example of such a design. He calls it a repeated measures analysis of covariance. See the attachment for the R script for this example

Chapter 4 of the notes that @David posted explain why 'modern' methods are preferred over 'classical' .

In my view I would used a two level mixed effects model with level 2 defined by the individual and level 1 defined by measurement occasion. This naturally follows the structure of the data you have and automatically allows for some element of dependence over time (compound symmetry), thereby mitigating against type 1 errors.

I would fit a series of more and more complicated models as you learn about you data ( because all models are wrong, some are useful) unless that offends you registered protocol. For example

Model 0

Two level random intercepts model around an overall intercept - this would give you mean of response and partition the unexplained variance into between individuals within individuals between occasions. You may want to look at residuals at each level to see if you have really aberrant values.

Model 1 additionally including time of measurement either categorical (0,1 2) or better (more power) the the actual decimal point time 0, 0.31 1.89. I am using zero so that you get a meaningful intercept, the mean of the response at baseline. I would have random intercepts and random slopes for time so each individual is allowed to have their own trajectory around the general trend. This will give you a very good idea of what can be explained; the covariance between slopes and intercepts is a key term as this will indicate whether the individuals are diverging in their trajectories (positive covariance)

Model 2 - add in the 4 factor group choosing coding so that the intercept is meaningful, eg no treatment at baseline. I presume that this is a level 2 variable in that individuals are only in one group and do not cross on occasions. The standard errors of estimated differentials will take account of the within individual dependence. You could stop here.

Model 3 : include the time by factor interaction I would do this as the trends for the interventions may be different, you are assuming that this is not the case, but you could test with a deviance statistic if this really the case .

Further models - I would include additional terms for heterogeneity ; this is getting advanced - as may be the interventions affect the variance as well as the mean.

This may help

a straightforward tutorial

http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/repeated-measures.pdf

see panel models

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

I agree with the approach Kelvyn Jones has suggested. Within that approach, you should be able to use contrasts to get the "comparison between four treatment groups at posttest and then at the follow up" you want. If you indicate what software you are using, someone may be able to give more details about how to do that. HTH.

Thank you all for your responses. I will follow what Kelvyn Jones and Bruce Weaver suggested. I did some analyses using mlwin in the past, however, this seems doable in SPSS, doesn't it? Any good resources with syntax that immediately comes to mind?

https://www.pilesofvariance.com/ has the syntax for many models including SPSS. The book is rather wordy, I prefer some equations, but it is fairly comprehensive, and it gives a lot of sound practice. I like the underlying idea that multiple models are needed to understand what is going,; all models are wrong but some are useful, to paraphrase George Box.

The IDRE website at UCLA also has many examples of code for multilevel models for all of the most popular packages. Try a search on .

Dear Ewelina Smoktunowicz

I hope this article benefiting you;

https://ntnuopen.ntnu.no/ntnu-xmlui/bitstream/handle/11250/2622330/no.ntnu%3Ainspera%3A37217695%3A34533089.pdf?sequence=1&isAllowed=y

Best regards,

Hamid

I haven't read the above replies, sorry for the possible replications. It seems that nobody referred to the method which uses baseline values as covariates which is very valid to your question Ewelina. Namely you can perform a linear mixed effects model analysis where baseline values are covariates. I don't see why your research question is not related to the interaction term Time*Group by the way.