The honest answer is that, as a PhD student, you are going to need to learn to conduct analysis of experiments that goes beyond the t-test.

You will need at least one graduate level course in analysis of experiments, books, and dedication.

My personal advice: do not miss the opportunity to learn analysis of experiments while in a PhD program.  Take advantage of the courses and faculty willing to help you.

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As a few answers indicate, this design is a somewhat complex one.  For now, you may need the help of someone in your department to help you specify the model, and decide what analysis is appropriate.

I'm not so sure how close your time points are, but you could look at cluster based permutation testing.  This is a weak method of FDR control but simple to apply. 

You could also use either a mixed or multivariate design anova, although you might be losing power if your sample sizes are not high enough. This would overcome having to do a large number of tests which would never survive a multiple comparisons correction.  Please feel free to get in touch if you wish to discuss further. Good luck!

A good source is

https://www.amazon.com/Large-Scale-Inference-Estimation-Prediction-Mathematical/dp/0521192498

I haven't used SPSS for awhile. In R it would just be

p.adjust(c(your p values), method = "BY")

for Benjamini, Hochberg, and Yekutieli method for FDR, but there are other options. 

Hi Britt, It sounds to me like you have a doubly multivariate repeated measures design - which, while easier enough to run in SPSS, is not so easy to interpret. You need to manually specify the constrasts in a syntax command file. If you do this, the analysis will control for Type 1 error. However, you will need a reasonable sample sie to start with but not too bad as this is repeated measures (which lessens the n required) but also between groups, so this power you might want to calculate.  Best wishes  Kate.

Your count of 200+ tests gives the pseudo reviewers a chance to comment on type 1 errors being high. How many outcomes do you have? how many times each outcome was used in the t-test- recount your number of t-tests- even though the total number of tests are high, are they high for a single outcome?

Sometimes stating upfront that you have a conservative p value of 0.01 will help.

http://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/FDR

The honest answer is that, as a PhD student, you are going to need to learn to conduct analysis of experiments that goes beyond the t-test.

You will need at least one graduate level course in analysis of experiments, books, and dedication.

My personal advice: do not miss the opportunity to learn analysis of experiments while in a PhD program.  Take advantage of the courses and faculty willing to help you.

*     *      *

As a few answers indicate, this design is a somewhat complex one.  For now, you may need the help of someone in your department to help you specify the model, and decide what analysis is appropriate.

An (apparently) easy way without loosing too much power could be

1) For the control vs all treatment comparaisons, you may search for "Dunnett's" test

2) You can then combine this with FDR/FWER control methods to apply the correct alpha level of each Dunnett test.

Note that you must choose between FWER and FDR control, because that corresponds to completly different ideas and interpretation of the results.

The choice between non-parametric and parametric as nothing to do with FDR/FWER control (but note that using parametric models with strong assumptions may allow an optimal FWER control, that is the one which keeps the highets power). Quite often in gene expression experiments, non-parametric tests are simply useless because of small sample size that makes non-parametric test unable to dect any difference, whatever its size is, when trying to control FWER or even FDR.

As suggested by others, an optimal solution would be a joint model of all the factors in your experiment and suited contrasts. But that also means strong assumptions, or complex models for which help of a statistician will be required.

Salvatore is right here. Don't get your statistics crowd-sourced from ResearchGate! It's OK for bailing people out with an interesting problem, but your question reveals that you need to understand a lot about what you are doing analysing your data if you are to stand over the methods and results.

Sign up for courses, and play around with your own data. I learned more statistics analysing my first research project than I learned as an undergrad.

And the short answer is that you are doing the wrong thing. No hypothesis that you can specify is tested using 216 t-tests. First write your hypothesis or hypotheses in simple language. Then identify the pattern that should be in the data if the hypothesis is right, then match that with a statistical test.

Otherwise you will find yourself having to invent hypotheses to account for a bunch of 'significant' t-tests, many of which are going to be false positives.