I have experimental results from two days where I wasnt able to keep the same conditions from day1 to day2, so I have two sets of data:

control day1 -- 2x treatment groups day1 control day2 -- 2x treatment groups day2

I intend to perform a t-test per treatment and day:

--> groupT1/day1 vs control day1

--> groupT2/day1 vs control day1

--> groupT1/day2 vs control day2

--> groupT2/day2 vs control day2

Is this the correct approach? I feel ANOVA does not make sense even though there are several group, since I want to compare each to the control.


Another issue is to compare the treatment groups against each other for both days. My idea is to do standard scaling fit to each control group (day1 and day2) and then transform the respective treatment groups based on the standard scaler.

Is this a correct approach?


The correct approach would be a 2 (day) by 3 (treatment group) ANOVA.

The interaction between day and treatment group will tell you whether the treatment effects vary by day. If they do, you can follow up with "slice" tests, where you slice along each day and essentially perform a oneway ANOVA for treatment group within each day. If any of the slice tests are significant, you can perform post-hoc pairwise contrasts between treatment groups to compare T1 to control and T2 to control within each day. Note this method uses the MSwithin from the 2 x 3 ANOVA for each test, which makes it different from performing a large set of t-tests like you propose. Also, you should put an alpha correction on these tests.

If the interaction is not significant, you can interpret the main effect of treatment group. If this effect is significant, you can then perform group-wise contrasts (T1 vs. control and T2 vs. control), which average across days (which is justified because you have determined day is not relevant to the treatment effect).


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