How to show statistical equivalence between groups of data?

#1
I'm trying to determine if these two groups of data are equivalent. How do I show that mathematically?

I have conducted an experiment in which three samples were each measured at two time points as shown in the image. I would like to compare these data and demonstrate (with some sort of statistic - p-value or similar) that they are statistically equivalent (or not). How do I do this?

Also please don't say t-test because that's only useful for determining if two sets of data are different; it doesn't work for showing similarity (unless you use TOST). I know TOST is one option (but I'm not sure if I'm doing it right), what other options are there, and how do I do them on Excel?

Thanks!
 

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hlsmith

Not a robit
#2
You should probably find the difference between the two time points and run an equivalence test that the value do not differ from '0' given some margin (e.g., +/- 5%) - probably falls back under something like a TOST. You could also, just plot a histogram for the differences.
 
#3
Thanks for the response. I tried to do a TOST but I think I did it wrong because my two p-values were the same. So to perform a TOST, you first take the difference between the data sets, then run the one-tailed t-test on the difference? Is that correct? I didn't take the difference first...

Plotting is a good idea. I compared the data on bar charts and that works okay but I would like a number (such as a p-value or similar) that I could put in a response to a reviewer on a manuscript. Maybe confidence intervals would work?

Just out of curiosity, can you think of any other tests besides the TOST that I could use?
 

hlsmith

Not a robit
#4
There is probably some type of exact test, but you still need to state a margin (threshold that they can be similar within.

If this value is not your primary objective for the study, perhaps just calculating the differences and 95 percentile bootstrap confidence intervals would be enough. You could also plot this and attach it as a supplement figure if it was important.