I have two sets of data collected from two groups (group 1 in red, group 2 in blue). Each data set has been fit with a sigmoid with 4 parameters: Bottom Plateau, Top Plateau, Point of Inflection, and Slope at Point of Inflection. So for each group, I now have an estimate of the four parameters as well as confidence intervals (not depicted) for each parameter:
My questions is this: how do I test whether a specific parameter, for example the Point of Inflection, is significantly different between the two models?
One idea I had is to take the estimates for all the subjects in a group and doing an independent samples t-test for each of the four parameters. I'm not sure if a) this would be a valid way to test for statistically significant differences and b) is there a better way to do it.
Thank you for your help!
Best Answer
I think you can use a t-test for this, so long as you can consider the inflection point as independent of your other parameters. If the parameters aren't independent (from your description I would guess this is more likely), you can also consider using a Hotelling's $T^2$ test to test whether your first set of parameters is different from the second set. The Hotelling's $T^2$ test is the multivariate generalization of the t-test.
The important thing to think about is what it means to be "significant". How different do these parameters have to be for them to really physically be different in your situation?