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I have a distribution of shape sizes under two different (biological) conditions. From prior knowledge, I do expect there to be two populations. I fit each condition to a two-Gaussian mixture model. Here's the data:

Here's the data.

I want to know if the mean of the first gaussian (i.e. the left peak) is statistically different between the two conditions.

How could I perform a statistical test? I was thinking to do unpaired T-test, but use the mean and variance from the Gaussian fit, and estimate the N by counting all data points under each curve. Where the curves overlap, I would just divide the data according to the composition of the gaussian mixture model.

For example, if at area = 160, gaussian 1 is 60% and gaussian 2 is 40% of net mixture model (gaussian1+gaussian2), and I have 10 measurements, then I would have N=6 for gaussian 1 and N=4 for gaussian 2 at this area. This way I build up each gaussian with a finite number of observations. Then I would have all the parameters to calculate a unpaired t-test.

Has anyone come across a similar situation? How wrong is my proposed method? Please enlighten me!

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