What is the correct method to test whether your real money monthly excess returns are similar to your backtest

I’m not great at statistics, but I believe its a test of whether the mean of my real money excess returns are statistically different than the mean of my backtest excess returns, without knowing whether the population / sample is normal, but knowing the sample mean / st dev and population mean / st dev… so is that a t-test?

Apologies in advance if I’ve butchered this

Yes t-test is good. Two-sample t-test.

Easiest for you to do in Excel?

Data>Data Analysis>t-Test: Two-Sample Assuming Unequal Variances (see image).

Call them in-sample and out-of-sample excess returns. Then Variable 1 is first column, Variable 2 is second column. Hypothesized mean diff = 0, click labels and perhaps use the default alpha(see image)

You are smart to use EXCESS RETURNS.

-Jim



perfect, thanks