Cherry Picking The Diamonds From The Stock Market

How do you statistically test the difference in returns from two stock indices?

I calculated my standard deviations and returns at geometric means.

I am a little confused as to how to treat the geometric mean. It seems likely to me that I should somehow be cautious as to what test statistic I use when I have returns at geometric means (and not an arithmetic means).

you pick up one…. then the other
whichever weighs more .

pick that one