I am asking this because I like to see if X and Y have significant differences, when X = (A + B)/2 and Y = (C + D)/2; A, B, C, and D were measured 100 times each. I will need the mean, SD, and N for X and Y for a t-test between X and Y.

Thanks,

- Thread starter RyanZheng
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I am asking this because I like to see if X and Y have significant differences, when X = (A + B)/2 and Y = (C + D)/2; A, B, C, and D were measured 100 times each. I will need the mean, SD, and N for X and Y for a t-test between X and Y.

Thanks,

Thanks. I was actually using SD and thought that error propagation works for both SD and SE. Correct me if I am wrong. Any insight on this will be helpful.

My experience of error propagation goes like this.

Find the SE of the means A and B (=SD/sqrt(n)). These give the uncertainties in A and B or SEa and SEb. This is where the n comes in.

Find A+B and the uncertainty in A+B = SEa+b =sqrt(SEa^2+SEb^2) (the notation is a bit wobbly but you'll get the idea. I have always used a table layout.)

Find X and the uncertainty in X = SEx = 1/2 the uncertainty in A+B = 1/2.SEa+b

Repeat for the uncertainty in Y SEy.

Find Y-X and the uncertainty in Y-X = SEy-x =sqrt(SEx^2+SEy^2)

The value of Y-X is tested against 0 using SEy-x.

Strictly this test should use the df of Y-X which I suspect is 399, but it wouldn't matter much if you used 100, or 200, or 400 df or used a z test, or just used 2*SEy-x to get a 95% CI on Y-X. Then ask does 0 lie within 2*SEy-x of the difference?