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1. Calculate corrected VARIANCE for each sample (NOT STANDARD DEVIATION)
Table for Sample 1: X, X-M, (X-M)^2;
s^2X = ∑(X-M)^2 / N - 1
Table for Sample 2: Y, Y-M, (Y-M)^2;
s^2Y = ∑(Y-M)^2 / N - 1
2. POOL the variances -- take an average of the two sample variances while accounting for any differences in the sizes of the two samples -- this is an estimate of the common population variance
dƒx = N -1
dƒy = N - 1
dƒtotal = dƒx + dƒy
s^2 pooled = (dƒx / dƒtotal) s^2X + (dƒy / dƒtotal) s^2Y
3. convert the pooled variance from squared standard deviation (variance) to squared standard error (another version of variance) by dividing the pooled variance by the sample size, first for one sample and then again for the second sample -- THESE ARE THE ESTIMATED VARIANCES FOR EACH SAMPLE'S DISTRIBUTION OF MEANS
s^2Mx = S^2 pooled / Nx
s^2My = S^2 pooled / Ny
4. add the two variances (squared standard errors), one for each distribution of sample means, to calculate estimated variance of the distribution of differences between means
S^2 difference = s^2 Mx + s^2 My
5. Calculate the square root of this form of variance (squared standard error) to get the estimated standard error of the distribution of differences between means
s difference = √s^2 difference
MAIN DIFFERENCE FOR INDEPENDENT SAMPLES T-TESTS is that we have kept all calculations as variances rather than standard deviations
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