Statistical Trick of the Day

January 30th, 2013

Did you know that you can combine two standard deviations? If the sample sizes of the two groups are equal, you don’t even need them! Just square the standard deviations to get variances, average them, and take the square root to turn the value back into an SD. If sample sizes are not equal, you can take the weighted average of the separate variances, then take the square root. Ta-da! I found this out working on Anthropomotron. One of the papers had almost all of the elements needed to calculate a confidence interval for a sample of males and females combined, except the data presented were separated by sex. A bit of Googling came up with the equal sample size solution and from there I figured that weighing would also work (and the number I got isn’t crazy).

Update: Wikipedia confirms weighing the variances, so I must be right! I didn’t think of accounting for the degrees of freedom like the article suggests.


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