The Best Procedure for Averaging Two Estimates of Standard Deviation

What is the best procedure for averaging two estimates of the standard deviation of a normally distributed trait?

Answer:

The best procedure for averaging two estimates of the standard deviation of a normally distributed trait is to take a weighted average of the estimated standard deviations, weighting them by their degrees of freedom, and then take the square root of the result.

When faced with the task of averaging two estimates of the standard deviation of a normally distributed trait, it is crucial to consider the variability of the estimates and the sample sizes (degrees of freedom) associated with each estimate. The most appropriate way to combine these estimates is by taking a weighted average of the standard deviations and then recalculating the overall standard deviation.

Choice B, which recommends taking a weighted average of the squares of the estimated standard deviations and then taking the square root of the result, is the correct approach. By incorporating the degrees of freedom into the weighting process, we give more weight to estimates with larger sample sizes as they are more reliable indicators of the true standard deviation.

The weighted average accounts for both the variability of the estimates and the sample sizes, providing a more accurate overall estimate of the standard deviation. This method ensures that potential biases from using simple averages are minimized, leading to a more reliable result.