OMB Meeting Book - January 8, 2015

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5.3. Huber’s method, which dynamically adjusts trimming to the empirical data distribution and then follows a procedure similar to 5.2. This method is an M-estimator. 5.4. Use the median absolute deviation (‘MAD’) from the median and a normalizing factor of 1.4826, i.e., s = 1.4826 MAD. 5.5. Plot a Q-Q normal graph, select the range of data which is linear in the center, and compute s as the slope of the line fit. Note that all of methods 5.1)-5.5) will result in a lower bound for s, and are therefore maximally liberal (in favor of the test method in question). These methods will generate comparable estimates of s for typical datasets. These methods are heavily dependent upon the normal distribution assumption, and are really only appropriate if it is known a priori that the data do, in fact, follow a normal distribution, and any deviation from this must, in fact, be error. It is the author’s opinion that methods 5.1) are due to an error in thinking . What starts as a valid ‘robust’ theory for estimates of location is improperly twisted into a heavily biased estimate of scale . In the author’s opinion, method 3) is best compromise for the use of PT data to develop estimates of reproducibility effects.

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Recommended to OMB by Committee on Statistics: 07-17-2013 Reviewed and approved by OMB: 07-18-2013