Analytical method for detecting outlier evaluators

Table 1 Detected ‘outlier’ audiologists from AAA of CHEARS. Each audiologist’s coefficient estimate is compared with the 10% truncated mean of all audiologists’ coefficient estimates

Alternative	Power	\(\widehat{FDR}\)	Outlier Audiologists	Outlier Audiologists Corrected by FDR
\(H_{1,j}: \left\| \varvec{L}_{10\%, j}\varvec{\beta }\right\| =5\)	0.80	0.72	2, 4, 8, 13, 14, 15, 16, 17,	4, 13, 16, 41, 48
			22, 24, 28, 36, 39, 41, 42, 47,
			48, 49, 52, 54, 55, 57, 58, 59
\(H_{1,j}:\left\| \varvec{L}_{10\%, j}\varvec{\beta }\right\| =5\)	0.47	0.50	4, 13, 14, 15,	4, 13, 48^b
			22, 48, 54, 55^a
\(H_{1,j}: \left\| \varvec{L}_{10\%, j}\varvec{\beta }\right\| =10\)	0.80	0.44	4, 13, 14, 55	4, 13
\(H_{1,j}: \left\| \varvec{L}_{10\%, j}\varvec{\beta }\right\| =10\)	0.86	0.50	4, 13, 14, 22, 55	4, 13
-	(0.55, 1.00)	0.28	4, 13, 15, 16, 17, 22,	4, 13, 16, 22,
			24, 40, 41, 45, 48, 63	24, 40, 41, 48, 63

To compare the results to standard practice where 0.05 is used as the significance level, last row reports the results from using \(\alpha =0.05\) as the threshold for rejecting tests \(H_{0,1},\ldots , H_{0,68}\), where 68 is the number of audiologists in AAA of CHEARS; The range of the power of these 68 hypothesis tests under \(\alpha =0.05\) was reported in the Power column.
^a When we compare the coefficient estimates to the untruncated mean, an additional Audiologist 59 is detected;
^b An additional Audiologist 22 is detected after the FDR correction when we compare the coefficient estimates to the untruncated mean. For other situations, using the untruncated mean for comparison yields the same results as using the truncated mean

ISSN: 1471-2288