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. 2007 Aug;42(4):1718–1738. doi: 10.1111/j.1475-6773.2006.00661.x

Table 2.

Effect of Random Measurement Error (Reliability = 0.25) on Outcome Estimation Based on Classical Test Theory*

“True” Proportion of Deaths Meeting the Threshold for Being Rated “Preventable” Frequency of “True Positives” Frequency of “False Positives” “Estimated” Proportion of Deaths Meeting the Threshold for Being Rated “Preventable”
0.99 0.88 < 0.01 0.88
0.95 0.78 0.02 0.79
0.70 0.49 0.11 0.60
0.50 0.33 0.17 0.50
0.30 0.19 0.21 0.40
0.05 0.02 0.18 0.21
0.01 < 0.01 0.12 0.12
0.005 < 0.01 0.10 0.10
*

These calculations are based upon methods described in Oppenheimer and Kher (1999) and assume that both the underlying measure of preventability and the error term (random measurement error) are independent and normally distributed.