Interval estimation of the intraclass correlation coefficient based on Bartlett’s score procedure

Summary

We derive confidence interval procedures for the intraclass correlation coefficient σ based on the likelihood score, the bias corrected score and the bias and skewness corrected score. These procedures are then compared, through simulation, with six other procedures, compared by Donner and Wells (1986), in terms of coverage probabilities and coverage lengths. A methods due to Thomas and Hultquist (1978, the BAL method) and the method based on the maximum likelihood estimate of σ (the ML method) provide, on the average, the shortest lengths. Both these methods are overly liberal. Another method of Thomas and Hultquist (the TH method) and the method based on Fisher’s Z-transform (the F method) provide largest lengths, on the average. The TH method is liberal and the F method is overly conservative. The remaining methods, on the average, clump together in terms of average coverage lengths. However, the bias corrected score procedure (the BAB Method) performs best in terms of coverage probabilities, in the sense that the coverage probabilities are closest, on the average, to the nominal confidence coefficient. A closer look at the simulation results indicate that when σ is very small (i.e. σ ≤ .1) the BAL method is best, otherwise the BAB method is best.