#### Abstract

Observations on return to estrus from anestrus postpartum beef cows were used as the basis for a simulation study to develop a method to determine numbers of locations and animals per treatment per location to achieve a specified power of test. Estimates of among location and total variance were obtained by REML from the data set and then used to generate simulated data for the binomial trait. Each combination of several pre-determined factors was replicated 1000 times. Pre-determined factors were number of locations, number of animals per treatment per location, desired detectable difference due to treatment, alpha-probability level and ratio of among location to total variance. Two methods were used to test for treatment differences. In Method 1, simulated data were analyzed using a mixed model with the variance components used for the simulation based on estimates from the postpartum cow data. For Method 2, variance components were re-estimated from each replicate of the simulated data and used in the mixed model equations. The number of significant differences due to treatment was counted for the 1000 replicates. The fraction of replicates with significant differences is an empirical estimate of the power of the test. The comparison of power of test between the two methods indicates Method 2 may be preferable for empirical estimation of power of test.

#### Keywords

Simulation, Power, Binomial data

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EMPIRICAL ESTIMATES OF POWER FOR BINOMIAL DATA WITH MIXED MODELS

Observations on return to estrus from anestrus postpartum beef cows were used as the basis for a simulation study to develop a method to determine numbers of locations and animals per treatment per location to achieve a specified power of test. Estimates of among location and total variance were obtained by REML from the data set and then used to generate simulated data for the binomial trait. Each combination of several pre-determined factors was replicated 1000 times. Pre-determined factors were number of locations, number of animals per treatment per location, desired detectable difference due to treatment, alpha-probability level and ratio of among location to total variance. Two methods were used to test for treatment differences. In Method 1, simulated data were analyzed using a mixed model with the variance components used for the simulation based on estimates from the postpartum cow data. For Method 2, variance components were re-estimated from each replicate of the simulated data and used in the mixed model equations. The number of significant differences due to treatment was counted for the 1000 replicates. The fraction of replicates with significant differences is an empirical estimate of the power of the test. The comparison of power of test between the two methods indicates Method 2 may be preferable for empirical estimation of power of test.