Batch Size Effects in the Analysis of Simulation Output

Batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment. Several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and/or independence, and the resulting incorrect probabilities of the confidence interval covering the mean. This paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions. These effects include (1) correct probability of covering the mean, (2) an increase in expected half length, (3) an increase in the standard deviation and coefficient of variation of the half length, and (4) an increase in the probability of covering points not equal to the mean. For any sample size and independent and normal batch means, the results are (1) the effects of less than 10 batches are large and the effects of more than 30 batches small, and (2) additional batches have lesser effects on confidence intervals having lower confidence levels. The results also are useful in the context of using independent replications for establishing confidence intervals on the mean.