Confidence intervals and replication: Where will the next mean fall?

Abstract

Confidence intervals (CIs) give information about replication, but many researchers have misconceptions about this information. One problem is that the percentage of future replication means captured by a particular CI varies markedly, depending on where in relation to the population mean that CI falls. The authors investigated the distribution of this percentage for σ known and unknown, for various sample sizes, and for robust CIs. The distribution has strong negative skew: Most 95% CIs will capture around 90% or more of replication means, but some will capture a much lower proportion. On average, a 95% CI will include just 83.4% of future replication means. The authors present figures desi..