Robert Maillardet

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

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 varsigma 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 designed to assist understanding of what CIs say about replication, and they also extend the discussion to explain how p values give information about replication.

Discrete random variables

After these lectures, we will be able to: • Define discrete and continuous random variables. • Differentiate between discrete and continuous random variables. • Differentiate between when to use cumulative distribution functions and probability mass functions. • Give examples of at least four different discrete distributions. • Recall when to and how to use: – binomially distributed random variables. – geometric distributed random variables. – hypergeometric distributed random variables. – Poisson distributed random variables.