A good friend of mine asked me recently about how to do A/B testing. As he explained, A/B testing refers to the process in which when someone visits a website, the site sends them to one of two (or possibly more) different ‘landing’ or home pages, and which one they are sent to is chosen at random. The purpose is to determine which page version generates a superior outcome, e.g. which page generates more advertising revenue, or which which page leads a greater proportion of visitors to continue visiting the site.

# Jonathan Bartlett

## The difference between the sample mean and the population mean

Someone recently asked me what the difference was between the sample mean and the population mean. This is really a question which goes to the heart of what it means to perform statistical inference. Whatever field we are working in, we are usually interested in answering some kind of question, and often this can be expressed in terms of some numerical quantity, e.g. what is the mean income in the US. This question can be framed mathematically by saying we would like to know the value of a parameter describing some distribution. In the case of the mean US income, the parameter is the mean of the distribution of US incomes. Here the population is the US population, and the *population mean* is the mean of all the incomes in the US population. For our objective, the population mean is the *parameter* of interest.

## When is complete case analysis unbiased?

My primary research area is that of missing data. Missing data are a common issue in empirical research. Within biostatistics missing data are almost ubiquitous – patients often do not come back to visits as planned, for a variety of reasons. In surveys participants may move in between survey waves, we lose contact with them, such that we are missing their responses to the questions we would have liked to asked them.