Understanding basic numbers: examples from Brexit, Covid and common medical conditions

Abstract

The UK Brexit debate and the current Covid pandemic have been fertile grounds for people seeking poor use of statistics, and demonstrate a need to reiterate some basic principles of data presentation. Communicating basic numbers to convey the correct message is a vital skill for a public health professional but even basic numbers can be difficult to understand, and are susceptible to misuse. The first issue is how to understand ‘orphan’ numbers; numbers quoted without comparison or context. This leads on to the problems of understand numbers as proportions and how to make comparisons using proportions. Percentages, and in particular percentage changes, are also a major source of misunderstanding and the baseline percentage should always be given. The use of relative risk can also convey the wrong message and should always be accompanied by a measure of absolute risk. Similarly, numbers needed to treat should also refer to baseline risks. Communicating numbers is often more effective using natural counts or frequencies rather than fractions or proportions, and using pictorial representations of proportions can also be effective. The paper will also examine the problems of using simple ratios to try and adjust one continuous variable by another in particular the use of the BMI and for standardising death rates by institution. The misuse of reporting occurs in primary sources such as academic papers, but even more so in secondary reporting sources such as general media reports. It is natural to try and convey complex messages using a single summary number, but there are assumptions behind these summaries that should be questioned. It is usually better to give the individual numbers rather than a ratio of them.