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Statistical methods 

Statistical methods
Statistical methods

Gail Williams

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date: 16 May 2022

Statistics is the study of mathematically based techniques used to collect, analyse, and interpret quantitative data. In public health, this occurs in a complex of biological, clinical, epidemiological, social, ecological, and administrative systems.

Sometimes we want to describe, explore, or summarize data without extending our findings beyond the coverage of the data we have—that is, the sample. More usually, however, we want to extend, or generalize, our findings from the sample to a larger group, sometimes called the ‘target’ population. In this situation, we need to consider carefully two aspects of our data collection. Firstly, what was the actual source of our data, and how did we select the sample from the population? If we deliberately excluded some persons in our sampling, or made it more difficult for some than others to be included in our sample, then the sample may not represent the population equitably—we may have a biased sample. Secondly, we expect that if we repeat the data collection, even under identical conditions, we will get somewhat different results. This variability, called sampling variability, needs to be taken into account in deciding how precisely findings from our sample reflect what is happening in the population.

Owing to the ready availability of high-speed computers, development of sophisticated programming languages and statistical software, and expansion in theoretical developments, we now have access to a wider range of statistical techniques than ever before. It is important that analytical methods used are appropriate to our sampling strategy, the type of data we have collected, and the research questions we want to answer. We then usually want to generalize our results to a population. This process of drawing conclusions about populations by using samples is called statistical inference.

In this chapter, we discuss the basic concepts that underpin the issues raised earlier. The ideas of probability theory are heavily involved in random sampling, which takes place under the assumption of a probability model that governs the selection of the sample. As we shall see, probability models are also involved in helping us quantify the uncertainty in our sample estimates. We will also discuss a range of statistical techniques which are in common usage, outlining the underlying assumptions, and focusing on interpretation. Finally, we will reflect on the implications of analytical method for study design, in relation to study size and power.

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