# FOUNDATIONS

**This is the largest theme. It introduces the core foundational topics and terminology from which to build your statistical understanding and thinking skills. It covers many topics at a broad level; the aim is to give you the bigger picture of statistics straight away so that we can explore ideas with real examples early in the course, and also, so that you can orientate yourself with the bigger picture of statistics when we go into more details later in the course. **

**We first cover how data are organised and methods for exploring and summarising data (Topic 2: Understanding and exploring data). We then discuss the idea of a random sample from a population and the main distinguishing features of an experiment and an observational study (Topic 3: Basic study design principles). This is followed by an introduction to statistical inference (Topic 4). This topic focuses on the concepts that underlie statistical inference – sampling variation and sampling distributions; covers the logic and ideas behind confidence intervals (CI) and hypothesis tests and teaches you how to interpret CIs and p-values. These ideas apply to much of statistical inference, regardless of the type of statistic or statistical test. **

**To illustrate confidence intervals and hypothesis tests, we use the example of estimating a single population mean, a so called “one sample” example, and do all of our calculations based on something called the normal approximation. This is the simplest setting but sometimes this normal approximation is not appropriate, we will pick up on when this is so and what we should use instead in later themes which dig a little deeper into inference (theme 3) and consider simple comparisons (theme 4). **

**Lastly we briefly cover the very basics of probability and in particular its relationship to statistical inference (Topic 5). Many courses omit probability but we include it here for three reasons. First, probability underpins much of statistical inference, being used to express uncertainty so a little knowledge of it may give a deeper intuition of these topics. Second even a little bit of clear probabilistic thinking can help make sense of everyday events involving risk and chance, so it is an important part of statistical literacy. Lastly, probability is used directly in medical screening and diagnostic studies. **