3.2. Hypothesis testing roundup

At this point it may be helpful to review some key ideas about hypothesis testing, and the relationship between sample and population.

The following videos are from a previous year’s version of the course so there may be a couple of unfamiliar terms, or mentions of ‘the exercise you did last week’ (which you haven’t heard of!) but I think overall these could be a useful resource for revising some ideas in hypothesis testing

Note in some of these videos I talk about confidence intervals; these are a useful concept but haven’t been covered on the course so far so feel free to let the idea wash over you if it isn’t making sense

3.2.1. Sample vs population

As scientists we always work with a sample of data, but we are interested in generaliing our results to the wider population.

3.2.2. What is the sampling distribution of the mean?

To determine statistical significance, we need to understand how much our test statistic would vary due to random chance across different samples drawn from the same population.

• The sampling distribution of the mean is the distribution you wuld obtain if you repeatedly took many different samples of size \(n\) from the population and calculated the mean for each sample

• The null distribution is the sampling distribution of the mean (or different test statistic) that we would expect to observe if the null hypothesis were true

3.2.3. Estimating the sampling distribution of the mean from a sample

The estimated sampling distribution of a statistic (based on a single observed sample) is not identical to the sampling distribution we would get if we were able to draw lots of different samples from the actual population.

3.2.4. The \(t\) distribution

The \(t\) distribution is a specific case of an estimated sampling distribution of the mean