Jo Hardin is a professor of mathematics and statistics at Pomona College. Her statistical research focuses on developing new robust methods for high throughput data. Recently, she has also worked closely with the statistics education community on ways to integrate data science early into a statistics curriculum. When not working with students or on her research, she loves to put on a pair of running shoes and hit the road.
One of the foundational aspects of statistical analysis is inference, or the process of drawing conclusions about a larger population from a sample of data. Although counter intuitive, the standard practice is to attempt to disprove a research claim that is not of interest. For example, to show that one medical treatment is better than another, we can assume that the two treatments lead to equal survival rates only to then be disproved by the data. Additionally, we introduce the idea of a p-value, or the degree of disagreement between the data and the hypothesis. And last, we dive into confidence intervals, which measure the magnitude of the effect of interest (e.g. how much better one treatment is than another).
In this chapter, you will investigate how repeated samples taken from a population can vary. It is the variability in samples that allow you to make claims about the population of interest. It is important to remember that the research claims of interest focus on the population while the information available comes only from the sample data.
In this chapter, you will gain the tools and knowledge to complete a full hypothesis test. That is, given a dataset, you will know whether or not is appropriate to reject the null hypothesis in favor of the research claim of interest.
You will continue learning about hypothesis testing with a new example and the same structure of randomization tests. In this chapter, however, the focus will be on different errors (type I and type II), how they are made, when one is worse than another, and how things like sample size and effect size impact the error rates.
As a complement to hypothesis testing, confidence intervals allow you to estimate a population parameter. Recall that your interest is always in some characteristic of the population, but you only have incomplete information to estimate the parameter using sample data. Here, the parameter is the true proportion of successes in a population. Bootstrapping is used to estimate the variability needed to form the confidence interval.