Chapter 4 Inferential statistics

From a conceptual point of view, this week’s module might just be the most important that we cover in this subject. I don’t say that to freak you out, but in many ways it just is the genuine truth. The reason that this might be the most important one is because the topics that we cover in this module are ones that many people frequently misunderstand or misappropriate - to the point of scientific fraud.

Inferential statistics are the subject of very heated debate in statistics, primarily about whether p-values and the like are really the right way to do science and statistics. We won’t really go there because that’s neither here nor there in terms of what the aim of this module really is: to not only show you one way of hypothesis testing, but to also equip you with the knowledge needed to understand how other people test hypotheses - or, sometimes, fail to do so.

Before you go into this module - make sure that you have 5.4 Variability, 5.5 Distributions and 5.6 Central Limit Theorem firmly under your belt as they will be relevant here.

By the end of this module you should be able to:

• Describe the steps taken to test a statistical null and alternative hypothesis
• Correctly define a p-value
• Explain the difference between Type I and Type II error, and how these relate to statistical power
• Construct a basic confidence interval for a point estimate, and interpret it

Figure 4.1: xkcd: Null Hypothesis