Misunderstood-Hypothesis Testing
The most misunderstood, and difficult, concept for students studying statistics to understand is hypothesis testing.
In statistics, we want to study populations. Because populations are very large and difficult to study, we use information from a sample taken from the population to draw conclusions about the population. In particular, we want to test claims about population parameters (i.e. a population mean or a population proportion) through a process called hypothesis testing. Basically, a hypothesis test is a statistical procedure that involves checking if the information obtained from a sample supports an assumption or claim made about a population. At the end of a hypothesis test, we make a decision about whether or not we believe the claim made about the population.
Hypothesis testing is one of the most important, and widely used, topics in the area of inferential statistics. For example, hypothesis testing is used to:
- Test claims about population means, population proportions, or population variances.
- Test the difference between two population means, two population proportions, or two population variances.
- Goodness-of-fit tests.
- Tests of independence of two categorical variables.
- Analysis of variance.
- Testing the validity of multiple regression models.
An analogy I use to help students understand the concept of a hypothesis test is a criminal trial where the students are jurors for the trial. The jury is presented with two hypotheses about the defendant, only one of which is true: the defendant is innocent (the null hypothesis) and the defendant is guilty (the alternative hypothesis). The law requires that the jury assume the defendant is innocent (i.e. the null hypothesis is true) unless proven guilty. During the trial, evidence is presented by the crown attorney. The jurors must test the hypothesis that the defendant is innocent against the evidence presented. At the end of the trial, the jurors will deliver one of two verdicts: “Guilty” (the evidence is strong enough to reject the hypothesis that the defendant is innocent) or “Not Guilty” (the evidence is not strong enough to reject the hypothesis that the defendant is innocent).
The use of a trial as an analogy to explain the ideas of a hypothesis test is very common because a trial perfectly mirrors the concept of a hypothesis test. In a statistical hypothesis test, we have two hypotheses (claims about the population): the null hypothesis and the alternative hypothesis. Only one of these two hypotheses is true, and we use the hypothesis test procedure to determine which hypothesis is most likely true. The hypothesis test is conducted assuming the null hypothesis is true. Evidence is presented that is weighed against the null hypothesis. If the evidence is strong enough, we reject the null hypothesis in favour of the alternative hypothesis (i.e. the evidence is strong enough to convince us that the null hypothesis is false and the alternative hypothesis is true). If the evidence is not strong enough, we do not reject the null hypothesis (i.e. the evidence is weak and we continue to believe the null hypothesis is true).
TweetExample for "Misunderstood-Hypothesis Testing":
https://upload.wikimedia.org/wikipedia/commons/4/41/Scale_of_justice.png
Leave a Reply