STATISTICAL CONCEPTS
Hypothesis Tests
When observing differences in data, a data analyst understands the possibility that these differences could be the result of random chance.

Suppose we want to know if men are more likely to sign up for a given programming class than women. We invite 100 men and 100 women to this class. After one week, 34 women sign up, and 39 men sign up. More men than women signed up, but is this a “real” difference?

We have taken sample means from two different populations, men and women. We want to know if the difference that we observe in these sample means reflects a difference in the population means. To formally answer this question, we need to re-frame it in terms of probability:

“What is the probability that men and women have the same level of interest in this class and that the difference we observed is just chance?”

In other words, “If we gave the same invitation to every person in the world, would more men still sign up?”

A more formal version is: “What is the probability that the two population means are the same and that the difference we observed in the sample means is just chance?”

These statements are all ways of expressing a null hypothesis. A null hypothesis is a statement that the observed difference is the result of chance.

Hypothesis testing is a mathematical way of determining whether we can be confident that the null hypothesis is false. Different situations will require different types of hypothesis testing, which we will learn about in the next lesson.