## 2.9 Null hypotheses

In the Monday Breakups activity, we explored the research question,

Are breakups more likely to be reported on Mondays?

Notice that the research question uses the phrase “more likely.” When we ask if something is “more likely”, we are comparing it to something else. What is the comparison that we are making? In other words, we might ask, “more likely, as compared to what”?

In the case of Monday breakups, the implicit comparison was with a “no effect” model, where breakups are equally likely every day. The “no effect” model gives us a baseline to compare our results to. Many statistical analyses involve a comparison between the observed data and a “no effect” model.

In the case of Monday breakups, we have the following:

• Observed evidence: In a random sample of 50 breakups, 13 (26%) were reported on Monday.
• “No effect” model: Breakups are equally likely to be reported on each day. The probability of a Monday breakup is 1/7 (~14%)

Because our research question involves a comparison, we compare the observed result with the “no effect” model. In this case, 26% > 14%, so it seems that breakups really are more likely on Mondays.

But wait! The observed result comes from a random sample of 50 breakups. Even if there really was no effect—that is, even if breakups were equally likely every day—we would expect to see some variation in the observed results from a random sample, just to due random chance. Maybe, just by chance, we got a sample with a lot of Monday breakups! Before we can make a comparison, we need to account for the role of randomness.

When we account for variation due to random chance, we can define the “no effect” model as: “breakups are equally likely each day, and and any variation in observed results is due to random chance.”

The “no effect” model is basically a hypothesis about how the world might be. We call this hypothesis a “null hypothesis.” Null hypotheses specify two things:

1. a “no effect” probability model, and
2. a source of variation.

For the Monday breakups study, the null hypothesis is:

Null hypothesis: Breakups are equally likely to be reported each day (14% probability each day). Any variation is due to random chance.

Statistical hypothesis testing involves a comparison between the observed result and the null hypothesis. The box below summarizes the key points about null hypotheses:

##### The null hypothesis
• Imagines a world where there is no effect or no pattern
• Used as a baseline to compare observed evidence to
• Specifies two things: a “no effect” probability model, and a source of variation