Crossword Puzzles and the Null Hypothesis
Most Sundays I enjoy working on the crossword puzzle in my local newspaper. I typically fill it in with a pen since pencil can be hard to read on newspaper. Of course it can get messy as I make mistakes and have to write over them in ink.
I occasionally think of that comment all these years later. We academics can sometimes come off as though we are always right, although most of us know we are not. We even have a basic concept reminding us of this, called the null hypothesis.
If you have taken a statistics class, you’ve probably heard this term. Basically, the null hypothesis means that when we are testing any hypothesis we have to first consider the possibility that we are wrong.
Let’s say we hypothesize that there is a relationship between exam scores and hours spent studying; those who spend more time studying will have higher scores. We can conduct a simple survey asking about hours spent studying and compare this measure with the exam scores to test our hypothesis. Seems reasonable, right?
Technically, this is our alternative hypothesis. Although it sounds strange to call our research hypothesis the “alternative,” the use of this word reminds us that we must be open to being wrong. The null hypothesis is basically the opposite of our alternative hypothesis; in this case, the null hypothesis would be that there is no relationship between hours spent studying and higher test scores.
This is painful for instructors to consider—we want students to study! But we still have to admit that we might be wrong. We can word the null hypothesis in a variety of ways, so long as it represents a “nullification” of our research hypothesis. We might even offer a null hypothesis that students who spend less time studying will have higher test scores—even if this seems unlikely. Critically evaluating our hypotheses is a central part of the scientific method.
There is even a formal way to present and discuss the alternative hypothesis and null hypothesis. The alternative hypothesis (again, in this case that more time spent studying is related to higher test scores), is denoted by H1, while the null hypothesis is denoted by H0:
H0: More hours studying are not related to higher test scores
H1: More hours studying are related to higher test scores
Imagine that we have conducted a random sample of sufficient size to conduct a statistical test. In this case, we might choose to conduct correlation analysis, which tests for relationships between our two variables, hours studying and exam scores (note that correlation can not asses causation; we would need to conduct an experiment with a control group and an experimental group to do that).
Each statistical test uses slightly different mathematical measures—these are beyond the scope of this post—but they all enable us to test for statistical significance. This means that our findings are unlikely to be the result of chance, but instead indicate that a relationship between our variables exists.
Now back to the null hypothesis. If we conduct our statistical test and the measure is statistically significant, we typically can reject the null hypothesis in favor of the alternative hypothesis. If our findings were not statistically significant, we would fail to reject the null hypothesis.
Notice that either way we frame our results using the null hypothesis; the possibility that we are wrong remains front and center. And of course the result of one study doesn’t necessarily mean that something is proven true in all situations. We have to keep returning to the null hypothesis as we continue studying social phenomena.
Researchers might not like being wrong, but sometimes they are. Sometimes we have trouble admitting this. The null hypothesis is a constant reminder that we must be humble about our findings. Even when we write them in ink, we have to be ready for rewrites.