Null Hypothesis Definition and Examples, How to State


  1. What is the Null Hypothesis?
  2. How to State the Null Hypothesis

What is the Null Hypothesis?

Null Hypothesis Overview

The null hypothesis, H0 is the commonly accepted fact; it is the opposite of the alternate hypothesis. Researchers work to reject, nullify or disprove the null hypothesis. Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to reject the null hypothesis. Read on or watch the video for more information.

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Why is it Called the “Null”?

The word “null” in this context means that it’s a commonly accepted fact that researchers work to nullify. It doesn’t mean that the statement is null (i.e. amounts to nothing) itself! (Perhaps the term should be called the “nullifiable hypothesis” as that might cause less confusion).

Why Do I need to Test it? Why not just prove an alternate one?

The short answer is, as a scientist, you are required to; It’s part of the scientific process. Science uses a battery of processes to prove or disprove theories, making sure than any new hypothesis has no flaws. Including both a null and an alternate hypothesis is one safeguard to ensure your research isn’t flawed. Not including the null hypothesis in your research is considered very bad practice by the scientific community. If you set out to prove an alternate hypothesis without considering it, you are likely setting yourself up for failure. At a minimum, your experiment will likely not be taken seriously.


Not so long ago, people believed that the world was flat.
null hypothesis

  • Null hypothesis: H0: The world is flat.
  • Alternate hypothesis: The world is round.

Several scientists, including Copernicus, set out to disprove the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternate. Most people accepted it — the ones that didn’t created the Flat Earth Society!. What would have happened if Copernicus had not disproved the it and merely proved the alternate? No one would have listened to him. In order to change people’s thinking, he first had to prove that their thinking was wrong.

How to State the Null Hypothesis

How to State the Null Hypothesis from a Word Problem

You’ll be asked to convert a word problem into a hypothesis statement in statistics that will include a null hypothesis and an alternate hypothesis. Breaking your problem into a few small steps makes these problems much easier to handle.

How to State the Null Hypothesis

Example Problem: A researcher thinks that if knee surgery patients go to physical therapy twice a week (instead of 3 times), their recovery period will be longer. Average recovery times for knee surgery patients is 8.2 weeks. 

how to state the null hypothesis
Hypothesis testing is vital to test patient outcomes.

Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is “I expect the average recovery period to be greater than 8.2 weeks.”

Step 2: Convert the hypothesis to math. Remember that the average is sometimes written as μ.

H1: μ > 8.2

Broken down into (somewhat) English, that’s H1 (The hypothesis): μ (the average) > (is greater than) 8.2

Step 3: State what will happen if the hypothesis doesn’t come true. If the recovery time isn’t greater than 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or less than 8.2 weeks.

H0: μ ≤ 8.2

Broken down again into English, that’s H0 (The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2

How to State the Null Hypothesis: Part Two

But what if the researcher doesn’t have any idea what will happen?

Example Problem: A researcher is studying the effects of radical exercise program on knee surgery patients. There is a good chance the therapy will improve recovery time, but there’s also the possibility it will make it worse. Average recovery times for knee surgery patients is 8.2 weeks. 

Step 1: State what will happen if the experiment doesn’t make any difference. That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.

H0: μ = 8.2

Broken down into English, that’s H0 (The null hypothesis): μ (the average) = (is equal to) 8.2

Step 2: Figure out the alternate hypothesis. The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

H1: μ ≠ 8.2

In English again, that’s H1 (The  alternate hypothesis): μ (the average) ≠ (is not equal to) 8.2

That’s How to State the Null Hypothesis!

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Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.

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