The null hypothesis is the proposition that implies no effect or no relationship between phenomena or populations. Any observed difference would be due to sampling error (random chance) or experimental error. The null hypothesis is popular because it can be tested and found to be false, which then implies there is a relationship between the observed data. It may be easier to think of it as a *nullifiable* hypothesis or one the researcher seeks to nullify.

The alternate hypothesis, H_{A} or H_{1}, proposes that observations are influenced by a nonrandom factor. In an experiment, the alternate hypothesis suggests that the experimental or independent variable has an effect on the dependent variable.

**Also Known As: **H_{0}, no-difference hypothesis

### How to State a Null Hypothesis

There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement.

For example, say a researcher suspects that exercise is correlated to weight loss, assuming a diet remains unchanged. The average length of time to achieve a certain weight loss is an average of 6 weeks when a person works out five times a week. The researcher wants to test whether weight loss takes longer if the number of workouts is reduced to three times a week.

The first step to writing the null hypothesis is to find the (alternate) hypothesis. In a word problem like this, you're looking for what you expect as the outcome of the experiment. In this case, the hypothesis is "I expect weight loss to take longer than 6 weeks."

This can be written mathematically as: H_{1}: μ > 6

In this example, μ is the average.

Now, the null hypothesis is what you expect if this hypothesis does *not* happen. In this case, if weight loss isn't achieved in greater than 6 weeks, then it must occur at a time equal to or less than 6 weeks.

H_{0}: μ ≤ 6

The other way to state the null hypothesis is to make no assumption about the outcome of the experiment. In this case, the null hypothesis is simply that the treatment or change will have no effect on the outcome of the experiment. For this example, it would be that reducing the number of workouts would not affect time to achieve weight loss:

H_{0}: μ = 6

### Null Hypothesis Examples

"Hyperactivity is unrelated to eating sugar" is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a null hypothesis.

Another example of a null hypothesis would be, "Plant growth rate is unaffected by the presence of cadmium in the soil." A researcher could test the hypothesis by measuring the rate of plant growth of plants grown in a medium lacking cadmium compared with the rate of growth of plants grown in a medium containing different amounts of cadmium. Disproving the null hypothesis would set the groundwork for further research into the effects of different concentrations of the element in soil.

### Why Test a Null Hypothesis?

You may be wondering why you would want to test a hypothesis just to find it false. Why not just test an alternate hypothesis and find it true? The short answer is that it's part of the scientific method. In science, "proving" something doesn't occur. Science uses math to determine the probability a statement is true or false. It turns out it's much easier to disprove a hypothesis than to ever prove one. Also, while the null hypothesis may be simply stated, there's a good chance the alternate hypothesis is incorrect.

For example, if your null hypothesis is that plant growth is unaffected by duration of sunlight, you could state the alternate hypothesis several different ways. Some of these statements might be incorrect. You could say plants are harmed by more than 12 hours of sunlight or that plants need at least 3 hours of sunlight, etc. There are clear exceptions to those alternate hypotheses, so if you test the wrong plants, you could reach the wrong conclusion. The null hypothesis is a general statement that can be used to develop an alternate hypothesis, which may or may not be correct.