The null hypothesis, H0, is the commonly accepted fact; it is the opposite of the alternative hypothesis. Researchers work to reject, nullify or refute it. Researchers propose an alternative hypothesis, one that they believe explains a phenomenon, and then work to reject it.

## Why is it called "null"?

The word "null" in this context means that it is a commonly accepted fact that researchers work to nullify. It does not mean that the statement is null (i.e., that it means nothing) in itself. (Perhaps the term should be called the "voidable hypothesis," as that would give it less confusion.)

## How the null hypothesis works

It is a theory based on insufficient evidence that requires further testing to prove whether the observed data are true or false. For example, a null hypothesis statement may be "the growth rate of plants is not affected by sunlight." It can be verified by measuring the growth of plants in the presence of sunlight and comparing it with the growth of plants in the absence of sunlight.

Rejecting the null hypothesis lays the groundwork for further experimentation and seeing if there is a relationship between the two variables. Rejecting it does not necessarily mean that the experiment has not produced the required results, but rather sets the stage for further experimentation.

## Differentiating the Null Hypothesis

To differentiate it from other forms of hypothesis,a null hypothesis is written as H0, while the alternative hypothesis is written as HA or H1. A significance test is used to establish confidence in a null hypothesis and determine the possibility that the observed data are not caused by chance or manipulation of the data.

The researchers test the hypothesis by examining a random sample of plants grown with or without sunlight. If the result shows that there is a statistically significant change in the observed change, it is rejected.

## What is an alternative hypothesis?

An alternative hypothesis is the inverse of a null hypothesis. An alternative hypothesis and a null hypothesis are mutually exclusive, meaning that only one of the two hypotheses can be true.

There is statistical significance between the two variables. If the samples used to test the null hypothesis are false, it means that the alternative hypothesis is true and that there is statistical significance between the two variables.

## Why do I have to try it? Why not test an alternative hypothesis?

The short answer is that, as a scientist, you are obliged to do so; it's part of the scientific process. Science uses a battery of processes to test or disprove theories, making sure that any new hypotheses have no flaws. Including a null hypothesis and an alternative is a safeguard to ensure that your research is flawless. Not including the null hypothesis in your research is considered a very bad practice on the part of the scientific community. If you set out to prove an alternative hypothesis without considering it, you are likely doomed to failure. At the very least, your experiment may not be taken seriously.

## Purpose of hypothesis testing

Hypothesis testing is a statistical process that involves testing a hypothesis about a phenomenon or a population parameter. It is a fundamental part of the scientific method, which is a systematic approach to evaluating theories through observations and determining the probability that a claim is true or false.

A good theory is one that can make accurate predictions. For an analyst who makes predictions, hypothesis testing is a rigorous way to back up their prediction with statistical analysis. It also helps to determine whether there is sufficient statistical evidence to support a given hypothesis about the population parameter.

## The logic of the null hypothesis test

It is a formal approach to deciding between two interpretations of a statistical relationship in a sample. An interpretation is called a null hypothesis (often symbolized as H0 and read as "H-naught"). This is the idea that there is no relationship in the population and that the ratio in the sample only reflects a sampling error. Informally, it is that the relationship of the sample "happened by chance". The other interpretation is called the alternative hypothesis (often symbolized as H1). This is the idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population.

## Testing Techniques

Again, any statistical relationship in a sample can be interpreted either way: It may have occurred by chance or it may reflect a relationship in the population. Therefore, researchers need a way to decide between the two. Although there are many specific null hypothesis testing techniques, they are all based on the same general logic. The steps are as follows:

Suppose for the moment that the null hypothesis is true. There is no relationship between population variables.

Determine the probability of the sample relationship if the null hypothesis is true.

If the sample ratio is extremely unlikely, reject the null hypothesis in favor of the alternative hypothesis. If it is not extremely unlikely, keep the null hypothesis.

#### Mehl and his colleagues conclusions

Following this logic, we can begin to understand why Mehl and his colleagues concluded that there is no difference in loquacity between women and men in the population. In essence, the following question was posed: "If there were no differences in the population, how likely is it that we will find a small difference of d = 0.06 in our sample?"

His answer to this question was that this sample relationship would be quite likely if the null hypothesis were true. Therefore, they maintained the null hypothesis, concluding that there is no evidence of a sex difference in the population. We can also see why Kanner and his colleagues concluded that there is a correlation between discomfort and symptoms in the population. They wondered, "If the null hypothesis were true, how likely is it that we will find a strong correlation of +.60 in our sample?" His answer to this question was that this relationship in the sample would be quite unlikely if the null hypothesis were true. Therefore, they rejected the null hypothesis in favor of the alternative hypothesis, concluding that there is a positive correlation between these variables in the population.

## Probability of Sample Outcome

A crucial step in testing is to find the probability of the sample result if the null hypothesis were true. This probability is called the p-value. A low p-value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis. A high p-value means that the sample outcome would be likely if the null hypothesis were true and leads to the retention of the null hypothesis.

But how low must the p-value be for the sample result to be considered unlikely enough to reject the null hypothesis? In testing, this criterion is called α (alpha) and is almost always set at 0.05. If there is less than a 5% chance of obtaining a result as extreme as that of the sample if the null hypothesis were true, then the null hypothesis is rejected.

When this occurs, the result is said to be statistically significant. If there is more than a 5% chance of obtaining a result as extreme as that of the sample if the null hypothesis is true, then the null hypothesis is maintained. This does not necessarily mean that the researcher accepts the null hypothesis as true, but that there is currently insufficient evidence to conclude that it is true. Researchers often use the expression "do not reject the null hypothesis" instead of "retain the null hypothesis", but they never use the expression "accept the null hypothesis".

###### Example:

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

Null hypothesis: H0: The world is flat.

Alternative hypothesis: The world is round.

Several scientists, including Copernicus, set out to refute the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternative. Most accepted it - those who didn't created the Flat Earth Society! What would have happened if Copernicus had not disproved the null hypothesis and merely proved the alternative? No one would have listened to him. To change people's thinking, he first had to prove his thinking wrong.

## How to pose the null hypothesis from a word problem

You will be asked to convert a word problem into a statistical hypothesis statement that will include a null hypothesis and an alternative hypothesis. Dividing the problem into a few steps makes these problems much easier to handle.

Example of problem: A researcher believes that if patients who have knee surgery go to physical therapy twice a week (instead of three), their recovery period will be longer. The average recovery time of knee surgery patients is 8.2 weeks.

#### Step 1: Discover the hypothesis from the problem.

The hypothesis is usually hidden in a problem of words, and is sometimes a statement of what is expected to happen in the experiment. The hypothesis in the previous question is "I expect the average recovery period to be greater than 8.2 weeks".

#### Step 2: Convert the hypothesis into mathematics.

Remember that the mean is sometimes written as μ.

H1: μ > 8.2

Broken down, that's H1 (The hypothesis): μ (the mean) > (is greater than) 8.2

#### Step 3: State what will happen if the hypothesis is not met.

If the recovery time is not more than 8.2 weeks, there are only two chances, that the recovery time is equal to 8.2 weeks or less than 8.2 weeks.

H0: μ ≤ 8.2

Broken down, this is H0 (The null hypothesis): μ (the mean) ≤ (is less than or equal to) 8.2

## But what if the researcher has no idea what's going to happen?

Example of problem: A researcher is studying the effects of a radical exercise program on knee-operated patients. There is a good chance that therapy will improve recovery time, but there is also a chance that it will worsen it. The average recovery time of knee surgery patients is 8.2 weeks.

#### Step 1: Indicate what will happen if the experiment makes no difference.

That's the null hypothesis: that nothing will happen. In this experiment, if nothing happens, the recovery time will still be 8.2 weeks.

H0: μ = 8.2

Broken down, this is H0 (the null hypothesis): μ (the mean) = (equals) 8.2

#### Step 2: Discover the alternative hypothesis.

The alternative hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

H1: μ ≠ 8.2

That's H1 (The Alternative Hypothesis): μ (the mean) ≠ (not equal to) 8.2

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## Bibliographic References

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.

Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.

Cohen, J. (1994). The world is round: p < .05. American Psychologist, 49, 997–1003.

Hyde, J. S. (2007). New directions in the study of gender similarities and differences. Current Directions in Psychological Science, 16, 259–263.

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