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What are errors in hypothesis testing?

Hassaan Waqar

Hypothesis testing is used in statistics to verify a hypothesis made by researchers or analysts. It is used to test whether findings deduced from some sample data can be generalized to the wider population or not.

There are different methods of testing hypotheses. They depend on the nature of the data and the reason for the analysis.

How does hypothesis testing work

Hypothesis testing begins by stating a null hypothesis and an alternate hypothesis.

The null hypothesis defines the status quo. It claims that there is no significant difference between data obtained before and after an intervention or condition and that any difference occurs merely by chance.

Null hypothesis is represented by $H_{o}$.

The alternate hypothesis claims that there is a significant difference between data obtained before and after an intervention or condition and that this difference cannot occur merely by chance.

Alternate hypothesis is represented by $H_{a}$.

Data is then collected and analyzed. Finally, a decision is made regarding the null hypothesis. It is either rejected by the given data, or researchers fail to reject it.

Errors

Sometimes, our conclusions about an experiment may not match reality. There can be errors in analysis. The two types of errors in hypothesis testing are: Type I Error and Type II Error.

Type I Error

A Type I error is when the null hypothesis is true, but we reject it in favor of the alternate. It is sometimes known as a false positive. This means we falsely believe that differences before and after an experiment are due to the treatment when that is not the case.

Type II Error

Type II error- when the null hypothesis is false, but we do not reject it. It is sometimes known as a false negative. This means we believe that differences before and after an experiment are only due to chance and not treatment. This results in wastage of experimental resources though the results have been achieved.

The illustration below summarizes both these errors:

Errors in hypothesis testing

Example

Suppose a pharmacist wants to determine the effectiveness of new medicine. They test it on a sample population and carry out follow-up tests.

What do both errors mean?

Type I Error: The first error could be committed if the null hypothesis was rejected when it was actually true. This means pharmacists favored the alternate hypothesis. The alternate hypothesis was that the drug was effective, even when it was not. Therefore, the pharmacist overestimated the effectiveness of the drug.

Type II Error: The second error could be committed if the null hypothesis was not rejected, though it should have been. This means the drug was effective, but the pharmacist thought that it was not. So resources were wasted, and the experiment was discarded.

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Hassaan Waqar