# Statistics - Type I & II Errors

Type I and Type II errors signifies the erroneous outcomes of statistical hypothesis tests. Type I error represents the incorrect rejection of a valid null hypothesis whereas Type II error represents the incorrect retention of an invalid null hypothesis.

## Null Hypothesis

Null Hypothesis refers to a statement which nullifies the contrary with evidence. Consider the following examples:

### Example 1

• Hypothesis - Water added to a toothpaste protects teeth against cavities.

• Null Hypothesis - Water added to a toothpaste has no effect against cavities.

### Example 2

• Hypothesis - Floride added to a toothpaste protects teeth against cavities.

• Null Hypothesis - Floride added to a toothpaste has no effect against cavities.

Here Null hypothesis is to be tested against experimental data to nullify the effect of floride and water on teeth's cavities.

## Type I Error

Consider the Example 1. Here Null hypothesis is true i.e. Water added to a toothpaste has no effect against cavities. But if using experimental data, we detect an effect of water added on cavities then we are rejecting a true null hypothesis. This is a Type I error. It is also called a False Positive condition (a situation which indicates that a given condition is present but it actually is not present). The Type I error rate or significance level of Type I is represented by the probability of rejecting the null hypothesis given that it is true.

Type I error is denoted by $\alpha$ and is also called alpha level. Generally It is acceptable to have Type I error significance level as 0.05 or 5% which means that 5% probability of incorrectly rejecting the null hypothesis is acceptable.

## Type II Error

Consider the Example 2. Here Null hypothesis is false i.e. Floride added to a toothpaste has effect against cavities. But if using experimental data, we do not detect an effect of floride added on cavities then we are accepting a false null hypothesis. This is a Type II error. It is also called a False Positive condition (a situation which indicates that a given condition is not present but it actually is present).

Type II error is denoted by $\beta$ and is also called beta level.

Goal of a statistical test is to determine that a null hypothesis can be rejected or not. A statistical test can reject or not be able to reject a null hypothesis. Following table illustrates the relationship between truth or falseness of the null hypothesis and outcomes of the test in terms of Type I or Type II error.

JudgmentNull hypothesis ($H_0$) isError TypeInference
RejectValidType I Error (False Positive)Incorrect
RejectInvalidTrue PositiveCorrect
Unable to RejectValidTrue NegativeCorrect
Unable to RejectInvalidType II error(False Negative)Incorrect