Statistics Tutorial
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Type I & II Error
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 vapd null hypothesis whereas Type II error represents the incorrect retention of an invapd null hypothesis.
Null Hypothesis
Null Hypothesis refers to a statement which nulpfies 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 nulpfy 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 probabipty 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% probabipty 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 $ eta $ 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.
| Judgment | Null hypothesis ($ H_0 $) is | Error Type | Inference |
|---|---|---|---|
| Reject | Vapd | Type I Error (False Positive) | Incorrect |
| Reject | Invapd | True Positive | Correct |
| Unable to Reject | Vapd | True Negative | Correct |
| Unable to Reject | Invapd | Type II error(False Negative) | Incorrect |