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- Statistics - Discussion

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

**Hypothesis**- Water added to a toothpaste protects teeth against cavities.**Null Hypothesis**- Water added to a toothpaste has no effect against cavities.

**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.

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.

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.

Judgment | Null hypothesis ($ H_0 $) is | Error Type | Inference |
---|---|---|---|

Reject | Valid | Type I Error (False Positive) | Incorrect |

Reject | Invalid | True Positive | Correct |

Unable to Reject | Valid | True Negative | Correct |

Unable to Reject | Invalid | Type II error(False Negative) | Incorrect |

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