**Type I Error And Type II Error Overview**

**Type 1 error definition**

**Type 1 error definition**

- A type 1 error arises when a null hypothesis is denied in statistical testing despite the fact that it is valid i.e. a false positive conclusion.
- This error happens when the hypothesis that should have been approved is rejected.
- The degree of significance of the test is frequently referred to as the error symbol (alpha), which stands for type I error.
- While the null hypothesis is dismissed as a consequence of a testing error, a false negative error results.
- According to the null hypothesis, there is no link between two variables, and any association that does exist is the result of chance.
- A type 1 mistake takes place when the null hypothesis is upheld even when there is no correlation between the variables.
- This mistake might lead to the researcher concluding that the hypothesis holds true even when it does not.

**Type 1 error causes**

**Type 1 error causes**

- When a factor other than the variable influences the other variable and the outcome is such that the null hypothesis is supported, this is a type 1 mistake.
- In such circumstances, the outcome looks to have been driven by other factors besides chance. In actuality, though, it was decided by chance.
- Prior to testing a hypothesis, a probability is set as a level of significance, which means that the hypothesis is tested while acknowledging the possibility that the null hypothesis will be denied if it is correct.
- Therefore, type 1 error may come from chance or the level of significance chosen prior to the test, without taking into consideration the duration of the test or the size of the sample.

**Probability of type 1 error**

**Probability of type 1 error**

- The likelihood of a Type I mistake is often calculated beforehand and is interpreted as the importance of testing the hypothesis.
- If Type I error is fixed at 5 percent, there are approximately 5 in 100 possibilities that the null hypothesis, H0, will be denied when it is true.
- The degree of significance in a test is another name for the rate or likelihood of type 1 mistakes, which is represented by the symbol.
- At a certain sample size, type 1 error can be decreased, but doing so raises the likelihood of type II error.
- The likelihood of the two mistakes are inversely correlated, therefore lowering the chance of one error raises the probability of the other. It is impossible to concurrently reduce both mistakes.
- Thus, after assessing the effects of the mistakes, the researchers must choose the right degree of type 1 error based on the kind and nature of the test.

**Type 1 error examples**

**Type 1 error examples**

- Let’s use the example of a player who is attempting to determine the correlation between the number of victories achieved by his team and the fact that he is wearing new shoes.
- In this case, he may recognise the alternative hypothesis and conclude that a correlation exists if the frequency of successes for his team was higher while he was using his new shoes than while he was not.
- However, the success of his team can depend more on pure chance than on his shoes, leading to a type 1 mistake.
- He should have rejected the null hypothesis in this instance, since a team’s success may have been the result of luck or chance.

**Type II error definition**

**Type II error definition**

- The Type II mistake is when the null hypothesis is accepted even when it is false.
- Type II mistake may be defined as accepting the hypothesis when one should not have.
- The type II error results in a false negative result.
- To put it another way, a type II mistake refers to the failure to accept a competing hypothesis when the researcher lacks sufficient power.
- The Type II mistake is also known as the beta error and is indicated by the Greek letter (beta).
- According to the null hypothesis, there is no link between two variables, and any association that does exist is the result of chance.
- Type II errors happen even when there is a link between the variables because the null hypothesis is accepted if the connection between the variables is assumed to be the result of chance or luck.
- This mistake might lead the researcher to conclude that the hypothesis is false, when, in fact, it is true.

**Type II error causes**

**Type II error causes**

- The inadequate power of the statistical test is the main contributor to a type II error, similar to a Type II error.
- This happens when the statistical analysis is weak and leads to a Type II mistake.
- The sample size and other elements might potentially have an impact on the test’s outcomes.
- Even if a link between the two variables under study does exist, it may not be statistically significant when a small sample size is used.
- Even if the alternative hypothesis is correct, the researcher may reject it because they believe the association is the result of chance.
- Before starting the test, it is crucial to choose an acceptable sample size.

**Probability of type II error**

**Probability of type II error**

- You may determine the likelihood of making a Type II error by deducting the test’s power from one.
- There are around two chances in 100 that the null hypothesis, H0, will be accepted when it is false if Type II error is fixed at a 2 percent rate.
- The rate or likelihood of type II error, often known as the second kind of mistake, is represented by the symbol.
- By raising the degree of significance, the likelihood of Type II error can be decreased.
- This situation raises the likelihood of rejecting the null hypothesis even when it is true, which reduces the likelihood of accepting the null hypothesis when it is false.
- But since type I and type II errors are related to one another, lowering one tends to raise the likelihood of the other.
- Identifying which of the mistakes is least harmful to the exam depends on the type of test being administered.
- Therefore, it is prudent to accept type I error over type II error if type I error necessitates retesting the chemicals utilised in medication that should have been approved, but type II error increases the risk that a number of users may be poisoned.

**Type II error examples**

**Type II error examples**

- For example, let’s consider the scenario where a shepherd wakes up all night for five nights in a row, believing there is no wolf in the community.
- He could believe there isn’t a wolf in the village where it might live if he doesn’t spot one for five nights and launch an assault on the sixth.
- When the shepherd concedes that there is no wolf in this scenario, he commits a type II error by accepting the null hypothesis even if it is untrue.

Type I error vs Type II error |
||

Basis for comparison |
Type I error |
Type II error |

Definition |
Type 1 error, in statistical hypothesis testing, is the error caused by rejecting a null hypothesis when it is true. | Type II error is the error that occurs when the null hypothesis is accepted when it is not true. |

Also termed |
Type I error is equivalent to false positive. | Type II error is equivalent to a false negative. |

Meaning |
It is a false rejection of a true hypothesis. | It is the false acceptance of an incorrect hypothesis. |

Symbol |
Type I error is denoted by 伪. | Type II error is denoted by 尾. |

Probability |
The probability of type I error is equal to the level of significance. | The probability of type II error is equal to one minus the power of the test. |

Reduced |
It can be reduced by decreasing the level of significance. | It can be reduced by increasing the level of significance. |

Cause |
It is caused by luck or chance. | It is caused by a smaller sample size or a less powerful test. |

What is it? |
Type I error is similar to a false hit. | Type II error is similar to a miss. |

Hypothesis |
Type I error is associated with rejecting the null hypothesis. | Type II error is associated with rejecting the alternative hypothesis. |

When does it happen? |
It happens when the acceptance levels are set too lenient. | It happens when the acceptance levels are set too stringent. |

**References**

**References**

- Kothari (1990) Research Methodology. Vishwa Prakasan. India.
- https://magoosh.com/statistics/type-i-error-definition-and-examples/
- https://corporatefinanceinstitute.com/resources/knowledge/other/type-ii-error/
- https://keydifferences.com/difference-between-type-i-and-type-ii-errors.html
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