# 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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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• 1% – https://www.stt.msu.edu/~lepage/STT200_Sp10/3-1-10key.pdf
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