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type i and type ii errors

# Type I and Type II Errors

Module - 6 Statistical Inference
Type I and Type II Errors

Overview

Type I and Type II Blunders are two sorts of mistakes that can happen in statistical hypothesis testing. A Type I blunder happens when we dismiss a genuine null hypothesis, whereas a Sort II mistake happens when we fail to dismiss a wrong null hypothesis. Understanding the contrast between these mistakes and how to play down them is basic in making exact and educated choices based on statistical examination.

Introduction:

In statistical hypothesis testing, we make decisions based on the data we observe. In any case, these choices are inclined to blunders. Type I and Type II mistakes are the two sorts of blunders that can happen in speculation testing. It is fundamental to get it these blunders to form the correct choices based on the statistical investigation.

Definition of Type I Error:

Type I error is a false positive result in hypothesis testing.It happens when we fail to dismiss the invalid speculation, even though it is wrong. In other words, we conclude that there's no noteworthy impact or difference when there's a genuine impact or distinction. The likelihood of making a Type II error is signified by the Greek letter beta (β) and depends on the test estimate, impact estimate, and centrality level.

Definition of Type II Error:

Type II error is a false negative result in hypothesis testing. It occurs when we fail to reject the null hypothesis, even though it is false. In other words, we conclude that there is no significant effect or difference when there is a real effect or difference. The probability of making a Type II error is denoted by the Greek letter beta (β) and depends on the sample size, effect size, and significance level.

Example of Type I and Type II Errors:

Suppose a medical test is conducted to determine if a person is pregnant or not. The null hypothesis is that the person is not pregnant, and the alternative hypothesis is that the person is pregnant.

• Type I Error: This occurs when the test incorrectly rejects the null hypothesis (person is not pregnant) when it is actually true. In this case, a Type I error would mean that a person who is not pregnant is incorrectly identified as pregnant by the test. This could lead to unnecessary medical treatments or procedures.
• Type II Error: This occurs when the test incorrectly fails to reject the null hypothesis (person is not pregnant) when it is actually false (person is pregnant). In this case, a Type II error would mean that a person who is pregnant is incorrectly identified as not pregnant by the test. This could delay necessary medical treatments or procedures.

Both Type I and Type II errors can have serious consequences, and it's important for medical professionals to carefully consider the potential for error when interpreting test results.

Minimizing Type I and Type II Errors:

In hypothesis testing, we need to minimize both Type I and Type II mistakes. However, it isn't continuously conceivable to diminish both blunders at the same time. Assume we need to diminish the likelihood of a Sort I mistake (i.e., we want to be more conservative). In that case, ready to diminish the importance level (α), which can increment the likelihood of a Type II mistake. Alternately, in the event that we need to reduce the probability of a Sort II mistake (i.e., we need to be more delicate), ready to increment the test estimate or impact measure, which is able decrease the likelihood of a Type I error.

Relation to Power and Sample Size:

The power of a hypothesis test is the probability of rejecting the null hypothesis when it is false (i.e., not making a Type II error). Power is inversely related to the probability of making a Type II error (β). Increasing the sample size or effect size can increase the power of a hypothesis test. Additionally, increasing the significance level (α) can increase power, but it also increases the probability of making a Type I error.

Conclusion:

Type I and Type II errors are crucial concepts in hypothesis testing. Type I errors occur when we reject the null hypothesis when it is true, and Type II errors occur when we fail to reject the null hypothesis when it is false. It is essential to minimize both types of errors and balance the significance level (α) and the sample size/effect size to achieve the desired level of power in hypothesis testing.

Key takeaways

1. Hypothesis testing is an important tool in statistics that helps us make decisions about the population based on sample data.
2. Type I error occurs when we reject a null hypothesis that is actually true, while Type II error occurs when we fail to reject a null hypothesis that is actually false.
3. The probability of Type I error is denoted by alpha, while the probability of Type II error is denoted by beta.
4. The power of a test is the probability of correctly rejecting a false null hypothesis and is equal to 1 minus the probability of Type II error.
5. The level of significance of a test is the maximum probability of Type I error that we are willing to accept, and it is usually set to 0.05 or 0.01.
6. Type I and Type II errors are important considerations when interpreting the results of hypothesis tests and should be taken into account when making decisions based on statistical analysis.

Quiz

1. What is a Type I error in hypothesis testing?

A) Rejecting the null hypothesis when it is true

B) Failing to reject the null hypothesis when it is false

C) Rejecting the alternative hypothesis when it is true

D) Failing to reject the alternative hypothesis when it is false Answer: A

2. What is a Type II error in hypothesis testing?

A) Rejecting the null hypothesis when it is true

B) Failing to reject the null hypothesis when it is false

C) Rejecting the alternative hypothesis when it is true

D) Failing to reject the alternative hypothesis when it is false Answer: B

3. Which type of error is more serious in hypothesis testing?

A) Type I error

B) Type II error

C) Both errors are equally serious

D) It depends on the specific context and consequences of the error

4. Which of the following can reduce the risk of both Type I and Type II errors?

A) Increasing the sample size

B) Decreasing the sample size

C) Increasing the level of significance

D) Decreasing the level of significance

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