## What is a Type II Error?

Type II error, commonly referred to as β error, is the probability of retaining the factual statement which is inherently incorrect. This is an error of false positive, i.e. the statement is false factually and we are positive about it.

### Explanation

Type Errors is very commonly used in creating the hypothesis and to identify the solution based on the probability of their occurrence and to identify the factual correction of the data on which hypothesis has been structured.

Following is the diagram showing the creation of the null hypothesis, alternative hypothesis, sample mean, and the probability of error.

With every test we undertook, there always exists a probability of error in decision making, and such a decision may be a kind of Type I or Type II error. In simple words, we say, while undertaking decision making, we might reject the correct facts, or we might accept the wrong facts. Rejection of correct fact is Type I error, and acceptance of incorrect facts is Type II error. In the working world, this error proves very dangerous because the whole analysis and experiment prove wrong as the base itself is wrong.

Following is the matrix of which type of error one might undertake, if facts are wrongly accepted:

A decision was taken to Retain |
A decision was taken to Reject |
|||

( Positive) | ( Negative) | |||

Null Hypothesis is true |
True Positive | True Negative | ||

(1- a) | (a)= Type I error | |||

Null Hypothesis is False |
False Positive | False Negative | ||

(β)= Type II Error | ( 1 – β) |

From the above matrix, we can say that:

- Correct Null Hypothesis and Correct decision of retaining are in an actual positive decision that will prove analysis to be true. This is the expected conclusion of the study.
- Correct Null Hypothesis and incorrect decision making to retain it will not prove to be fruitful. Such a True Negative decision is termed as Type 1 error or an error.
- Incorrect Null Hypothesis and inaccurate decision making to retain it will jeopardize full analysis. One will never be able to reach a conclusion where the base itself of interpretation is wrong. Such False-positive decision is termed as Type II error or β.
- Incorrect Null Hypothesis and incorrect decision making to reject is the actual expectation from all the analysis. False Negative decisions should be rejected without any second thought.

### Example of Type II Error

- In human beings, women tend to become pregnant. However, while doing the verification, the doctor mistakenly diagnoses a man as pregnant. This is termed as Type II error, where the base itself is wrong.
- Also, doctors diagnose women as not pregnant; however, in actuality, she is pregnant. This is termed as Type I error, where facts are correct, but one is rejecting the same.

### How Does Type II Error Occur?

Various factors may result in such error

#### #1 – Any Change in the Population is Comparatively Very Small to Detect

If in the population itself, the tendency to change is not visible, then any hypothesis testing will not be able to cater to the correct facts. Such a scenario will lead up to the acceptance of incorrect facts, which will result in Type II error.

#### #2 – Sample Size Covers Very Small Portion of Population

The sample should represent the complete population. Thus, if the sample is not an ideal representation of the population, then it is highly unlikely that it will give the correct picture for the analysis. The analyst will not be able to identify the correct facts. As a result, an analyst will rely on the wrong facts and will result in a Type II error.

#### #3 – Incorrect Sample Selection

Generally, random sampling is used globally, as it is considered as one of the most unbiased methods of selection of sample. However, many times, it results in inappropriate picking of samples. This leads to incorrect coverage of the population and results in Type II error.

### Can Type II Errors Be Avoided?

#### #1 – Repeat Analysis until One Reaches the Needed Significance

Significance specifies to what probability the null hypothesis is factually correct or not. At the end of all analysis, one expects to accept the Null Hypothesis and ensure that given facts are correct. However, many times by single analysis, such significance cannot be achieved. Such a single analysis may be resulting in Type I or Type II error. If, in the repetitive analysis, the same kind of output comes, then one will be able to ensure that no errors occur.

#### #2 – With Each Repetition of Analysis, Change the Size of the Test of Significance

As discussed in point 1). Significance shows the appropriateness of the null hypothesis. If at the end of the first cut, one found that the sample is not adequately getting covered, then increase the size of significance and try to reiterate the same. This will help in understanding the behavior, and one will be able to avoid Type II error.

#### #3 – Alpha Level Around 0.1 Is the Ideal One

Generally, alpha around 0.1 will result in rejecting of hypothesis. Any rejection will allow multiple verifications. As a result, the chances of occurrence of error will reduce. Type II error occurs when anything is getting wrongly accepted. If there is no scope of acceptance, such error will not occur.

### Importance

- It is more dangerous as compared to Type I error.
- Any analysis is getting worked out on a few necessary details and a few underlying assumptions. In the hypothesis also, in the end, one will determine whether the test statistic is in line with the given fact or not. Such test specific will display whether the sample mean is equivalent to population mean or not.
- Due to some kind of error in analysis, the null hypothesis appears to reach significance; then one will accept the fact given in the Null Hypothesis.
- However, in actual such a null hypothesis is not ought to be accepted. As a result, one needs to be highly sure while accepting the null hypothesis statement. By re-verifying it, one will get better significance will boost the correctness of fact.

### Type I Error vs Type II Error

Following are the basic difference between the two types of error

Sr No |
Type I error |
Type II error |
||

1 | It occurs when the correct Null Hypothesis is not accepted. | It occurs when an incorrect null hypothesis is getting accepted | ||

2 | Such errors are true negative. | Such errors are false positive | ||

3 | It is denoted by alpha. | It is denoted by Beta | ||

4 | Null hypothesis and type 1 error | Alternative hypothesis and type 2 error | ||

5 | If the resultant effect of this error is worse than a Type I error, one should consider alpha with a value higher than 0.10 | If the resultant of a Type I error is worse, one should set alpha with a value lower than 0.01. |

### Conclusion

Type II error is a false negative, the resultant effect of accepting the incorrect Null Hypothesis. In the practical world, such error results in the failure of the full project as the base is inaccurate. Such base may be like details, facts, or assumptions, which will jeopardize complete analysis.

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