Type II Error

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 a false positive, i.e., a statement is factually false, and we are positive about it.

Explanation

Type Errors are commonly used to create a hypothesis, determine a solution based on the probability of their occurrence, and identify the factual correction of the data on which the hypothesis has been structured.

The diagram shows the creation of a null hypothesisNull HypothesisNull hypothesis presumes that the sampled data and the population data have no difference or in simple words, it presumes that the claim made by the person on the data or population is the absolute truth and is always right. So, even if a sample is taken from the population, the result received from the study of the sample will come the same as the assumption.read more, alternative hypothesis, sample mean, and error probability.

Type II Error

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With every test we undertake, there always exists a probability of error in decision making, and such a decision may be a Type I or Type II error. In simple words, while undertaking decision-making, we might reject the correct facts or accept the wrong facts. Rejection of correct facts is a Type I error, and acceptance of incorrect facts is a Type II error. This error can be very dangerous in the corporate world as the whole analysis and experiment can get wrong if 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 RetainA decision was taken to Reject
   
 ( Positive) ( Negative) 
Null Hypothesis is true True Positive True Negative
 (1- a) = Type I error 
Null Hypothesis is False False Positive False Negative
 (β) = Type II Error (1 – β) 

A decision was taken to Reject

Example of Type II Error

  • In human beings, women tend to get pregnant. However, while verifying, a doctor mistakenly diagnoses a man to be pregnant. This is termed a Type II error, where the base itself was wrong.
  • Suppose the doctor diagnoses a woman as not pregnant when she is pregnant. This can be termed a Type I error, where the facts are correct, but the one rejects the same.

How Does Type II Error Occur?

Various factors may result in such an error.

Factors of type 2 error

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#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 testingHypothesis TestingHypothesis Testing is the statistical tool that helps measure the probability of the correctness of the hypothesis result derived after performing the hypothesis on the sample data. It confirms whether the primary hypothesis results derived were correct.read more will not be able to cater to the correct facts. Such a scenario will lead to accepting incorrect facts, resulting in Type II errors.

#2 – Sample size covers a very small portion of the population

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

#3 – Incorrect sample selection

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

Can Type II Errors Be Avoided?

#1 – Repeat analysis until one reaches the required significance

Significance specifies to what probability the null hypothesis is factually correct or not. At the end of all analyses, one accepts the null hypothesis and ensures that the given facts are correct. However, often, only a single analysis cannot achieve such significance. This unilateral analysis may result in Type I or Type II errors. If the same kind of output comes in the repetitive analysis, then one will ensure that no errors occur.

#2 – In 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 one finds that the sample is not adequately covered, the size of significance can be increased, and the same can be reiterated. This will help understand the behavior and avoid a Type II error.

#3 – Alpha level around 0.1 is the ideal

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

Importance

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

Type I Error vs Type II Error

Following are the basic difference between the two types of error

Sr NoType I errorType II error
1It occurs when the correct null hypothesis is not accepted.It occurs when an incorrect null hypothesis is getting accepted
2Such errors are truly negative.Such errors are false-positive
3It is denoted by alpha.It is denoted by Beta
4Null hypothesis and type 1 errorAlternative hypothesis and type 2 error
5If the resultant effect of this error is worse than a Type I error, one should consider alpha with a value higher than 0.10If 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 resulting from accepting an incorrect null hypothesis. In the practical world, such errors fail the full project as the base is inaccurate. Moreover, such a base may be like details, facts, or assumptions, jeopardizing the complete analysis.

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