Difference Between Type 1 and Type 2 Error

Difference Between Type 1 and Type 2 Error

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Vikram
Vikram Singh
Assistant Manager - Content
Updated on Oct 13, 2023 15:30 IST

Type – 1 error is known as false positive, i.e., when we reject the correct null hypothesis, whereas type -2 error is also known as a false negative, i.e., when we fail to reject the false null hypothesis. In this article, we will discuss difference between type 1 and type 2 error.

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Researcher/scientist assumes to prove or disprove their finding. These assumptions are also known as hypotheses. There are mainly two types of hypotheses Null and Alternative Hypothesis. Null and Alternative hypotheses are mutually exclusive statements. A null hypothesis statement is that there is no relation between the two variables. In contrast, an alternative hypothesis is a statement that refers to the statistical relationship between the two variables. While doing hypothesis testing, we encounter two types of errors, i.e., type-1 and type-2 errors. This article will discuss the difference between type- 1 and type-2 errors.
Type-1 and Type -2 errors are interconnected; reducing one can increase the probability of another. Type – 1 error is a false-positive finding, while type-2 error is a false-negative finding in hypothesis testing.

Table of Content

Difference between Type-1 and Type-2 Error

Parameter Type -1 Error Type – 2 Error
Definition It refers to the non-acceptance of the hypothesis that ought to be accepted. It refers to the acceptance of a hypothesis that ought to be rejected.
Represents A false hit A miss
Equivalent to False Positive False Negative
Notation alpha beta
Probability of committing an error Equals to the level of significance Equals to the power of test
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Type -1 Error (Error of the first kind)

  • It is also known as a false-positive.
  • It occurs if the researcher rejects a correct null hypothesis in the population.
  • Measured by alpha (significance level).
  • If the significance level is fixed at 5%,
  • Cause of Type – 1 Error
  • It can be reduced by decreasing the level of significance.
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Type -2 Error (Error of the second kind)

  • It is also known as a false negative.
  • It occurs if a researcher fails to reject a null hypothesis that is actually a false hypothesis.
  • Measured by beta (the power of test).
  • The probability of committing a type -2 error is calculated by 1 – beta (the power of test).
  • Cause of Type – 2 Error:
  • It can be reduced by increasing the level of significance.
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Graphical representation of type – 1 and type – 2 Errors:

2023_03_Null-and-Alternate-Hypothesis.jpg

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Examples of Type -1 and Type – 2 Errors

Now, let’s take an example to understand better type – 1 and type – 2 errors:

Example -1: A man goes to test the coronavirus (COVID -19). So, the possible errors are

Type -1 Error (False Positive): Test results are positive, but you don’t.

Type – 2 Error (False Negative): Test results are negative, but you do.

 

Example – 2 A man goes to trial and is being tried for murder.

Null Hypothesis: Man is innocent until proven guilty.

Alternative Hypothesis: Man is guilty.

Type -1 Error (False Positive): Found guilty, but you are innocent.

True Positive: Found guilty and being guilty.

True Negative: Found Innocent and being innocent

Type -2 Error (False Negative): Found innocent, but you are guilty.

Key Differences

  • When the null hypothesis is correct, and the researcher rejects the null hypothesis, this type of error is known as a type -1 error, whereas when the null hypothesis is false. If the researcher fails to reject it, then this type of error is known as a type – 2 error. 
  • Type -1 error is also known as false-positive, whereas type – 2 error is known as false-negative.
  • By decreasing or increasing the significance level, we can reduce the type – 1 or type – 2 errors.
  • Type – 1 and type – 2 errors are inversely related, i.e., if one increases, the other decreases.
  • Type – 1 error is measured by alpha (the significance level), whereas type – 2 error is measured by 1 – beta (the power of test).

Conclusion

In this article, we have briefly discussed what is briefly discussed Type-1 and Type-2 error, and the difference between these with the help of examples and graphical representation.

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FAQs

What is the difference between type 1 and type 2 error?

Type-1 is error refers to the non-acceptance of the hypothesis that ought to be accepted, while type-2 refers to the acceptance of a hypothesis that ought to be rejected.

Why is Type 1 error also called a false positive?

It is called a false-positive as it occurs when a researcher wrongly concludes that there is a significant effect or relationship between variable, but there is no relationship.

How is level of significance related to type 1 error?

Level of significance represents the probability of rejecting a true null hypothesis, with the increase of the level of significance the type 1 error also increases.

What is the relationship between type-1 and type-2 error?

Type-1 and type-2 are inversely related, i.e., when type-1 increases the type-2 error decreases and vice -versa.

Can type-1 and type-2 error be avoided completely?

No, the errors can't be avoided but it can be reduced, i.e., errors can be minimized by carefully designing their studies, using appropriate statistical test, and analyzing the results.

About the Author
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Vikram Singh
Assistant Manager - Content

Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio

Comments

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I have the following example: How to compute type I and type II errors H0 false Ho is true Reject H0 TP=30 (Correct outcome) FP = 30 (Type I error) Fail to R. H0 FN=10 (Type II error) TN=930 (correct outcome) Many thanks

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