Type I and Type II errors

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In statistical testing, there can be incorrect outcomes. These outcomes are classified into type I and type II errors.  Here, type I error is a false positive and type II error is a false negative. An incorrect rejection of a true null hypothesis (H0) is a type I error. An incorrect failed rejection of a false null hypothesis (H0). Lets consider an example of a fire alarm while making a null hypothesis (H0) that there is no fire.

Type I error (false positive)

A fire alarm going off when there is no fire (false alarm).

Test: Is there a fire?
Result (alternative hypothesis): Yes (Alarm sounded)
Null hypothesis (H0): No
Actual result: No (true null hypothesis)
In this case, the null hypothesis (H0) is that there is no fire and there actually was no fire, so this is a true null hypothesis. Since, we sounded the alarm and incorrectly rejected the true null hypothesis. This is a type I error.

Type II error (false negative)

No alarm going off when there is a fire.

Test: Is there a fire?
Result (alternative hypothesis): No (No alarm sounded)
Null hypothesis (H0): No
Actual result: Yes (false null hypothesis)
In this case, the null hypothesis (H0) is that there is no fire and there actually was a fire, so this is a false null hypothesis. Since we did not sound the alarm and incorrectly failed to reject (accepted) the false null hypothesis. This is a type II error.

Here, is a table that shows the outcomes of a statistical test [0]. The correct outcomes are shown in green, and the incorrect outcomes are the type I and type II errors.

Alternative Hypothesis
Positive Negative
Actual
Result
Positive True Positive True Negative (Type II error)
Negative False Positive (Type I error) False Negative

 

Next >> Statistical significance

References:
[0] Liu, Bing. Web data mining: exploring hyperlinks, contents, and usage data. Springer Science & Business Media, 2007. p-81

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  1. […] process of statistical significance, guarantees that our type I (false positive) errors rate is less than […]

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