Type I and Type II Errors

Type I and Type II errors are subjected to the result of the null hypothesis. In case of type I or type-1 error, the null hypothesis is rejected though it is true whereas type II or type-2 error, the null hypothesis is not rejected even when the alternative hypothesis is true. Both the error type-i and type-ii are also known as “false negative”. A lot of statistical theory rotates around the reduction of one or both of these errors, still, the total elimination of both is explained as a statistical impossibility.

Type I Error

A type I error appears when the null hypothesis (H0) of an experiment is true, but still, it is rejected. It is stating something which is not present or a false hit. A type I error is often called a false positive (an event that shows that a given condition is present when it is absent). In words of community tales, a person may see the bear when there is none (raising a false alarm) where the null hypothesis (H0) contains the statement: “There is no bear”.

The type I error significance level or rate level is the probability of refusing the null hypothesis given that it is true. It is represented by Greek letter α (alpha) and is also known as alpha level. Usually, the significance level or the probability of type i error is set to 0.05 (5%), assuming that it is satisfactory to have a 5% probability of inaccurately rejecting the null hypothesis.

Type II Error

A type II error appears when the null hypothesis is false but mistakenly fails to be refused. It is losing to state what is present and a miss. A type II error is also known as false negative (where a real hit was rejected by the test and is observed as a miss), in an experiment checking for a condition with a final outcome of true or false.

A type II error is assigned when a true alternative hypothesis is not acknowledged. In other words, an examiner may miss discovering the bear when in fact a bear is present (hence fails in raising the alarm). Again, H0, the null hypothesis, consists of the statement that, “There is no bear”, wherein, if a wolf is indeed present, is a type II error on the part of the investigator. Here, the bear either exists or does not exist within given circumstances, the question arises here is if it is correctly identified or not, either missing detecting it when it is present, or identifying it when it is not present.

The rate level of the type II error is represented by the Greek letter β (beta) and linked to the power of a test (which equals 1−β).

Also, read:

Table of Type I and Type II Error

The relationship between truth or false of the null hypothesis and outcomes or result of the test is given in the tabular form:

Error Types When H0 is True When H0 is False
Don’t Reject Correct Decision (True negative)

Probability = 1 – α

Type II Error (False negative)

Probability = β

Reject Type II Error (False Positive)

Probability = α

Correct Decision (True Positive)

Probability = 1 – β

Type I and Type II Errors Example

Check out some real-life examples to understand the type-i and type-ii error in the null hypothesis.

Example 1: Let us consider a null hypothesis – A man is not guilty of a crime.

Then in this case:

Type I error (False Positive) Type II error (False Negative)
He is condemned to crime, though he is not guilty or committed the crime. He is condemned not guilty when the court actually does commit the crime by letting the guilty one go free.

Example 2: Null hypothesis- A patient’s signs after treatment A, are the same from a placebo.

Type I error (False Positive) Type II error (False Negative)
Treatment A is more efficient than the placebo Treatment A is more powerful than placebo even though it truly is more efficient.

 

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