# Type-1 Error

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## Definition: Type-1 Error

Statistical errors are an integral part of hypothesis testing. Type-I Error is the error which is used to reject a true null hypothesis (Ho). It is also known as “Error of the first kind”.

In simple words, Type- I error indicates that a given condition is true, when it is actually false. It means that we believe a falsehood.

The probability of type-I error is denoted by α (alpha). α is also called as the bound on Type I error. It is the level of significance of the test.

FORMULA:

Since, α is a conditional probability, which can be calculated as follows:

α = P(Rejecting H0│H0 is True)

Errors in Hypothesis Testing:

 Decision Ho True Ho False Reject Ho Type I Error (α) Correct Assessment Fail to reject Ho Correct Assessment Type II Error (β)

Since Type I is the more serious error (usually), that is the one we concentrate on. We usually fix α to be very small (0.05, 0.01).

EXAMPLE:

When a person is accused of a crime, we put him on trial even after knowing his innocence. Type- I error in this case is that the person is truly innocent but the jury finds him guilty.

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