INFERENCE - Errors, Power, Effect Size, and Assumptions

What is a Type 1 Error?

Rejecting the null hypothesis when its true

Accepting the alternative when its false

MOST concerned with

eg could convict an innocent person

A false positive

What is a Type 2 Error?

NOT rejecting a false null hypothesis

Failing to accept the alternative when its true

eg failing to convict a guilty person

A false negative

What is the probability of a Type 1 Error?

Alpha = Probability computed using the distribution that assumes H0 true of rejecting the null. = Probability beyond the critical values = Probability of a Type 1 Error

How to prevent making a Type 1 Error?

Have a low significance level

What’s the probability of a Type 2 Error?

Beta = Probability of not rejecting the null given that the null is false

Low significance level increases probability of making error

What is the Power of a test?

Probability the test correctly rejects a false null hypothesis / reaches the correct decision

What impacts Power?

• Increases as sample size increases → bc distributions of sample stats become narrower + so less stats on the left of the critical value

• Increases as value of Alpha/Significance Level increases

• Increases when true value of parameter is farther from hypothesised value n null