Lecture 9- Hypothesis Testing 2

Question 1

What is a type 1 error?

Answer 1

Rejecting Rejecting the null hypothesis when it is true Rejecting the null hypothesis hypothesis when it is true

p= alpha

Question 2

What is a type 2 error?

Answer 2

Retaining the null hypothesis when it is false

p = β (beta)

Question 3

Could you have both a type 1 and type 2 error at the same time?

Answer 3

No, they are mutually exclusive

They can however influence each other

Question 4

Draw the 2 by 2 matrix of the possible outcomes in hypothesis testing

Also draw the accompanying graph

Answer 4

Look at slides for answers (both are circled in orange)

Question 5

How do you minimize type 2 errors?

Answer 5

Reducing β and increasing power (1 – β ) this means we can reject the null hypothesis when it is false….

-Increasing alpha increases power and therefore reduces the probability of a Type II error (increases the probability of rejecting the
null when it is false)

• Increasing n
• Using a powerful statistical test like ANOVA
• Have good experimental design

Question 6

What is the consequence of increasing alpha to decrease type 2 errors?

Answer 6

Produces a higher probability of a Type I error (rejecting the
null when it is true)

Question 7

Under what circumstances do you set alpha high and under what circumstances to you set it high?

Answer 7

• set alpha very low (e.g. .01) when consequences of Type I error are severe e.g. risk to public health
• set alpha higher (e g 05) when consequences of Type I errors are not too serious

Question 8

What is the effect of increasing n?

Answer 8

• bigger n = less variability means narrower sampling distribution
• reduced β (alpha doesn’t change)