Hypothesis Testing

Question 1

What is a hypothesis test?

Answer 1

A method of making statistical decisions about populations or processes based on empirical data

Question 2

What is the aim of hypothesis testing?

Answer 2

Assess the strength of evidence provided by data

Question 3

Describe 5 steps to hypothesis testing

Answer 3

1. Formulation of practical problem in terms of statistical hypotheses
2. Conduct study
3. Calculate p-value
4. Examine significance level of the test
5. Further assessment

Question 4

What is a null hypothesis?

Answer 4

A statement of the assumed population characteristics

Question 5

What is an alternative hypothesis?

Answer 5

A hypothesis which contradicts the null hypothesis

Question 6

What does the alternative hypothesis express?

Answer 6

The range of situations that we wish the test to be able to diagnose

Question 7

Give an example of a null hypothesis with regards to heart rate of children who have received anaesthetic

Answer 7

The mean minimal heart rates of children who have received anaesthetic is equal to “x”

Question 8

Give an example of an alternative hypothesis with regards to heart rate of children who have received anaesthetic

Answer 8

The mean minimal heart rates of children who have received anaesthetic is not equal to “x”

Question 9

What is a test statistic?

Answer 9

A function of the data plus the information in the null hypothesis

Question 10

What 2 properties must a test statistic satisfy?

Answer 10

1. Probability distribution must be calculable under the assumption null hypothesis is true
2. Behave differently when null hypothesis is true from when alternative hypothesis is true

Question 11

What are the 3 most common associated distributions in a test statistic?

Answer 11

1. Normal
2. t
3. Chi-squared

Question 12

Why do null hypothesis tend to be “not rejected” rather than “accepted”?

Answer 12

Test statistics are constructed so a lack of information tends to result in non-significant values of the test statistic

Question 13

What is the p-value?

Answer 13

• Assumption that null hypothesis is true
• Probability that if repeats the study many times the test statistic would be as extreme or more extreme than test statistic obtained
• More extreme means less likely

Question 14

Describe a “small” p result in practice

Answer 14

• Small p-value means null hypothesis is rejected in favour of alternative hypothesis
• Not small p-value means there is insufficient evidence to reject null hypothesis in favour of alternative hypothesis

Question 15

What is the significance level?

Answer 15

Probability of rejecting null hypothesis when it is true

Question 16

What is power?

Answer 16

The probability of rejecting the null hypothesis when the alternative hypothesis is true

Question 17

Describe the relationship between significance level and power

Answer 17

If the significance level of a test is decreased the power is also decreased

Question 18

What is a Type I Error?

Answer 18

This occurs when a null hypothesis is rejected when it is true

Question 19

What is the probability of making a Type I Error?

Answer 19

It is equivalent to the significance level of the test

Question 20

What is a Type II Error?

Answer 20

This occurs when a null hypothesis is not rejected when it is false

Question 21

What is the probability of not making a Type II Error?

Answer 21

It is equivalent to the power of a test

Question 22

Name 3 determinants of the most appropriate test

Answer 22

1. Scale of measurement
2. Whether samples are paired or independent
3. Two samples or more than two samples

Question 23

What method is used as a guide to determine the most appropriate test?

Answer 23

Decision tree