10 Non-Parametric Tests

Question 1

What is the definition of non-parametric tests?

Answer 1

Tests which do not require the knowledge or assumption that the data involved is normally distributed

These are also known as distribution free tests

Question 2

What is the sign test used for?

Answer 2

To test whether the median of the population takes a specific value or to test preferences between two populations

Question 3

What is the alternative hypothesis in hypothesis testing?

Answer 3

The hypothesis that there is a significant effect or difference

Question 4

What does the null hypothesis represent?

Answer 4

The hypothesis that there is no significant effect or difference

Question 5

What is the significance level typically used in hypothesis testing?

Answer 5

Commonly 0.05 or 5% unless stated otherwise

Question 6

In the sign test, what model is used to determine the critical region?

Answer 6

A binomial model with p = 0.5

This is based on the idea that the median is in the middle.

Question 7

True or false: The sign test can be used for paired values.

Answer 7

TRUE

This is called a paired sign test.

Question 8

What is the purpose of the Wilcoxon Signed-Rank Test?

Answer 8

To test a null hypothesis that the mean or median of a sample is a specific value

Question 9

What is the assumption regarding the sample in non-parametric tests?

Answer 9

The sample is randomly chosen and representative of the population

This ensures the validity of the test results.

Question 10

What does the significance level indicate in hypothesis testing?

Answer 10

The probability of rejecting the null hypothesis when it is true

Question 11

What is the median in statistics?

Answer 11

The middle value of a data set when arranged in order

It is a measure of central tendency.

Question 12

Fill in the blank: The Wilcoxon Signed-Rank Test is more accurate than the sign test because it considers the _______.

Answer 12

size of the differences

Question 13

What is the critical region in hypothesis testing?

Answer 13

The range of values that leads to the rejection of the null hypothesis

It is determined by the significance level.

Question 14

What is the assumption about the underlying population in the Wilcoxon Signed-Rank Test?

Answer 14

Data follows a symmetrical distribution

This allows the test to be valid for both mean and median.

Question 15

What is the ** paired** Wilcoxon Signed-Rank Test used for?

Answer 15

To test whether there is a difference in the mean/medians of two populations using paired samples

This test is applicable when comparing two related samples.

Question 16

In a two-tailed test, what should you choose as the test statistic?

Answer 16

The smallest total

Question 17

What are the two types of Wilcoxon tests mentioned?

Answer 17

• Wilcoxon Signed-Rank Test
• Wilcoxon Rank-Sum Test

The Rank-Sum test is used when paired data is not available.

Question 18

What is a Type I error in the context of hypothesis testing?

Answer 18

Rejecting the null hypothesis when it is in fact true

This error indicates a false positive result.

Question 19

What is a Type II error in hypothesis testing?

Answer 19

Failing to reject the null hypothesis when it is in fact false.

This error indicates a false negative result.

Question 20

What assumptions are made about the population when carrying out a Sign or Paired sign test?

Answer 20

There are no assumptions made the underlying population for the sign test

Question 21

What assumptions are made about the population when carrying out a Wilcoxon Signed-Rank test?

Answer 21

The distribution of differences is symmetrical

Question 22

What assumptions are made about the population when carrying out a Wilcoxon Rank-Sum test?

Answer 22

The samples are independent from populations with similar shaped distributions