Section 8 (Pgs 94-108)

Question 1

Basically, when are non-parametric methods used?

Answer 1

When the variables are not normally dsitributed

When the data is skewed

Question 2

What do non-parametric methods use instead of the actual values of the data?

Answer 2

Ranks of the data

Question 3

Are non-parametric methods more or less powerful than parametric methods?
Why?

Answer 3

Less powerful

They do not utilise all the data

Question 4

What 3 variables are most likely to warrant the use of non-parametric methods?

Answer 4

Counts
Ranks
Scores

Question 5

What can sometimes achieve normality for counts, ranks and scores?

Answer 5

Square root transformation

Question 6

What should you always do before deciding on non-parametric methods?

Answer 6

Explore methods of transforming the data

Question 7

What should you look at to determine whether data is normally distributed?

Answer 7

Normal plot
Box-and-whisker diagram
Shaprio-Wilk statistic
Coefficient of skewness

Question 8

What is the most appropriate measure of centre in normally distributed data?

Answer 8

Mean

Question 9

Is not normally distributed data normally symmetrically or non-symmetrically distributed?

Answer 9

Non-symmetrically (skewed)

Question 10

What is the most appropriate measure of centrality in non-normally distributed data?

Answer 10

Median

Question 11

When is non-parametric tests of the average of a single sample indicated?

Answer 11

Data is not plausibly normal (normal plot, box-and-whisker plot, shapiro-wilk statistic, coefficient of skewness)
Transformations to address the problem cannot be found
Sample size is small?

Question 12

What 2 non-parametric procedures can be used to test hypothesis about the median of a single sample?

Answer 12

Sign test

Wilcoxon signed rank sum test

Question 13

What principle is the sign test based on?

Answer 13

The numbers of observations above and below the hypothesised median
If the null hypothesis is true, these should be equal

Question 14

Which out of the sign test and the wilcoxon signed rank sum test is preferable?
Why?

Answer 14

Wilcoxon signed rank sum test

Based on ranks and therefore incorporates some measure of the actual values

Question 15

Why is the sign test sometimes used instead of the wilcoxon signed rank sum test?

Answer 15

Data must be approximately symmetrically distributed for the wilcoxon signed rank sum test

Question 16

In the sign test, what is the hypothesised median normally approximately distributed to?
What is the other option?

Answer 16

Normal distribution

Binomial distribution

Question 17

What does n in the sign test equal?

Answer 17

The number of observations not equal to the reference median

Question 18

Why is a correction for continuity included in the sign test?

Answer 18

As the data (which is discrete) is being approximated to the normal distribution (which is continuous)

Question 19

In what does the sample size affect the ability to reject a null hypothesis?

Answer 19

It is difficult to obtain sufficient evidence to reject a null hypothesis with a small sample size

Question 20

In what way does sample size determine the ability of study to detect a real effect?

Answer 20

A large sample size makes it easier for a study to detect a real effect

Question 21

What is the proper phrase for the ability of a study to detect a real effect?

Answer 21

Power of the study

Question 22

For a sample size of <25, what is the test statistic in the Wilcoxon signed rank sum test?

Answer 22

W

Question 23

For a sample size of >25, what is the test statistic in the Wilcoxon signed rank sum test?

Answer 23

Z

Question 24

How do you rank data in the Wilcoxon signed rank sum test?

Answer 24

Determine the difference between each value and the hypothesised median
Ignore the signs and zero difference, rank the differences in order of magnitude
Determine the sum of the positive (and negative) ranks above (and below) the hypothesised value
The test statistic W is the smaller of the 2 rank sums

Question 25

When are the results from non-parametric and parametric tests comparable?

Answer 25

When the assumptions for the parametric test are met

Question 26

When are observations dependent (paired)?

Answer 26

If they are applied to the same individual or to individuals matched for factors likely to affect the outcome

Question 27

What non-parametric test is used to compare dependent samples?

Answer 27

Wilcoxon matched pairs rank sum test

Question 28

What non-parametric test is used to compare independent samples?

Answer 28

Mann-Whitney Test

Question 29

In basic terms, how do you do the Wilcoxon matched pairs rank sum test?

Answer 29

By applying the Wilcoxon signed rank sum test to the differences between the pairs of measurements

Question 30

What test statistic is used for the Mann-Whitney if neither n1 or n2 is >10?

Answer 30

T

Question 31

What test statistic is used for the Mann-Whitney if either n1 or n2 is >10?

Answer 31

Z

Question 32

In the Mann-Whitney, when comparing U to T, why is U more useful?

Answer 32

It provides information about actual probability - the probability that a randomly selected observation from the smaller group will be smaller than a randomly selected observation from the larger group