Non Parametric Tests

Question 1

How are parametric tests different to non-parametric tests?

Answer 1

Require a variable that is a continuous measurement (interval or ratio data)

Normally Distributed Data

Parametric tests are more powerful (more likely to detect true differences)

Less probable to commit a type 2 error

Question 2

What is central limit theorem?

Answer 2

As size sample increases, sampling distribution becomes normally distributed and mean becomes population mean

Question 3

How do non-parametric tests differ from parametric tests?

Answer 3

Data not continuous (not ratio or interval)

Makes fewer assumptions about the population from which the sample has been drawn

Less fussy about the type of data used e.g. can use data from a likert scale

We can use these tests when there is no normal distribution

To analyse data, it’s ranked

Significance testing conducted on ranked data

Question 4

What is meant by ranked data?

Answer 4

The value is replaced in a dataset by its rank (position) after we sort the data

e.g. dataset= 25, 64, 72 become 1, 2, 3

Question 5

What happens in a Wilcoxon matched pairs test?

Answer 5

2 values
Work out difference
Difference values are ranked
Sum the difference

Can also:
Work out the square of the difference
Sum the squared difference

Question 6

How are Wilcoxon matched pairs tests ranked? What happened for the positive and negative values?

Answer 6

Sum positive ranks (e.g. 6)
Sum negative ranks (e.g. 7)
T is the lowest value of the summed scores (T would be 6 for example)

While ranking we ignore the sign
Once ranked, signs can then be attached

Question 7

How is the significance of a Wilcoxon matched pairs test measured?

Answer 7

A score must be equal to or smaller than the critical value
Compare T score in a significance table

Question 8

What happens in a Mann Whitney U test? What group is selected?

Answer 8

2 grouped values
Square both values
These are summed, 2 groups of sums
The values are then ranked irrespective of their group

Select the sum of ranks for the largest group, but if both groups are the same size then either can be used

Question 9

How is a Mann Whitney U test found to be significant?

Answer 9

Significance table to check the significance of U
Table is N x N
Table gives 2 ranges of values for significance
Value needs to be in either of those ranges to be significant