Practical 5: comparing means: non parametric groups

Question 1

Name the parametric tests for means and proportions?

Answer 1

Means - one sample t test, independent samples t test, paired samples t test
–> Data needs to be normally distributed

Proportions - one sample chi square, pearsons chi square (crosstabs), McNemar Test (two paired samples)
–> For these need to check the assumptions hold < 20% of cells have expected frequencies less than 5

Question 2

Name the non-parametric numerical tests that compare means?

Answer 2

1 sample - Wilcoxon

Independent samples - Mann-Whitney (Wilcoxon sum ranked)

Two paired samples t test (Wilcoxon signed ran for paired tests)

Question 3

What are the assumptions for Wilcoxon signed rank test?

Answer 3

Skewed continuous data or discrete/interval data (ordinal data 5 points)

Observations need to be randomly and independently drawn

Null is that the median equals a certain value

Analyse –> non-paraetric test –> one sample –> test fields (input variable) –> settings –> settings (customise and compare means to pre-set value wilcoxon signed rank)

Question 4

What needs to be reported from the Wilcoxon signed rank test?

Answer 4

Standardised test statistic - Z

Asymptotic significance - p

Question 5

What is the Mann-Whitney U test

Answer 5

Is the non-parametric comparable of independent samples t test (comparing two groups mean)

Split file by groups and compare distribution first

Analyse - non-parametric tests –> independent samples –> in settings choose customised tests and choose Mann-Whitney U test

Report Mann-Whitney U - test statistic
P value

To report –> distribution of VARIABLE was statistically different across GROUPS

Question 6

When is related sample wilcoxon signed rank test used?

Answer 6

To compare non-normally distributed paired data

Choose non-parametric - related samples - put paired groups in test fields - in settings and customisable tests choose related samples wilcoxon signed rank

Report standardised test statistic - Wilcoxon rank sum Z
Report asymptotic p value

Question 7

List the tests for comparing groups if the assumptions don’t hold

Answer 7

Assumptions - enough data - up to 20% cells can have expected count < 5 // the minimum expected count is larger than 0

One sample chi square - binomial exact test
Independent groups (Pearson’s chi square) - Fisher’s exact
Paired sample chi square - binomial exact test

Question 8

When the one sample binomial exact test is performed what statistics are reported?

Answer 8

Exact test p value

For independent samples chi (Pearson’s) the nonparametric equivalent is fisher’s

Question 9

What are the assumptions for the McNemar test?

Answer 9

That there are at least 25 discordant cells

Observations are paired

Discordant observations are at least 25 (no - yes // yes - no)

Question 10

In SPSS for McNemar test how do we run the nonparametric versions - binomial exact test?

Answer 10

DO THE SAME THING

In SPSS - McNemar test is always done valid for a binomial exact distribution so whether or not the assumptions are violated the same value counts

Question 11

What is the McNemar-Bowker test?

Answer 11

• A version of the McNemar test with more than three levels - i.e. before and after time points with three levels (never, sometimes, always)

The Pearson’s or Fishers can also be with two groups that have more than two levels