# Non parametric Tests

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How do you know if the distribution is not normal?
When the bars are different sizes for example a few 10 and a few 20
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Where is the most data recorded?
On a ratio or interval scale are normally distributed
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When data is heavily skewed, the step size between points is what?
on the scale is probably constant
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What should happen at the simplest level?
One should probably be using a non parametric test for ordinal data
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What is examples of non parametric tests?
Spearman's rank, Wilcoxon T, Mann Whitney U, Friedman's, Kruskal Wallis
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What is a Mann Whitney U?
Designed to look at difference between treatments in a between groups design
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When is it used?
When there are only two treatment levels (1 IV with exactly 2 levels
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What does it require?
DV to be on at least an ordinal scale
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What is the rational?
If we arrange all the data into an ascending sequence, when the null hypothesis is true, we would expect the scores of the two groups to be randomly distributed
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What happens when the null hypothesis is false?
We would expect the scores of the two groups to be clustered at either end of the sequence
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Mann Whitney U test example?
Experiment: compare two groups of subjects learning lists of words and pictures, rank all scores, if the null hypothesis is true the rank totals should be the same, if the null hypothesis is false the rank totals should be different
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What happens to calculate U?
U=N1N2 + Nx(Nx+1)/2 - Tx
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What are all the components of this equation?
N1-number of subjects in group 1, N2 - number of subjects in group 2, Nx - number of subjects in larger rank total, Tx - total rank (the larger one)
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When is the null hypothesis accepted or rejected according to Mann-Whitney U?
We then compare the observed value of the test statistic, U, to a critical value, We reject the null hypothesis when : Uobserved
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Where is SPSS found?
Independent samples, Mann Whitney U, Define Groups
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What is a Wilcoxon related samples Test?
Designed to look at differences between treatments in a within subjects design
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What is it used for?
When there are only two treatment levels
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What is the rationale?
Test is based on the difference between the 2 scores for each subject, it uses both direction (which score is greater) and magnitude of the differences (how much greater)
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If H0 is true then differences in one direction will be as large as the differences in the other then?
that is what the test statistic will measure – … but it will use ranks of magnitudes rather than actual magnitudes so it can be used on skewed data
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The test statistic we are interested in is what?
Smaller of the T values (whether thats T+ or T-
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What do we compare
The observed value of the test statistic, W to a critical value
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When do we reject the null hypothesis?
Wobserved
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What happens when there are tied ranks?
We take the average of the range of ranks that ties cover and allocate this to other ties
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What happens if there is a zero difference score?
ALl those subjects essentially get removed from analysis, Their score does not contribute to the W statistic, simply reduce N by the number of subjects where this happens
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Where is Wilcoxon found in SPSS?
Analyse/Nonparametrictests/2related samples
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What is the Kruskal Wallis H test?
Designed to look at differences between treatments in between group tests, used when there are multiple levels, requires DV to be an ordinal scale
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What is the rationale?
When the null hypothesis is true we expect a random distribution of ranks across groups: average ranks of levels should be equal, however when the null hypothesis is false we expect a systematic distribution of ranks across groups:different average
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For example?
we want to test the effects on learning of different types of reinforcement given to a child
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What are the three conditions?
No reinforcement, positive, negative
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What do you do next?
work out H
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using what
An equation where where N is the total number of scores Ri is the sum of ranks for each level of the variable ni is the number of scores in each level of the variable
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Where can you find it in SPSS?
Analyse/Non parametric tests/ k independent samples
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In SPSS what does it convert it to?
Chi squared
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How can we test the difference?
Kruskal- Wallis only tells us that the 3 conditions differ but not which ones
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What can we use?
multiple Mann-Whitney tests and apply the Bonferroni correction (multiply the p value by the possible number of tests
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Why use Bonferroni ?
TO reduce the chances of obtaining a false positive
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What is Friedman's test?
Designed for paired samples in both within subject and matched subject design, used when there are multiple levels
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What does it require
The Dv to be an ordinal scale
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What is the friedman's test rationale?
Each individuals scores are ranked:
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When the null hypothesis is true what do we expect?
random distribution of ranks across the subjects: rank totals of d.v. for the different levels of the i.v. will be about equal
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What happens when the null hypothesis is false?
we expect a systematic distribution of ranks across the subjects: rank totals of d.v. for the different levels of the i.v. will be different
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For example what is the Friedman test/
Same as before but run over several days in a within subject design manner
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What happens next
Rank within each subject
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What is the equation?
We calculate X2 R
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Where is it found in SPSS?
Analyse|NonparametricTests|k Related Samples
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As with Kruskall Wallis, the Friedman test does not tell us which condition differs?
is praise is better than no reinforcement? – is criticism worse than no reinforcement? – is praise better than criticism?
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What can we use?
Multiple Bonferroni corrected wilcoxon tests
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What is a real world example?
Repeated exposure to social stress alters the development of agonistic behavior in male golden hamsters.
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## Other cards in this set

### Card 2

#### Front

Where is the most data recorded?

#### Back

On a ratio or interval scale are normally distributed

### Card 3

#### Front

When data is heavily skewed, the step size between points is what?

### Card 4

#### Front

What should happen at the simplest level?

### Card 5

#### Front

What is examples of non parametric tests?