Normality And Non Parametric Tests

Question 1

What is a z score

Answer 1

The number of standard deviations a data point is from the mean

Question 2

Parametric tests

Answer 2

Normal distribution
Interval or ratio data
More powerful but more strings attached
Defined by ‘parameters’ - means and SD

Question 3

Non parametric tests

Answer 3

Not normally distributed
Or data not interval or ratio

Question 4

When is a Kolmogorov-smirnov test (K-S) test used

Answer 4

Normality test to see if scores differ significantly from normal distribution

P<.05 then scores sig different from normal

Sample of 50 +

Question 5

When is a Shapiro-Wilk test used

Answer 5

Normality test
But has more power to detect differences
Sample <50

Question 6

Skewness

Answer 6

Symmetry of distribution
Positive skew - scores clustered to left
Negative skew - scores cluster to right

Question 7

Kurtosis

Answer 7

‘Peakedness’ of the distribution

Positive Kurtosis - peaked with long thin tails

Negative - relatively flat

Question 8

Kurtosis and skewness values

Answer 8

If distribution was 0 the value of skewness and Kurtosis would be 0
The further from 0 the more likely the data’s not normally distributed

Question 9

There is calculations you can do…

Answer 9

1. Check histogram for evidence
2. Divide skewness or Kurtosis value by standard error to produce Z score ( scores between - and + 1.96 suggest normal distribution)
3. Larger sample sizes - important to check actual size rather than sig - less than +/- 1 little problem
   More than - acknowledge
   More than +/- 2 problematic

Question 10

What do non parametric tests do

Answer 10

Check if scores are drawn from same population or not

Question 11

Reporting Mann Whitney U test

Answer 11

Median, interquartile range and Z scores

Question 12

Reporting a Wilcoxon signed rank test

Answer 12

Median, interquartile range, Z score, p-value