Parametric and Non-Parametric Tests

Question 1

What are the Parametric and Non-Parametric tests and what makes them different?

Answer 1

2 categories of statistical testing.
Parametric relies on their being parameters that must be met
Non-parametric does not rely on any prior parameters.

Question 2

What are the criteria that are needed to do a parametric test?

Answer 2

1. Ratio-level data
2. Typically assumes normal distribution
3. Typically assumes similar variance

Non-parametric tests are used on all data types and make no assumptions about the distribution or variance.

Question 3

List the stages of the parametric check list

Answer 3

1. Is your data ratio-level? if not then use NP
2. Assess normality - normal distribution? if not use NP
3. Assess similarity of variance - if SD of MOST variable sampleis < 10 x SD of least variable sample the variance is sufficiently similar to proceed with parametric.

Question 4

When would you not use the parametric check list?

Answer 4

with small samples. Select parametric if you see no reason to think it won’t fit the criteria. Otherwise the non-parametric is never wrong.

Question 5

Can you do a parametric test if any one of the check list is not comliant with the criteria?

Answer 5

No! You would do a non-parametric test.

Question 6

Aside from the frequency histograms, what would you use to test for normality?

Answer 6

1. Skewness and Kurtosis
   - Both are measures of how distored the curve is from normal distribution.
2. Kolmogorov-smirnov test (for N >2000 - not often used)
3. Shapiro-Wilk test (N <2000)

Question 7

How do you work out the skewness and Kurtosis result from the statistics provided?

Answer 7

on SPSS the tests produce a Statistic and Standard Error numbers.
Statistic/Std error = skewness/kurtosis

The result must be within -2 to +2 for the distribution to be normal, thus thumbs up for parametric! Outside these parameters and you must use NP.

Question 8

What results do you get in a shapiro-wilk output and which one is of most interest?

Answer 8

1. S-W statistic
2. degree of freedom (df)
3. Sig value (P-value)

Sig value is of most interest.

Question 9

What does the Ho for the Shapiro-Wilk test predict?

Answer 9

That there IS normal distribution.
<0.05 we ACCEPT the Ho that our data is NORMALLY distributed - Parametric
>0.05 we REJECT the Ho that our data is skewed - NP

Question 10

What is used to test Equal Variance (or homogeneity of variance)?

Answer 10

Levenes test as calculated on the mean (there are a number of different results which are based on other descriptive stats e.g. median)
We look at the Sig value:

<0.05 we REJECT the Ho because they DO have equal variance - Parametric
>0.05 we ACCEPT the Ho that there is NO equal variance - NP