Student Learning Outcomes
At the completion of this unit of instruction students will
be able to:
In parametric statistics - the type described in previous studies - there were certain assumptions made about the distribution of the data. With Non parametric types of statistics no assumptions are made about the way in which scores are distributed.
Q: So, which type should you use?
A: Well, it is really determined by the type of data you collect.
Parametric tests are more powerful and should be used unless
assumptions have been clearly not met or when dealing with certain
types of data.
Non parametric statistics are especially useful with variables
that do not lend themselves to interval type data, e.g. ranks
or frequencies such as in questionnaire responses (when dealing
with nominal [categorical] or ordinal [ranking] data). These situations
often occur in qualitative and descriptive studies and less often
in experimental studies.
Chi-Square
Useful when you have nominal data in different categories
and want to know if the categories differ significantly from one
another.
In text you had the example of whether the results on one tennis
court differ significantly from the results on the others. Another
example would be to compare the responses of a group of males
and group of females on a question to determine if there were
significant differences (e.g. would you prefer snacks in PEHLS
graduate classes to consist primarily of (1) vegetables, (2) cookies,
or (3) either is fine with me?).
Some restrictions with Chi-Square
1. Observations must be independent (person can't give several observations because obviously the person's observations will be related)
2. Categories must be mutually exclusive (can only score in one category)
3. Is not applicable for small samples. Can't have less than
1 in any cell and no more than 20% of cells can have less than
5. N for 2x2 contingency table should be at least 20
Mann-Whitney U Test
Similar to the parametric t-test
Can be used with v. small or v. large groups and requires ordinal (rank) measurements.
Q: Think about a meaningful way in which you could design a
study that collected raw data that you would convert into ranks
to compare two different groups.
A: It could be anything that is similar to the example you developed for a t-test. In this case however your subjects are not receiving any treatment but are being tested to see if differences exist. For example in your class we could test to see if a difference existed between the midterm scores of males and females, or students studying full-time and part-time students. In these examples because the composition of your groups is very different you might not be able to assume the data would be normally distributed.
Note text example compared experienced and inexperienced golf
teachers. The skill difference between the two groups suggests
that the assumptions of normality would not exist - thus Non parametric
statistics.
Wilcoxon Matched-Pairs Signed-Ranks Test
Similar to dependent t-test in which the scores of two groups are related - maybe because the same subjects tested twice. Because you are testing the same people twice and anticipate a relationship, in an experimental study you would have to use a dependent t-test rather than an independent t-test.
With Non parametric data instead of using the Mann-Whitney
U Test you would use the Wilcoxon Matched-Pairs Signed-Ranks Test.
Text example gives case of researcher interested in self-concept
of students before and after an adventure program.
Kruskal-Wallis ANOVA by Ranks
A Non parametric test of group differences with more than two independent groups (similar to regular ANOVA). For example, we could look at differences between students in karate, badminton, and line dance classes in terms of their expressed commitment to exercise.
Notice that you can do follow up comparisons of the means similar
to ANOVA
Friedman Two-Way ANOVA by Ranks
Similar to repeated measures in ANOVA which uses chi-square as the test for significance.
For example, we could examine differences in graduate student achievement as measured by a multiple choice exam, short answer exam, or oral exam. This might be an interesting way of discovering that our measurement of learning is highly dependent on the tool used for assessment!
Spearman Rank-Difference Correlation
Similar to correlation - when we are interested in examining relationships - but used in situations when assumptions of parametric statistics cannot be met (similar to Pearson r).
For example, a coach might be interested in seeing whether
a correlation exists between her athletes' playing ability in
one sport compared to another (assuming they all played both sports).
She, and the other coach could rank these athletes and use the
Spearman Rank-Difference Correlation to see the relationship.
This would be quite interesting because we would start to see
the extent to which athletic ability is transferable.
Concluding Thoughts
Do notice that the statistical techniques described in this
chapter are comparable in many ways to the statistical techniques
already described for examining correlations and differences.
The big difference is the type of data being collected and the
extent to which it meets assumptions of normality.
(Revised 2/9/99)