Test Issues

Here are some thoughts about the tut question with possible (not model answers)

Question 2.
Step 1 is to determine the scales of measure for the two variables.
School Type is clearly nominal, while the Mathematics performance (given our principle of how to treat instruments) can be assumed to be interval.

a) The simplest approach here merely to look at appropriate stats from the table and that for nominal scales you have to choose between mods and frequency tables, while interval scales have the whole gait of mean, std dev, etc..

This is what is expected for Monday.


A more sophisticated approach would be for example note that given the spread of school types, the mode would be less helpful and the frequency table a more complete description of school type.

A more thorough process for maths ability would reflect that means and std dev's would give a quick overview off differences, while the histogram/box plot would provide a good summary of the shape and the skewness and kurtosis would be useful alternatives if there was no space for graphs.

b) The key to this exercise to try and think about what you know about schools in SA and to try to describe that with your numbers.

For example SA schools have massive differences in perfromance from schools with 100% pass rates every year to those with 0%. As such the variance is likely to be high. Urban schools often perfrom better than rural schools (often due to resource issues) while private schools for similar reasons tend to be better performers than government schools. In particular there are many elite private schools which are massively resourced. Rural private schools include a number of farm schools which are very poorly resourced as well as number of religious schools which vary dramtically in quality. As such we may expect a higher variance here. Given that a table of means and SD's might look like.

Urban Private Mean=75, SD=10
Urban Government Mean = 60, SD=15
Rural Private Mean=56, SD=25
Rural Government Mean=45,SD=20

These number were made up simply to reflect what I had presumed to be true above. IF an exercise like this apeared in the text I would outline the patterns and then ask you to make up the numbers.
c) The most NB is not to be fooled by the word relationship in the title. If you use the IV/DV decision chart and note that the IV (School type) is Nominal and the DV (Maths perform..) is interval than the table telss you that your answer should be something like a t-test or an Anova.

A bit of thought would suggest that your are in essence comparing the different school types and thus your are in fact on the left hand side (Compare means) of the main decision tree. You then note that there are 4 school types (hence >2 samples) and thus analysis type is Anova. (there is nothing to suggest a non parametric or multivariate anlysis so stick with anova.)

For the purpose of the test you don't need to distinguish between 1 way or n-way.


d) If there was more than 1 mease of maths perf. then you would have multiple measures of the DV and thus the analysis would be multivariate. Hence using the third row for multivariate analyses you would get that MANOVA is appropriate.




Question 3.

Again note that all variables are interval.

a) Reread note for 2a above.
b) As everything is interval you are in the bottom right hand corner of the IV/DV table hence a choice between correlations and regression.
In the right hand side of the main table (relationships between vars) you should note that we have 1 DV (Turnover intentions) and several IV's (all the others). That suggests that the best analysis is regression. Note that prediction typically(but not exclusively) is associated with relationship analyses (regression the most common) , but most importantly identifies our IV's (the predictors) and the DV (the response - or what is predicted.)
c) In the case of non parametric data, we could either use CHAID as a nonparametric equivalent to regression or do a series of Spearman rank correlation coefficients.


These questions are a little harder (primarily in the lack of detail) than what will be in the test but cover the same sort of skills.