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Students take a two part Mathematics Placement Test: Arithmetic and Algebra.
There will be about 40 questions on each exam.
After the exams they will be given the opportunity to practice with tutorial
software and retake the exam to improve their scores.
We want to test for significant improved scores after using the tutorials.
Which Statistical tests can be used?
Hey themathprof.
The first question you will neeefd to ask is whether you are looking at paired data (i.e before/after scores) or general data (i.e. looking at before and after in a non-paired way as separate random variables).
In the first you look at individual paired trends which you can an overall view of change between each student and in the second, you look at the distributions of scores without looking at specific paired data.
Both can use means to get some level of change of scores and standard inferences on means or difference of means can apply.
The actual test will depend on the nature of the data and its properties.
Ok, Chiro.
If I'm looking at paired data (before/after) then I guess I would determine the Pearson Correlation coefficient, then check if the result is significant. Right?
If I'm thinking of the data as random variables, then I could compare the means & variances/standard deviations using t or z tests. Right?
Thanks for your help, Chiro.
What I was thinking of was actually using the pairs to get a difference distribution of D = Y - X where Y is the after mark and X is the before mark calculated in a pair-wise manner.
You can then test the hypothesis that the population mean of D is greater than 0.
You could also do a non-paired test of the difference of the means and test whether there is any significance (i.e. mu1 = mu2).