Researchers have developed a new computer-based self-paced course to teach algeb

Question

Researchers have developed a new computer-based self-paced course to teach 
algebra to students of varying ability. To test the effectiveness of the new 
method, researchers will administer a pre-test to 60 students taking part in the 
study. Half the students will be taught algebra in a traditional classroom, while 
the other half will receive instruction via the new method. A post-test will be 
given to all students upon completion of their instruction, and post-test results 
will be compared to pre-test results. 

A. Is this an observational or an experiment? 

B. Explain how you would randomize. That is, how would you decide which 
children get taught with which method? 

C. Imagine that researchers believe that children with high math ability are 
more likely to excel with this program than those with low math ability. 
Describe a matched-pairs design that could be used to test the researchers’ 
belief.

Explanation / Answer

A. This is an experiment with a control group.

B. You probably want a randomized block design, subdividing "students of varying ability" into blocks by ability, then randomly assigning from each block to treatment or untreated group. If you don't, you may not be able to detect the effect of the program in the "noise" created by one of the courses being richer in students of high ability than the other.

C. A matched pairs design would pair up low- and high-ability students, then assign pairs randomly to treatment or untreated. You'd probably want to identify and randomize other factors, such as age, gender, and family income (which correlates to all sorts of interesting things), when choosing pairs so that you don't inadvertently create a second pairing correlated with the first, and therefore indistinguishable as a causative factor from the first.

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