Testpreparation organizations like Kaplan Princeton Review e

Test-preparation organizations like Kaplan, Princeton Review, etc. often advertise their services by claiming that students gain an average of 100 or more points on the Scholastic Achievement Test (SAT). Do you think that taking one of those classes would give a test taker 100 extra points? Why might an average of 100 points be a biased estimate?

Solution

Its not sure that the test taker would get 100 extra points if he/she takes any one of the calsses. The value \'100\' is an unbiased estimator of the increase in extra points, so it can\'t guarantee the prediction of a students score accurately.

The extra points attained in SAT might depend on several other factors which is not included by these classes. They just simply add the value of SAT scores and take the average to come up with a number like \'100\'. While the fact is that this might be a highly unbiased value because there is high probability that the toppers will have a high increse in their SAT score while the students at the bottom may even lose some score.

For example if there are 100 students in any one of the classes above, and suppose the top 20 students had an increase of 250 points in SAT, middle 50 students had an avergae of 90 points increment and the bottom 30 have a 16.67 points increment, then also the average total increment is 100.

But the fact is that about 80% of the students didn\'t get 100 extra points.

So, its an unbiased estimate of the average increase in points.