6.5 Critical Analysis

Statistics are sometimes flawed by bias, intentional or not. To judge the conclusions of a study properly, you need information about its sampling and analytical methods.

Ex 1 A manager wants to know if a new aptitude test accurately predicts employee productivity. The manager has all 30 current employees write the test and then compares their scores to their productivities as measured in the most recent performance reviews. The data is ordered alphabetically by employee surname. In order to simplify the calculations, the manager selects a systematic sample using every seventh employee. Based on this sample, the manager concludes that the company should hire only applicants who do well on the aptitude test. Determine whether the manager’s analysis is valid. P.203

Ex 2 An advertising blitz by a computer training company features profiles of some of its graduates. The number of months of training that these graduates took, their job titles, and their incomes appear prominently in the advertisements.

(a) Analyse the company’s data to determine the strength of the linear correlation between the amount of training the graduates took and their incomes. Classify the linear correlation and find the equation of the regression.

(b) Use the regression to predict the income of a student who graduates from the company’s program after 20 months of training. Is this prediction reasonable?

(c) Does the linear correlation show that the company’s training accounts for the graduates high incomes? Identify possible extraneous variables.

(d) Discuss any problems with the sampling technique and the data.

To sum up, when evaluating claims based on statistical data:

• Is the sampling process free from intentional or unintentional bias?

• Could any outliers or extraneous variables influence the results?

• Is there any extrapolation that is too far removed from the data set to be relevant?

• Has causality been inferred with only correlational evidence?

p.209# 1, 3, 5, 8

p. 212# 1-2, 4-13