Contingency tables appear frequently in legal cases, such as those that allege that a company has discriminated against a protected class. The following table gives the number of employees of different ages who were laid off when a company anticipated a decline in business:16

Several long-time employees who were laid off fled a suit against the company for wrongful termination. All were over 50, and they claimed the company discriminated on the basis of age. To use data like these in a trial requires a more complete analysis than we are ready to do. For now, we€™ll settle for a descriptive analysis that lays the foundation.
Motivation
(a) From the employees€™ point of view. On the basis of the claim of their lawsuit, would the laid-off employees expect to find association in this table?
(b) From the company€™s point of view. If the company does not discriminate on the basis of age, would you expect to find association in this table?
Method
(c) From either point of view. Would it be more useful to find the percentages within the columns or the percentages within the rows?
(d) What statistic would you choose to represent the presence or absence of evidence of discrimination?
Mechanics
(e) Are age and employment status associated? Compute the appropriate summary statistic and interpret its value.
Message
(f) Summarize what you find in your analysis of the table.
(g) How would the presence of a lurking factor compromise the use of data such as these in a legal case?

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Laid off Retained Total <40 40 -49 50-59 60 or more 18 14 18 18 787 632 374 107 805 646 392 125 Age