Airline flight delays. Here are the numbers of flights on time and delayed for two airlines at five airports in one month. Overall on-time percentages for each airline are often reported in the news. The airport that flights serve is a lurking variable that can make such reports misleading.

Alaska Airlines America West On time Delayed On time Delayed Los Angeles 497 62 694 117 Phoenix 221 12 4840 415 San Diego 212 20 383 65 San Francisco 503 102 320 129 Seattle 1841 305 201 61

(a) What percentage of all Alaska Airlines flights were delayed? What percentage of all America West flights were delayed? These are the numbers usually reported.

(b) Now find the percentage of delayed flights for Alaska Airlines at each of the five airports. Do the same for America West.

(c) America West does worse at every one of the five airports, yet does better overall. That sounds impossible. Explain carefully, referring to the data, how this can happen. (The weather in Phoenix and Seattle lies behind this example of Simpson’s paradox.)

540 CHAPTER 24 Two-Way Tables and the Chi-Square Test