Question

A study was done on the timeliness of flights (on-time vs. delayed) of two major airlines: StatsAir and AirMedian. Data were collected over a period of time from five major cities and it was found that StatsAir does better overall (i.e., has a smaller percentage of delayed flights). However, in each of the five cities separately, AirMedian does better.

Which of the following is correct?

(a) This situation is mathematically impossible.
(b) This is an example of Simpson's Paradox.
(c) "City" is a lurking variable in this example.
(d) This is an example of a negative association between variables.
(e) Both (b) and (c) are correct.

Answer 1

The answer is Option E; both B and C are correct

Explanation:

Both (b) and (c) are correct. Simpson's paradox is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data. This result is often encountered in social-science and medical-science statistics, and is particularly confounding when frequency data are unduly given causal interpretations. Simpson's Paradox disappears when causal relations are brought into consideration.

Now, this question is an example of Simpsons paradox because the groups of collected data over a period of time from five major cities showed a trend that StatsAir does better overall, but this trend is reversed when the groups are studied separately to show that air median does better.

So, option B is correct.

Also, City is a variable that influences both the dependent variable and independent variable, causing a spurious association. That is it is the cause of why the 2 results are biased. Thus, city is a lurking variable.

So, option C is also correct