Simpson’s Paradox And Gender Discrimination

One sunny day we arrive at work in the university administration to find a lot of aggressive emails in our in‒box. Just the day before, a news story about gender discrimination in academia was published in a popular local newspaper which included data from our university. The emails are a result of that. Female readers are outraged that men were accepted at the university at a higher rate, while male readers are angry that women were favored in each course the university offers. Somewhat puzzled, you take a look at the data to see what’s going on and who’s wrong.

The university only offers two courses: physics and sociology. In total, 1000 men and 1000 women applied. Here’s the breakdown:


800 men applied ‒ 480 accepted (60 %)
100 women applied ‒ 80 accepted (80 %)


200 men applied ‒ 40 accepted (20 %)
900 women applied ‒ 360 accepted (40 %)

Seems like the male readers are right. In each course women were favored. But why the outrage by female readers? Maybe they focused more on the following piece of data. Let’s count how many men and women were accepted overall.


1000 men applied ‒ 520 accepted (52 %)
1000 women applied ‒ 440 accepted (44 %)

Wait, what? How did that happen? Suddenly the situation seems reversed. What looked like a clear case of discrimination of male students turned into a case of discrimination of female students by simple addition. How can that be explained?

The paradoxical situation is caused by the different capacities of the two departments as well as the student’s overall preferences. While the physics department, the top choice of male students, could accept 560 students, the smaller sociology department, the top choice of female students, could only take on 400 students. So a higher acceptance rate of male students is to be expected even if women are slightly favored in each course.

While this might seem to you like an overly artificial example to demonstrate an obscure statistical phenomenon, I’m sure the University of California (Berkeley) would beg to differ. It was sued in 1973 for bias against women on the basis of these admission rates:

8442 men applied ‒ 3715 accepted (44 %)
4321 women applied ‒ 1512 accepted (35 %)

A further analysis of the data however showed that women were favored in almost all departments ‒ Simpson’s paradox at work. The paradox also appeared (and keeps on appearing) in clinical trials. A certain treatment might be favored in individual groups, but still prove to be inferior in the aggregate data.

The Service Recovery Paradox – Customer Service At Its Best

Let’s say you buy a coffee machine. You go home, plug it in and it does what it’s supposed to do – make coffee. Depending on how easy it is to use, how well the coffee tastes, etc … you experience a certain level of satisfaction. Now suppose one day the coffee machine suddenly stops working. Obviously, your satisfaction will drop sharply. You call customer service and after a lot of try this and try that, all eating up your precious time, it works again. Your satisfaction will rise again, but not to the initial level. You might even decide that next time you’ll not buy from this company again, they don’t seem to be able to provide functioning machines.

This is how the story usually goes. But there’s a very interesting paradox that can lead to a surprising outcome. Given certain conditions (see below) and an exceptional customer service, studies have shown that after the failure the level of satisfaction can rise above the initial level. In other words: customers who have experienced a problem with the product and have been successfully helped by the manufacturer’s customer service can be more satisfied with the company than those customers who have not experienced any problem at all. This is called the service recovery paradox. A widely cited work regarding this paradox by Hart et al. (1990) in the Harvard Business Review states: “A good recovery can turn angry, frustrated customers into loyal ones. It can, in fact, create more goodwill than if things had gone smoothly in the first place”.

I made a crude graph to visualize this situation. Note that in a standard recovery the level of satisfaction rises, but not beyond the initial value. This is the situation we usually experience. A paradoxical recovery propels the level of satisfaction past this initial value.


There are some conditions that need to be met in order for the paradox to be able to occur.

The effect of the severity of the failure

 According to McCollough et al. (2000), satisfaction varies with the severity of the failure. Many service problems that customers experience are only mildly annoying, while others can be very severe. Hoffman et al. (1995) state that the higher the severity of the failure, the lower the level of customer satisfaction. Consequently, the existence of a recovery paradox depends on the magnitude of the failure. For example, perhaps an apology, empathy, and compensation could create a paradoxical satisfaction increase after a 20-minute wait at the front desk of a hotel. But would this paradoxical increase occur if the wait caused the guest to miss a flight? It is unlikely that any realistic recovery is capable of completely erasing the harm caused by such a severe failure.

In the event of a service failure, a recovery paradox is more likely to occur if the service failure is less severe than if the failure is more severe.

The effect of a prior failure

 A person’s satisfaction is a cumulative evaluation of all experiences with the firm (Cronin and Taylor, 1994). If the service failure occurred in a one-time only use, then the satisfaction judgment would be transaction-specific. However, an individual generally has a history of interactions with the firm, in which case satisfaction reflects the cumulative interactions over time between the individual and that firm (Bitner and Hubbert, 1994; Crosby and Stephens, 1987).

In the event of a service failure, a recovery paradox is more likely to occur if it is the firm’s first failure with the customer.

 The effect of the cause of the failure

 Service failures with persistant causes are more likely to repeat than failures with temporary causes. For example, when a hotel guest is assigned to an incorrect room category due to an outdated computer system, this could be considered a failure with a persistent cause. On the other hand, if the guest’s room assignment was botched because the front desk associate is in the initial stages of training, this could be viewed as an temporary cause. Customers are likely to be more forgiving of failures with temporary causes (Kelley et al., 1993). This is because the likelihood of a future inconvenience is minimal. Thus:

In the event of a service failure, a recovery paradox is more likely to occur if the customer perceives that the failure had a temporary cause.

The effect of perceived control

A service failure is any situation where something goes wrong, irrespective of responsibility (Palmer et al., 2000). Nevertheless, “the perceived reason for a product’s failure influences how a consumer responds” (Folkes, 1984, p. 398). Customers are more forgiving if they perceive that the firm had little control over the occurrence of the failure (Maxham and Netemeyer, 2002). Conversely, customers are less forgiving when they feel that the failure was foreseeable and should have been prevented (Folkes, 1984). For instance, did a wait occur because of a random spike in demand, or did it occur because the firm did a poor job in forecasting, planning or staffing? A bank customer may be understanding of a wait inside a bank lobby if there is an unexpected inflow of customers during a typically slow hour. On the other hand, the same customer may be less understanding if there is only one teller working during lunch hour on a Friday afternoon. Thus:

In the event of a service failure, a recovery paradox is more likely to occur if the customer perceives that the firm had little control over the cause of the failure.

For more on customer service, check out the 7 Laws of Customer Service.