Statistics, the Inspection Paradox and Customer Acceptance


One of my favorite funky newsletters is the Maritime Advocate. It often has very useful information, but I really suspect I read it because of a clever bit of marketing. The end of the newsletter often has a bit of silliness, like a list of painful puns or a few bad jokes.

While scrolling through a recent issue I came across a condensed description of the Inspection Paradox. I copy it here from the Maritime Advocate by way of the original blog:

“Airlines complain that they are losing money because so many flights are nearly empty. Passengers complain that flying is miserable because planes are too full. They could both be right. When a flight is nearly empty, only a few passengers enjoy the extra space. When a flight is full, many passengers feel the crunch. Once you notice the inspection paradox, you see it everywhere. Does it seem like you can never get a taxi when you need one? [Especially in Singapore?–ed]. When there is a surplus of taxis, only a few customers enjoy it. When there is a shortage, many people feel the pain.”

The original blog by Allen Downey, provides even more interesting examples and also explains why it seems like your Facebook friends always have more friends on Facebook than you do.

The paradox shows that statistics can be very helpful in decision making, but requires that it fully considers the observer. Is the user the observer, or the service provider the observer? It shows that statistics can be confusing, but just as often statistics are incorrectly presented.

Not too long ago I came across a statistic in a US Government announcement (I have not been able to find it again when writing this blog) that suggested that plug-in electric (BEV, Battery Electric Vehicles) vehicles are not successful because less than 50% of electric vehicle owners would buy a plug-in car for their next car.

This seemed odd, but I did find a report that provides this information.

The report was produced by IHS Markit and showed that, compared to gasoline cars which had repeat customers in the high 80th percentile, plug in electrics had repeat customers only in the 40th percentile.


The report provides no further discussion of this statistic, but when there is an unusual statistic, a conscientious researcher should support its worth, or at least provide a note of caution. None of this occurs in this report. The finding that less than half of consumers will repeat purchase a plug-in electric vehicle is worth further discussion because it is a misleading statistic that next was happily quoted by the EPA.

I suspect that people who own plug-in electric cars (one type of observer) already know the statistic is true, and that it has nothing to do with their loyalty to electric cars.

However, for those who do not own plug-in electrics (a different type of observer) the truth may be a bit more elusive.

Let’s consider the average plug-in electric car owner. At the moment the flexibility of plug in electrics is limited. While it is now possible to drive cross country in a plug-in electric car, it is not as flexible as using a gasoline powered car for long distance driving. Charging takes time, and searching for charging stations takes effort. As such, a single car owner would tend to buy a gasoline powered car. However, a multi-car owner would quickly consider a plug in electric as a second car, where they will use the gasoline car for the long haul work and the plug in electric for the short haul work. Assuming that both cars have the same life, once a consumer has purchased a plug in electric car, their next car will not be another electric car, because, at that time, the gasoline car will be due for replacement.

If such a consumer were asked what type of car they would purchase next, the answer would be: Gasoline (or Hybrid).

If all plug in electric car owners were this type of consumer, the loyalty rate as reported by IHS Markit for plug-in electric cars would be zero!

But the study shows that it is around 40%. This much higher number simply means that there are single car plug-in electric owners who will buy another plug-in electric car next and maybe also multi car plug-in electric owners who are ready to go all plug-in electric for both cars. This statistic more realistically shows that plug in electric owners are completely loyal to plug-in electrics and probably more loyal than gasoline car owners are to gasoline, which is only in the high 80th percentile. (Don’t forget that 20 years ago 100% of gasoline car owners would buy a gasoline car next)

To get a proper handle on consumer loyalty, a different question set would be needed and one is left to wonder why a very large research company dumps a statistic like this on the public without further explanation. There are only two possibilities; IHS Markit researchers are not too bright, or they are simply guns for hire and make an effort to perform research that will purposely draw users to the wrong conclusion. Noting that this has been a multi-year survey, I am betting on the latter option.

It is significant to note that engineers are ethically bound to avoid the use of statements containing a material misrepresentation of fact or omitting a material fact. (Although the term avoid has always bothered me, what is wrong with “will not”?) Meanwhile there are still too many engineers who spend more time wriggling around facts than simply speaking the truth.

There is a Statistician Code of Ethics produced by the ASA, but I am not sure if it can even be enforced and appears to be of very recent vintage (April 2018). I hope it gains acceptance and enforcement; bad statistics can truly harm the public.

As I said earlier, the Maritime Advocate is fun to read, because when you scroll down to the end of the newsletter there is always some silliness.

This is what closed out the Maritime Advocate issue that made mention of the Inspection Paradox:

Bread Dangers

More than 98 percent of convicted felons are bread users.

Fully HALF of all children who grow up in bread-consuming households score below average on standardized tests.

In the 18th century, when virtually all bread was baked in the home, the average life expectancy was less than 50 years; infant mortality rates were unacceptably high; many women died in childbirth; and diseases such as typhoid, yellow fever, and influenza ravaged whole nations.

More than 90 percent of violent crimes are committed within 24 hours of eating bread.

Bread has been proven to be addictive. Subjects deprived of bread and given only water to eat, begged for bread after as little as two days.

Bread is often a “gateway” food item, leading the user to “harder” items such as butter, jam, peanut butter, and even cream cheese.

Bread has been proven to absorb water. Since the human body is more than 90 percent water, it follows that eating bread could lead to your body being taken over by this absorptive food product, turning you into a soggy, gooey, bread-pudding person.

Newborn babies can choke on bread.

Bread is baked at temperatures as high as 450 degrees Fahrenheit! That kind of heat can kill an adult in less than two minutes.

Many bread eaters are utterly unable to distinguish between significant scientific fact and meaningless statistical babbling.