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December 27th, 2014 (Permalink)

New Book: Cognitive Productivity

Psychologist Luc P. Beaudoin's new book Cognitive Productivity: Using Knowledge to Become Profoundly Effective is now available as an ebook. A couple of smart and lucky readers have won copies―see the Resources, below―but now you can get yours without having to be smart or lucky!


December 23rd, 2014 (Permalink)

A Nutty Holiday Puzzle

It was a hectic day at the Allnut Gourmet Nut Company, as it was the last day to ship out orders that could be expected to arrive in time for Christmas. The company sold four different types of vacuum-packed canned nuts in its "Just Plain Nuts" line: chestnuts, almonds, cashews, and a mixture of almonds and cashews. If the shipment had to wait another day, at least some of the orders would have to be shipped with expedited delivery, which would cut into the company's profits.

Susan Allnut, who was in charge of shipping for the family business, was sitting in her office that morning when her phone rang. "Sue! Sue!" came a frantic voice over the line.

"Tom?" Sue replied, recognizing the voice of her brother, Thomas, who was in charge of production. "What's the matter?"

"Hold the shipment!" Tom shouted into her ear.

"Calm down, Tom!" she almost shouted back. "What's the matter?"

"The labels on the cans are all wrong!"

"What?" Sue felt a sinking feeling in the pit of her stomach. If the shipment was delayed more than a day or two, the company might lose money over the holidays. Black Friday this year could be very black indeed.

"We're going to have to open all the cans to find out what's in them, and then recan and relabel the whole shipment!"

"Now, don't panic, Tom, just tell me exactly what happened."

"The labels were loaded incorrectly into the labelling machine on the assembly line, and all the cans were labelled incorrectly!"

There was a long pause as Susan thought. "But you don't know what cans the wrong labels went on?" she finally asked.

"No, all we know is that they're on the wrong cans." Tom groaned.

There was another long pause, then Tom interjected: "Sue, are you still there?"

"Yes, I'm thinking! You mean none of the cans in the current shipment has the right label?"

"That's right! If it says 'almonds' on the can there won't be a single almond in there; if it says 'cashews', no cashews. It's a disaster!"

There was another long pause as Susan thought, and then she sighed with relief.

"Relax, Tom. It's bad but it's not a disaster. We won't have to open any cans; just switch the labels. It'll be a lot of work, but we can still get the shipment out today."

"But how are we going to know what labels to put on the cans without opening them?"

How, indeed? How did Susan Allnut solve the problem of the mislabeled cans? If you think you know the solution, click on the link below.


December 21st, 2014 (Permalink)

Wikipedia Watch

Check out Alison Hudson's defense of Wikipedia in an article published on Skeptoid earlier this month―see Source 3, below. Despite my specific criticisms and general skepticism about Wikipedia in these "watches" over the years, I agree with much of what Hudson writes. However, I do have a few specific disagreements that I'll lay out below.

In defending the reliability of Wikipedia, Hudson writes: "Vandalism happens, but itís usually caught fairly quickly and reverted; and the vandals are usually blocked and banned." However, this claim is unwarranted, and is a good example of what is called "survivor bias"―see Sources 1 and 2, below. We don't know how quickly "vandalism" is caught and corrected, or "vandals" banished, because we only know about those who are caught. For all we know, the vandals who are quickly caught are only the most incompetent ones.

Similarly, Hudson claims that "youíll notice that most of the longstanding [hoaxes] were able to survive mostly because they were small, unimportant topics that people werenít likely to be referencing anyway…." How many hoaxes have yet to be exposed? We don't know and, as a consequence, we can't accurately judge reliability in this way.

Hudson is on firmer ground when appealing to studies that have had experts examine articles for accuracy, and I have no specific objections to them, but then I haven't examined the studies myself. However, such studies seem to have focused on particular areas, such as information about drugs, that may attract better contributors than other areas. As a result, it's dangerous to generalize to the entire project based on such narrow studies. Instead, what is needed is a random selection of articles to be evaluated by appropriate experts and, judging from what Hudson reports, such a study has yet to be performed. Until it is, we're in a poor position to evaluate the general reliability of Wikipedia.

In general, my view is that Wikipedia is not an encyclopedia in the traditional sense because it lacks authoritativeness, which is different from reliability. At the least, it should not be used as encyclopedias have traditionally been used, that is, as authoritative statements of what is currently known about a topic.

Rather, Wikipedia should be used as a guide to further research, that is, as a sort of written directory to internet resources. It's alright for it to be your first stop in researching a topic, but it should seldom if ever be your last one, which is why educators should forbid citing it in research papers, except in unusual circumstances.

On a positive note, I entirely endorse the following sentiments:

…I often actually tell my students to start with Wikipedia when they conduct research. Many times students, like your typical Internet commenter, know a little bit about a topic but not nearly enough to go on at length. In fact, in some classes I will actually assign the Wikipedia article as a reading assignment and then have them answer some pointed questions based on the information found there. Theyíre going to read it anyways; I might as well acknowledge the fact and make sure everyoneís got the basics down before they begin the real research. … Of course, I also tell my students to verify information in a second source, because Iím aware that any single source of information may be flawed. Thatís not my stance just on Wikipedia, but on any important fact. Starting with Wikipedia is fine; but ending with Wikipedia is a lazy way to do research.


Rape Graph
December 14th, 2014 (Permalink)

Charts & Graphs

This installment's chart doesn't fit into any of the types of misleading graphs we've seen previously, but has its own unique problems.

First of all, a bar chart is not the best choice for conveying this information, which could be conveyed better in words, or perhaps in a pie chart that is subdivided into smaller slices. The bars represent a percentage of a whole―all rapes―with each bar representing a finer slice of that whole. This is why the bars get smaller as they descend the chart, except for the last bar which suddenly represents the remaining rapes outside of the 3 involving prison time. The chart shows that 40 out of 100 rapes are reported, 10 of that 40 lead to an arrest, 8 of that 10 are prosecuted, 4 of that 8 get a conviction, and finally 3 of that 4 lead to prison sentences.

Now, my point here is not to criticize these claims, since most of these statistics are gathered by the police and courts and may well be accurate. However, the claim that only 40% of rapes are reported to the police must be an estimate based on a survey, since the police cannot know for sure how many rapes are not reported to them. Nevertheless, let's accept these figures as accurate for the purpose of analyzing the way that the chart represents them.

The problem that I want to focus on is a conceptual one, namely, that the graph begins at the top talking about one thing―rapes―and ends up talking about a different thing―rapists. Its main point seems to be that only 3% of rapists end up doing prison time for their crimes, but what the next to last bar from the bottom represents is the number of rapes that end in prison time for the convicted rapist. At first glance, this may seem to be the same thing, but it's not. For it to be the same thing there would need to be a one-to-one relationship between rapes and rapists, that is, each rape would have to have been committed by a distinct rapist. We've seen this assumption before in a misleading chart about rape and rapists―see the Resource, below, under point 4―so it seems to be a tempting mistake to make.

To see that it is a mistake, suppose that the three imprisoned rapists were not only guilty of the rapes they were imprisoned for, but between them were guilty of the remaining 97 rapes out of the hundred. This would mean that not 3% of rapists did time, but 100%. Of course, this is a very unlikely scenario, but it is not unlikely that most rapists who go to prison are guilty of other rapes for which they don't serve time. In fact, according to another page from the same organization responsible for the graph: "rapists tend to be serial criminals"―see Source 1, below. So, even if only three rapes out of a hundred lead to a rapist going to prison, that rapist may well be guilty of other rapes which were either unreported, did not lead to the rapist's arrest, were not prosecuted, or for which he was not convicted. In this way, 3% of rapes leading to a prison sentence may cause greater than 3% of rapists to do hard time.


  1. "97 of Every 100 Rapists Receive No Punishment, RAINN Analysis Shows", Rape, Abuse & Incest National Network. This page has a graph similar to the one above but with slightly different numbers for some unexplained reason.
  2. "Reporting Rates", Rape, Abuse & Incest National Network.

Resource: Charts & Graphs, 1/13/2013

Acknowledgment: Thanks to Ryan J for reporting this chart.

Correction (12/29/2014): I've rewritten the last paragraph to correct a confusing and misleadingly worded example.

Solution to a Nutty Holiday Puzzle: "Listen, Tom," Susan Allnut continued, "you said that the labels are completely wrong; that if the label said that a certain type of nut was in a can, then no nuts of that type would be in the can, right?"

"That's right," Tom replied.

"One of the four types of can is a mixture of almonds and cashews, which means that one of the four types of label says 'almond and cashew mix'. So, there can't be any almonds or cashews in the cans with that label. But the only type of nut left is chestnuts, which means that the cans of chestnuts are mislabeled 'almonds and cashews'."

"That's great, Sue, but it's only one type of can!"

"Hold on, Tom! We also know that the nut mix can't be labelled 'almonds' or 'cashews', since there would be nuts of that type in the can. So, the mixture must be mislabeled 'chestnuts'."

"Terrific, but what about the other two types of nut?"

"That's easy! All that's left to account for are the cans of almonds and the cans of cashews, and we know that they're mislabeled, so the cans of almonds are labelled 'cashews' and the cans of cashews are labelled 'almonds'."

"Let me see if I've got this straight: all we have to do is switch the labels on the cans marked 'almonds' with those labelled 'cashews', and switch those on the cans that say 'chestnuts' with those that have the mix label. Then they'll all be labelled correctly."

"You've got it, Tom!"

Did you get it?

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