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 two of the three imprisoned rapists were not only guilty of the rapes they were imprisoned for, but 32 others out of the hundred that they got away with, and that the third rapist was guilty of the remaining 33. This would mean that not 3% of the rapists who committed the 100 rapes 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.

November 27th, 2014 (Permalink)

Thank You!

On this day of thanksgiving, thanks to all of those who have supported The Fallacy Files since I last thanked you―which isn't often enough! Special thanks to those who have donated directly via the PayPal button to the right! Thanks also to everyone who clicked on a Google ad!

It's not too late. With the holidays approaching, please consider doing any shopping at Amazon by way of one of the links from this website. It won't cost a penny extra and will benefit the site. Thank you all for helping to keep The Fallacy Files strong and free!

November 26th, 2014 (Permalink)

A Thanksgiving Family Feast Puzzle

This Thanksgiving, instead of sitting down in front of a television after the big meal and watching a football game, why not cozy up to a holiday-themed logic puzzle?

To celebrate Thanksgiving, Gretchen invited various family members to her house for dinner. Some invitees had prior commitments and sent their regrets, but six of her relatives attended, including Frieda. Each guest, including Eric, brought one item for the family meal, while Gretchen provided drinks. The following are eight facts about the dinner:

  1. Allie is an only child who did not bring the roast turkey.
  2. Bill is neither Gretchen's paternal grandfather nor her only brother, and he did not bring either the stovetop stuffing or the green bean casserole.
  3. Gretchen's visiting cousin did not provide the turkey.
  4. Carla brought either the candied yams or the mashed potatoes.
  5. Gretchen's favorite niece didn't bring the stuffing.
  6. David is Gretchen's only son but he didn't bring the turkey or the stuffing.
  7. A female family member was responsible for bringing the mashed potatoes.
  8. Gretchen's favorite aunt brought homemade cranberry sauce.

Can you determine the familial relationships to Gretchen of each family member who attended, as well as the dishes each brought to the Thanksgiving dinner?


November 23rd, 2014 (Permalink)

Sanity Check it Out

It's time once again to check the "sanity" of a number that, in this case, is found on some websites. Here is a quote from one such site:

…[M]ore than four million women are battered to death by their husbands or boyfriends each year [in the United States].

Is this a plausible number? How would you go about checking it by using what you already know as opposed to doing research? In other words, check the plausibility of the claim rather than simply accepting it. To get the most benefit from this exercise, don't just evaluate the number for plausibility, but make a case for your evaluation. When you're done, click on the link below to see one such check:

Sanity Check

Previous Entries in this Series:

November 19th, 2014 (Permalink)

Poll Watch: A "new numerical low"

Gallup: 'New numerical low' for Obamacare

The above is a recent headline from a Politico article―see Source 1, below, and read the whole thing: it's short! What is a "new numerical low"? According to the article:

Support for Obamacare continues to decline, with the law hitting a new low in approval, and a new high in disapproval, as the second enrollment period has opened for Americans, according to Gallup. Just 37 percent approve of the Affordable Care Act, 1 percentage point less than the previous low recorded in January, Gallup found in a new survey released Monday. The pollster notes the approval results are a “new numerical low” for Obamacare. … A majority of Americans disapprove of Obamacare, at 56 percent―a new high, Gallup said.

If you're a savvy poll-watcher, the fact that the drop in the approval rating is only one percentage point should set off your internal alarm. A single percentage point is never a significant result in a public opinion survey, and most national polls have a margin of error (MoE) of plus-or-minus three percentage points. The largest such polls have a MoE of around plus-or-minus two percentage points, so that even in the largest polls this would not be a significant change. The article ends:

The Gallup poll was conducted Nov. 6-9 and surveyed 828 adults. It has a margin of error of plus or minus 4 percentage points.

So, a one-percentage-point drop is well within the MoE, and not a statistically significant result. This is presumably why Gallup, in its own article on the poll―see Source 2, below―referred to this as a "new numerical low", that is, to distinguish the drop from a significant result. Such a small change is not just statistically insignificant, it's not practically significant or "significant" in any other sense of the word. It's possible that this is the start of a downward trend in the approval rating, but it's just as possible that it's the result of statistical noise. The only way to tell will be to check future polls. As Gallup's article goes on to say: "…with approval holding in a fairly narrow range since last fall, it may be that Americans have fairly well made up their minds about the law…".

I've never heard the phrase "new numerical low" before, and a web search produces results either reporting on this poll or unrelated to polling. The word "numerical" in the phrase appears to play a similar role to the word "nominal" in discussing prices. A "nominal" price is one that hasn't been adjusted for the effects of inflation. Similarly, a "numerical low" appears to be one that doesn't take into account the MoE, thus treating an insignificant result as if it means something. A price that has been adjusted for inflation is called a "real" price, in contrast to a "nominal" one. We should make a similar distinction between "numerical" lows and "real" ones in polling results.


  1. Lucy McCalmont, "Gallup: 'New numerical low' for Obamacare", Politico, 11/17/2014
  2. Justin McCarthy, "As New Enrollment Period Starts, ACA Approval at 37%", Gallup, 11/17/2014

Resource: How to Read a Poll

November 16th, 2014 (Permalink)

Check 'Em Out

Psychologist Barbara Drescher has two interesting articles on the Skeptic Society's new "blog" Insight that discuss the difference between intelligence and rationality―see the Sources, below. I have drawn a similar distinction between the intelligence spectrum from stupid to smart, and the "wisdom" continuum from foolish to wise. Smart people, such as the physicist whose story Drescher tells, can be foolish. This is not a contradiction though it might seem so, because intelligence is not the same thing as wisdom. As a result, we shouldn't assume that people who have foolish, irrational beliefs are, therefore, stupid.

My experience with Mensa was similar to Drescher's, except that I never actually joined. When I wrote to the organization and expressed interest in joining it sent me an envelope like that received by Drescher, which dampened my enthusiasm.

The second of Drescher's articles is the more important one because there she discusses what rationality is, and how it can be improved. Unfortunately, you probably can't do much to raise your native intelligence, but you can learn to be more rational by changing or improving your dispositions. Much foolishness results from lazy thinking and, while you may not be able to improve your native intelligence, you can become a less lazy thinker. Sometimes the slow but determined turtle beats the fast but lazy rabbit.

The problem about whether a married person is looking at an unmarried one that Drescher gives in the second article is one I've dealt with before, including two puzzles based on it―see the Resources, below.

Sources: Barbara Drescher,


November 8th, 2014 (Permalink)

Listen Up!

There's a new Skeptoid podcast by Craig Good about how to read, watch, or listen to the news with appropriate skepticism―there's also a transcript in case you'd rather read it. Go read or listen to the whole thing―it's short!―then return here as I have a few additional comments and amplifications. See the Source, below. I'll wait.

Oh, you're back! What took so long? Anyway, here are my comments, keyed to some of Good's section headings:

Source: Craig Good, "A Skeptical Look at the News", Skeptoid, 11/4/2014

Resource: Check 'Em Out, 12/9/2006


  1. Ad Hominem
  2. Emotional Appeal
  3. False Dilemma
  4. Genetic Fallacy

Previous Entry

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