Rationalissimus of the Elenchus

Applying general statistics to individuals in a Controversial Debate

People often take general population stats and act as if they can apply to individuals - usually themselves - because they share something in common with the group that the statistics are taken on.

Logical form:

X stat refers to A group (on average)

A1 is a subset of A group

Ergo, X also refers to A1


Harrison: Black people are 9 times more likely to experience police force against them than white people. This means that, as a black man, I'm more likely to be manhandled than you.

Sven: You know that's not necessarily true, right? Unless we know the spread of the data we can't tell which black individuals are having force used against them, and why. 

Another example:

Vera: Did you know that 1 in 3 women will be diagnosed with breast cancer?

Primrose: So I have a 33.3% chance of developing cancer. Damn...makes for scary reading, huh?

Beverley: This doesn't make any sense. We're all in our twenties; most people only start developing cancer later on in life. So unless you have some sort of genetic deficiencies, I doubt your cancer risk is that high.

In both cases, generalised statistics were used to make inferences about individuals in the broad groups these stats referred to. Harrison fallaciously concluded that because he's black, he is automatically more likely to have force used against him by police. Primrose fallaciously concluded that she has a 1/3 chance of developing cancer simply because at some point, 1 in 3 women are diagnosed with it. Both fail to take into account data spread and how data often clustered in one subgroup of the wider group, a subgroup which they do not belong to.

This is the ecological fallacy, but I was wondering whether it is ever valid or at least, 'less' fallacious, depending on context.

I'm not sure how Primrose could rescue her claim. But in Harrison's case, we should ask: why are black men more likely to have force used against them? If the answer can be explained by racial bias (conscious or not), then Harrison might be reasonable to reach the aforementioned conclusion, even if he isn't exactly 9 times more likely to have force used against him.

asked on Thursday, Jun 10, 2021 07:11:12 PM by Rationalissimus of the Elenchus

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Bo Bennett, PhD

This seems like a good example of the fallacy of division . The statistic is true of the whole population, but it is not (necessarily) true of any individual within the population.

answered on Friday, Jun 11, 2021 07:44:56 AM by Bo Bennett, PhD

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Monique Z

I don't see these examples as fallacious.

Example one:

Person A says that black people are 9 times more likely to have force used on them by the police compared to person B who is presumably not black. This is a fair assumption at face value if there are in fact statistics to prove it. Person B attempts to refute this claim by suggesting it's possible that they are not the kind of black people the studies are referring to. However, the point still remains that skin color is a predictor for police force. Person B needs to provide grounds for assuming the statistic don't apply in this case if that's their argument. 

Example 2: 

1 in three women have a chace of developing breast cancer. Beverly argues that because the onset of cancer usually happens later on in life that somehow she does not have a 33.3 percent chance of developing breast cancer. But this is beside the point, it still is the case that she has a 1 in 3 chance of developing breast cancer. 

answered on Friday, Jun 11, 2021 09:43:00 AM by Monique Z

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Bo Bennett, PhD writes:

This is fallacious because statistics (such as these) are looking at the whole population and do not consider specifics. As one example, statistics often have an uneven distribution. Consider 100 random people in a room but one is Jeff Bezos. The average wealth of each person in the room is a few billion dollars. It would be unreasonable to conclude that any given individual in the room is worth a few billion dollars. Group statistics MAY provide useful information about individuals in the group, but are only reliably useful for the group itself.

posted on Friday, Jun 11, 2021 10:17:01 AM
Monique Z writes:

[To Bo Bennett, PhD]

I do agree with what you said here. But the specific example I don't think shows an unreasonable presumption from a statistical standpoint.

consider example two: On average, 1 in three women will develop Brest cancer. The inference made is that a woman on average has a 33.3 chance to develop brest cancer. Statistically speaking this is correct. If, maybe someone concluded in a room full of three women one of them will have breast cancer, that would be a fallacy. But merely remarking that a woman has a 33.3 percent chance to develop brest cancer is not fallacious. 

[ login to reply ] posted on Friday, Jun 11, 2021 11:51:50 AM
Bo Bennett, PhD writes:
[To Monique Z]

I think it can be reasonably inferred that the 1 in 3 refers to in one's lifetime. If this were all the information one has, then I agree that it is not unreasonable to think that any single woman has a 1 in 3 chance in getting breast cancer. Perhaps it is the "curse of knowledge" problem I face in that I know data and science, and know that there are many factors that contribute to the likelihood of getting breast cancer. So if the national average is 1 in 3, someone who has no history of cancer in the family, eats well, avoids booze, etc. would have a much lower chance. But we cannot expect everyone to know this as it does seem domain specific. I can see this argued either way as a fallacy or not.

[ login to reply ] posted on Friday, Jun 11, 2021 03:57:51 PM

I'm less convinced it's a logical fallacy and more inclined to see it as a misunderstanding (or perhaps misinterpretation) and subsequent misuse of the statistics being cited.  [Of course, if the misuse is intentional and done for the purpose of swaying others toward a bad conclusion, that would be another thing – I'll assume it's not the case here].

Assuming that the statistics being cited (rate of police force and cancer diagnoses) in fact come from well-designed and conducted studies and are reported accurately, I suspect some of the bases of the studies aren't being considered.

In the cancer case, Vera started out talking about "breast cancer" and the other two moved the discussion to just "cancer" – perhaps they were still implying breast cancer, but that's not what the two statements said, so Primrose and Beverly may well be moving the goal posts by switching the topic of conversation.  As well, it's not clear when the 1-in-3 chance of a cancer diagnosis is anticipated.  Beverly seems to be implying that they're talking about a cancer diagnosis now, i.e., while they are in their twenties.  I suspect most legitimate studies about incidence of disease address chances of being diagnosed with the disease at some identifiable point in one's lifetime.  If that's the case here, it's a misuse of the statistic about diagnosis rates to claim that it can be applied now to these three twenty-somethings.

A statement like " 1 in 3 women will be diagnosed with breast cancer " is a simple, quick, and easy re-statement of the study results – and perhaps a good way to share general information.  However, I suspect the actual statement from the study might be a much lengthier version, perhaps something like: " from a group of women studied, we found that 33.3% of the women studied had been diagnosed with breast cancer at some point in their lives (or by some identified point in their lives, like perhaps a specific age).  Although the study did not consider every woman in the world, the techniques used in this study make it reasonable to assume that for other randomly selected groups of women, there would be similar results (within X %age points) for 19 times out of 20 (or whatever error criteria are applicable to the study). "

That longer statement would give Beverly (in addition to the "we're in our twenties" point), other bases for her "This doesn't make any sense":  (1) the Vera-Primrose-Beverly group doesn't seem to be all that randomly selected; (2) not all groups of women are expected to provide similar results – some are, but 1 out of 20 groups are expected to give different results.

In the Harrison-Sven example, I'm not sure how knowing the data spread will help identify individuals who are likely to experience police force against them.  

In each case, the study results tell us how often the element under study occurs (experience police force or cancer diagnosis).  From there, to make more sense out of the statistics and to render them more useful with respect to individuals, researchers would likely conduct some form of post hoc analysis or perhaps even totally new studies ... in hopes of determining if there are factors (other than just being black or a woman) that are associated with having force used against them or receiving a breast cancer diagnosis.  Then, unless Primrose displays some of the identified contributing factors, perhaps she could see the reading as less scary.  As well, if we were to discover that Sven (more often than Harrison) engages in activities or puts himself in situations that were closely associated with police violence, then we might well conclude that Harrison is, in fact, less likely to be manhandled than Sven.

I'm still less convinced that it's a logical fallacy and more inclined to see it as a misunderstanding, misinterpretation, or misuse of the statistics being cited – along with the incorrect implication that the misapplied premise about the statistic is true.  It's sort of like saying " Your big truck has a fuel tank that's twice as large as the tank on my small car; therefore, you can drive your truck twice as far as I can drive my car before we run out of fuel. "  I don't see it as a logical fallacy – it's just a false premise that tank size is the only factor affecting a vehicle's range.

answered on Friday, Jun 11, 2021 11:52:47 AM by Arlo

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Rationalissimus of the Elenchus

So, I've come to the realisation that I did not phrase this question correctly. As a result, I've created quite a bit of confusion in the thread and people aren't grasping why I thought these inferences were fallacious. I'm going to try to clear that up now, and also answer my own question.


In this case, the data they're discussing is a statistical report showing that there were  incidents of force used against white people in a given time period, and 9 incidents of force used against black people in the same period. It wasn't a simulation exercise, just pure quantitative data.

Harrison reasons that, as he is black, and the rate of force used against blacks is 9 x , he's more likely to have force used against him than Sven. As I pointed out, this  can be reasonable...if we know that the disparity is caused by racial bias; that means skin colour will now be an indicator of force used. However, we do not know that, and so it is inappropriate for him to draw this conclusion.


This example is even more poorly-worded. Vera talks about breast cancer, and Primrose ends up talking about  all  cancer. I meant to write "breast" (lol) there instead. 

Vera states 1 in 3 women will be diagnosed with breast cancer. Primrose concludes she has a 1 in 3 chance of getting it. While I get Monique Z's point - it's presumably a lifetime risk - no one gets cancer  simply because  they're women. And as Dr Bo points out, different lifestyles can lead to different cancer risks. So it is wrong to assume that Primrose's personal risk of breast cancer - or  any  cancer - is 1 in 3 based on those figures alone.

Really dropped the ball here, need to stop being obsessed with this website and sort my life out :(

answered on Friday, Jun 11, 2021 06:27:14 PM by Rationalissimus of the Elenchus

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Monique Z writes:

No worries, brother :) I personally think statistics are inherently deceptive in that it often misleads people into believing that a particular statistic is going to apply to them, when the truth is statistics only tell you the probably of that statistic applying to you in a crude sense.

Like in the example of police force. The way the data from this study is summarized would lead a black person to believe they are 9 times more likely to have police force used against them compared to their non black friends.

Same with the statistic about breast cancer. If the average women hears "one in three women develop brest cancer" she's likely going to think that means her odds of getting breast cancer is about 33.3 percent.

IMO the way the statistics are presented is what leads to the mistaken beliefs. The average person is I think unaware that statistical averages don't take into account distribution of outcome. I personally tend not to put much weight into statistics for this reason.

posted on Saturday, Jun 12, 2021 08:37:08 AM