Newb quetion on statistical fallacy

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I know this probably isnt the forum I was looking for, but Ive had trouble finding an answer to my question. I was having a discussion with a friend who used a stat that I felt contained a fallacy within it. Just curious if I was correct. He stated that blacks are twice as likely to die from police encounters than whites and presented a stat saying that 5.6 per 100,000 blacks died vs 3.0 per 100,000 whites dying. To me, thhose numbers scream fallacy. Am I right and if so, what is the problem with his stated stats? Thanks!

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@Daffypuck,

Disregarding that 5.6 is not twice 3.0, suppose the average is somewhere around 4 per 100,000. There are 300,000,000+ folks in the US. That would translate to 1,200 deaths by police encounter.
Does that sound reasonable?

Actual data is necessary.

1 Reply

@Daffypuck,

Without verifying them in any way, this seems like the correct way to look at the numbers.

This is fallacious:

Quote:

There are 300,000,000+ folks in the US. That would translate to 1,200 deaths by police encounter.

The entire population of the country is not routinely stopped by the police. The population if the US is irrelevant. It would be fair to ask for your friend's source (or just Google it.)

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@neologist,

Not only data is necessary but also accuracy enunciating the question.

Quote:

5.6 per 100,000 blacks died vs 3.0 per 100,000 whites dying.

Does this mean that 5.6 people died in 100,000 police encounters with black people or 100,000 encounters with people in general?

Anyway, there's no average to be made as 5.6 blacks and 3.0 whites died, which means 8.6 people died.

Remember that blacks represent between 12 and 17% of the US population.

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@timur,

Its not a matter of truth to the stated stats. Assuming the two stats are correct, I look at them as so small, that it makes them nominal, thus not subject to comparison. Im looking for the fallacy within the way he presented said stats. For comparison, if it was say, 120 deaths per 100,000 for blacks and only 4.3 per 100,000 for whites, then I would agree theres a disparity. But to say 3.0 vs 5.6 and conclude that your chances double because of the nearly double rate per 100,000 just doesnt jive with me.
Timur: Its 5.6 black deaths per 100,000 times a black encounters the police and the same for whites.

1 Reply

@Daffypuck,

It really depends on sample size. If the expected death rate is 3 per 100k and you got 5 after 100k events, that is within the realm of expected variability. 6 would be outside the 95% confidence limit. But if you had 200k events and got 11 instead of the expected 6, that is already outside the confidence limit. You can use a Poisson Distribution Calculator to find the probabilities, but let's say these values are based on one million events each for blacks and whites. That means 30 white deaths and 56 black ones. The probability of getting that number by chance is 0.00001427 so not likely. The populations are clearly different.

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Daffypuck wrote:

But to say 3.0 vs 5.6 and conclude that your chances double because of the nearly double rate per 100,000 just doesnt jive with me.

It should as it's the way it is.

In fact, it's even worse than that, according to "The Washington Times".

Quote:

“The odds that any given black man will shoot and kill a police officer in any given year is slim to none, about one in a million. The odds for any given white man? One in four million,” he said. “The odds that a black man will be shot and killed by a police officer is about 1 in 60,000. For a white man those odds are 1 in 200,000.”

Still, more whites are killed by the police than blacks, as whites represent more than 4 times the black population..

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Yall are getting close to answering my question, I really appreciate all the input. I am looking to debunk my friends statement that "blacks have twice the chance of death when arrested" argument based on the stats he gave. Im looking for the name of the type of fallacy/statistical fallacy in his stats he used to back up his argument. I know this forum isnt the exactly right place to be asking, but I just thought it was a good start.

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@Daffypuck,

I don't think you can. I think given the statement made with the numbers presented, he is correct. Your only hope would be to say that it was based on a small sample size.

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@Daffypuck,

Engineer raised an interesting point.
Is it number of deaths per persons arrested or number of deaths compared to general population?

1 Reply

@neologist,

Its number of deaths per 100,000 arrests. To better illustrate my point, Ill present the stats in a different mannor.
Blacks have a .0056% chance of death when being arrested
Whites have a .003% chance of death when being arrested
The way my friend presented the stats was very misleading. "Blacks are twice as likely to die when being arrested." Although that may be true based on the numbers, it is so insignificant that it really is a nominal statistic.

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@Daffypuck,

I understand your position. You are arguing that the difference is statistically significant but not meaningful. Your friend has the right of it. It is not insignificant that people die in police interactions and 5.6 is significantly more than 3.0. If you are trying to make the point that most police encounters do not result in death, you can do that. Your friend is correct that the difference is significant and meaningful.

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@Daffypuck,

Daffypuck wrote:

Its number of deaths per 100,000 arrests. To better illustrate my point, Ill present the stats in a different mannor.
Blacks have a .0056% chance of death when being arrested
Whites have a .003% chance of death when being arrested
The way my friend presented the stats was very misleading. "Blacks are twice as likely to die when being arrested." Although that may be true based on the numbers, it is so insignificant that it really is a nominal statistic.

Another way of looking at the numbers is;

5600 out of 100k blacks will die while being arrested.

3000 out of 100k whites will die while being arrested.

It is only 400 deaths away from being double.

But also if you think 5600 people dying while being arrested is an insignificant number, I am scared to wonder what you think a significant number should be.

1 Reply

@Krumple,

Im not arguing the morality of the what the stats are about, but the numbers themselves. What the numbers represent are irrelevant. All Im asking is there a statistical fallcy of sorts in his statement. Kind of like the gamblers fallacy. If you flip a coin 25 times and get heads all 25 times, someone who says that theyre due for a tails flip because theyve flipped heads 25 straight times is committing the gamblers fallacy. My friends stats arent that type of fallacy, but trying to make a statement to support his arguement that blacks have double the chance to die vs whites is a misleading statement. Im just curious if it falls in the catagory of a statistical fallacy. I may be wrong. Based on my percentage analogy, theres not much difference, however being nearly twice the chance, between a .003% and a .0056% chance of something happening.

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@Daffypuck,

Daffypuck wrote:

If you flip a coin 25 times and get heads all 25 times, someone who says that theyre due for a tails flip because theyve flipped heads 25 straight times is committing the gamblers fallacy.

True, but your friend is arguing the exact opposite. If you flip a coin 25 time and get heads, it is not a fair coin. It is predisposed to heads. That is statistically accurate. That is the argument your friend is making. Police stops of blacks have an unusual outcome compared to whites, so much so that the events aren't mathmatically equal. You are arguing that even though the coin came up 25 times in a row heads, it is a fair coin.

Daffypuck wrote:

My friends stats arent that type of fallacy, but trying to make a statement to support his arguement that blacks have double the chance to die vs whites is a misleading statement.

You keep saying this. No it is not. His presentation of the statistics is completely reasonable. If he was talking about the chance of getting an albino alligator in Florida vs Louisiana and he presented those statistics, everyone would agree that for some reason Louisiana alligators produce more albinos. There is no fallacy in the way he presents his numbers.

1 Reply

@engineer,

OK, thanks. I appreciate yalls input.

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Newb quetion on statistical fallacy

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