The right way to say this

[carson8]

Say I have the following statistical data:

In a given area, in 9 out of 10 cases of homicides, the victim is a male.

I'm having a heated argument with a friend about expressing this statistical data in terms of probabilities.

He says: "There's a 90% chance for a man to become the victim in a homicide case, in that area"

And I say that the right way to say this is: "Given a homicide has been committed in that area, there's a 90% chance the victim is a male"

I don't want to anticipate mine or his arguments to defend either of these phrases, but which way to express this statistical data in terms of probability is correct?

Thank you

 

[Harry_the_cat]

Definitely the second one.

The first one is saying that 9 out of 10 men will be murdered in that area.

 

[Dr.Peterson]

Say I have the following statistical data:

In a given area, in 9 out of 10 cases of homicides, the victim is a male.

I'm having a heated argument with a friend about expressing this statistical data in terms of probabilities.

He says: "There's a 90% chance for a man to become the victim in a homicide case, in that area"

And I say that the right way to say this is: "Given a homicide has been committed in that area, there's a 90% chance the victim is a male"

I don't want to anticipate mine or his arguments to defend either of these phrases, but which way to express this statistical data in terms of probability is correct?

Your friend is saying P(homicide | male) = 0.9; you are saying P(male | homicide) = 0.9. The latter is clearly what the data say.

I suppose your friend may well mean the right thing; it could just be his grammar that is messed up, especially if he puts stress on the word "man" when he says it. I'd ask him to clarify, and point out that his actual words mean the wrong thing. And statistics need to be expressed correctly; they are confusing enough when they are!

 

[Steven G]

If you are a male living in this area I would move out immediately just in case your friend is correct!

For the record, your friend is not correct.

 

[carson8]

Thank you all for your answers, I'll be back with some feedback.
Thank you

 

[carson8]

After some back and forth, there are some slight changes, please read below.

Data: In a given area, in 9 out of 10 cases of homicides, the victim is a male.

My friend statement is: "On average, a man in that area has 9 times more chances to get killed by another man, than by a woman"

And I say the right way to say this is: "Given a homicide has been committed in that area, there's a 90% chance the victim is a male, and if the victim is a male, there's a 90% chance the victimizer is another male"

Also, not only I believe my way is the right way to say this, but also that his way is wrong.
So, I would appreciate some comments on that too.

Again, thank you all so much.

 

[Dr.Peterson]

Data: In a given area, in 9 out of 10 cases of homicides, the victim is a male.

My friend statement is: "On average, a man in that area has 9 times more chances to get killed by another man, than by a woman"

His statement this time (which is quite different from what you said before) is about the killer rather than the victim! Clearly that can't be right.

It appears to mean, P(killer is man | victim is a man) = 0.9. This is wrong.

As I said before, but clarified to make the newly required distinction, the given statement says that P(victim is male | victim was killed) = 0.9. It says nothing about the killer.

Does your friend speak English? What reason does he give for thinking the data means that?

And I say the right way to say this is: "Given a homicide has been committed in that area, there's a 90% chance the victim is a male, and if the victim is a male, there's a 90% chance the victimizer is another male"

The last half is either your own invention, or is from a statement you haven't shown us. Again, nothing was said about the killer (your "victimizer"). If more was said, please tell us the whole thing, rather than making us guess.

 

[uruman]

Hello everyone, I am carson8s friend. My statement is:

"In a country where 9 out of 10 murders are committed by men, it is fair to say people in that country have 9 times more chances to get killed by a man than by a woman".

Would you consider this statement right or wrong?
Thank you very much all of you!

 

[carson8]

If more was said, please tell us the whole thing, rather than making us guess.

Sorry about the misunderstanding and the back and forth, you're absolutely right, nothing was said about the killer before.

Let's say the data we have is this:

In a country, 9 out of 10 murders are committed by men.

Here's how we would put it in terms of probabilities.

My friend says: "People in that country have 9 times more chances to get killed by a man than by a woman"
I would phrase it like this: "Given a homicide has been committed in that country, there's a 90% chance it was committed by a man"

Thank you

 

[JeffM]

If the data show that, in 9 homicides out of 10, the victim is a man, then it is correct to say

The probability that the victim of murder is male is 90%.

It is not correct to say

The probability that a man will commit murder is 90%.

It is not correct to say

The probability that a man will be murdered is 90%.

The quoted data do not shed any light on the probability of murder, nor do they shed any light on the probability that the sex of the murderer is male.

Dr. Peterson is absolutely correct: translating the meaning of statistical data into correct, understandable speech requires very great care. People may not say what they mean. People may not understand what they hear.

 

[Dr.Peterson]

Hello everyone, I am carson8s friend. My statement is:

"In a country where 9 out of 10 murders are committed by men, it is fair to say people in that country have 9 times more chances to get killed by a man than by a woman".

Would you consider this statement right or wrong?
Thank you very much all of you!

What you say here is valid (but see below), but it has nothing to do with what we have been discussing.

Why does the question keep changing??? The statement originally given was "In a given area, in 9 out of 10 cases of homicides, the victim is a male." This is entirely different from what you are now telling us you have been given.

Let's say the data we have is this:

In a country, 9 out of 10 murders are committed by men.

Here's how we would put it in terms of probabilities.

My friend says: "People in that country have 9 times more chances to get killed by a man than by a woman"
I would phrase it like this: "Given a homicide has been committed in that country, there's a 90% chance it was committed by a man"

Both are valid, now that you seem to agree at last on what you are talking about. Why do you think one is right and the other is wrong? And why aren't you satisfied with the original statement?

Actually, I don't care for the phrasing " 9 times more chances"; that, taken literally, is not about probabilities, but about opportunities! And many people would say that "9 times more" means "10 times as many", though I myself allow that idiom. This just isn't a mathematically literate statement. Yours is more so.

If I had reason to express it as you two have, I would say, "one is 9 times as likely to be killed by a man as by a woman", and "the probability that a given randomly chosen homicide was committed by a man is 90%."

 

[carson8]

What you say here is valid (but see below), but it has nothing to do with what we have been discussing.

Why does the question keep changing??? The statement originally given was "In a given area, in 9 out of 10 cases of homicides, the victim is a male." This is entirely different from what you are now telling us you have been given.


Both are valid, now that you seem to agree at last on what you are talking about. Why do you think one is right and the other is wrong? And why aren't you satisfied with the original statement?

Actually, I don't care for the phrasing " 9 times more chances"; that, taken literally, is not about probabilities, but about opportunities! And many people would say that "9 times more" means "10 times as many", though I myself allow that idiom. This just isn't a mathematically literate statement. Yours is more so.

If I had reason to express it as you two have, I would say, "one is 9 times as likely to be killed by a man as by a woman", and "the probability that a given randomly chosen homicide was committed by a man is 90%."

I understand your point, I didn't realize one statement was made in terms of probabilities and the other in terms of opportunities. But, the core of our argument (between me and my friend) is about whether or not to specify (somehow) that a murder has been committed, to then talk about either probabilities or opportunities.

For instance, you say: "the probability that a given randomly chosen homicide was committed by a man is 90%.".
The way I understand it, it makes sense because the crime has been committed already, and you're calculating the probability for the killer to be a man.

But, when you speak in terms of opportunities, and you say "one is 9 times as likely to be killed by a man as by a woman", I don't see it.
The reason is, it makes me think everybody in that country is sharing the same chances to be killed.
So, I would say it like this: "If one is to be murdered, then one is 9 times as likely to be killed by a man as by a woman"

Maybe this time I was able to illustrate what the argument is about.
Thank you

 

[Dr.Peterson]

I understand your point, I didn't realize one statement was made in terms of probabilities and the other in terms of opportunities. But, the core of our argument (between me and my friend) is about whether or not to specify (somehow) that a murder has been committed, to then talk about either probabilities or opportunities.

But, when you speak in terms of opportunities, ...

We don't talk about "opportunities", and in particular, I didn't! I was saying that "have 9 times more chances" sounds like "have 9 times more opportunities", which is not a probability statement. It means there are 9 times as many times when you could be killed. But I'm being picky there. He meant to express probability with terms like "the chance of this is 90%"; he just worded it oddly.

But, when you speak in terms of opportunities, and you say "one is 9 times as likely to be killed by a man as by a woman", I don't see it.
The reason is, it makes me think everybody in that country is sharing the same chances to be killed.
So, I would say it like this: "If one is to be murdered, then one is 9 times as likely to be killed by a man as by a woman"

I don't see it that way at all. My phrasing (which is about probability just as much as the other) applies only when a murder has been committed, so there is no need to separately state that. I listed two cases: being killed by a man and being killed by a woman; these will occur in the ratio 9:1 regardless of how likely it is to be killed in the first place. And I can't imagine how that can be taken to say everyone is equally likely to be killed; it says nothing at all about how likely one is to be killed. (It sounds like you're going back to the original error of confusing who is killed with who kills. I hope you aren't involved in law enforcement.)

Your version here isn't wrong; it just isn't necessary. If one is not killed, then one is not killed by either a man or a woman.

This is just a silly argument over words, and is wasting my time.

 

[Harry_the_cat]

“Then you should say what you mean,” the March Hare went on. “I do,” Alice hastily replied; “at least–at least I mean what I say–that's the same thing, you know.”
Lewis Carroll - Alice's Adventures in Wonderland

 

[carson8]

Let's say I have the following statistical data:

9 out of 10 murders are committed by men.

Can someone please tell me, if all the phrases below accurately describe the statistical data above?

A- "People have 9 times more chances to get killed by a man than by a woman"
B- "The probability that a given randomly chosen homicide was committed by a man is 90%"
C- "One is 9 times as likely to be killed by a man as by a woman"
D- "If one is to be murdered, then one is 9 times as likely to be killed by a man as by a woman"

It's just about the correct way to speak about the statistical data in terms of probabilities (or opportunities). My opinion is there's a lot of variables and conditions involved in a murder, and so B and D somehow consider those variables to have a value, or those conditions to be met when they specify that: "a murder has been committed already" (B), or that there's certainty the murder will be committed, "If one is to be murdered" (D). Following this same line of thoughts, I think A and C are not correct because those phrases assume everybody has the same chances to be killed equally, or have the same chances, whether those variables and conditions are met or not, or are likely to be met or not.

The underlying argument is about race, which is always a topic, so let's say the real data is:

9 out of 10 murders where the victim is of race X are committed by men of the X race

If A and C are correct, then I can say.

"A person of race X has 9 times more chances to get killed by a man of race X than by a woman of race X"

And I think this is wrong because the phrase assumes all persons of race X share the same probabilities of being murdered.

So I would say it like this.

"If a person of race X is to be murdered, then that person is 9 times as likely to be killed by a man of race X as by a woman of race X"

This is the argument about, how to say things accurately.
Thank you

 

[Deleted member 4993]

Let's say I have the following statistical data:

9 out of 10 murders are committed by men.

Can someone please tell me, if all the phrases below accurately describe the statistical data above?

A- "People have 9 times more chances to get killed by a man than by a woman"
B- "The probability that a given randomly chosen homicide was committed by a man is 90%"
C- "One is 9 times as likely to be killed by a man as by a woman"
D- "If one is to be murdered, then one is 9 times as likely to be killed by a man as by a woman"

It's just about the correct way to speak about the statistical data in terms of probabilities (or opportunities). My opinion is there's a lot of variables and conditions involved in a murder, and so B and D somehow consider those variables to have a value, or those conditions to be met when they specify that: "a murder has been committed already" (B), or that there's certainty the murder will be committed, "If one is to be murdered" (D). Following this same line of thoughts, I think A and C are not correct because those phrases assume everybody has the same chances to be killed equally, or have the same chances, whether those variables and conditions are met or not, or are likely to be met or not.

The underlying argument is about race, which is always a topic, so let's say the real data is:

9 out of 10 murders where the victim is of race X are committed by men of the X race

If A and C are correct, then I can say.

"A person of race X has 9 times more chances to get killed by a man of race X than by a woman of race X"

And I think this is wrong because the phrase assumes all persons of race X share the same probabilities of being murdered.

So I would say it like this.

"If a person of race X is to be murdered, then that person is 9 times as likely to be killed by a man of race X as by a woman of race X"

This is the argument about, how to say things accurately.
Thank you

You say:

9 out of 10 murders are committed by men.

Assuming we know

what murder is​

Then the question remains:

Murder of what?

Men​

Women​

Babies​

Rats​

any living being​

???