Use and abuse of statistics II
 

Here are the second lot of statistical "facts". The puzzle is what's wrong with them and can you give a better explanation.


5) 1 in 3 marriages end in divorce. (quoted almost endlessly - I think in the US the equivalent figure is 1 in 2)

6) Crash helmets cause head injuries. (This was actually used to avoid giving soldiers helmets in WWI)

7) 1 in 3 schoolkids have used drugs. (used on an anti-drug poster campaign)

Re: Use and abuse of statistics II
 

[quote="graeme"]Here are the second lot of statistical "facts". The puzzle is what's wrong with them and can you give a better explanation.


5) 1 in 3 marriages end in divorce. (quoted almost endlessly - I think in the US the equivalent figure is 1 in 2)

6) Crash helmets cause head injuries. (This was actually used to avoid giving soldiers helmets in WWI)

7) 1 in 3 schoolkids have used drugs. (used on an anti-drug poster campaign)[/quote]

As a motorcyclist who has looked into injury statistics, I can tell you of an effect of crash-helmet wearing that is both well attested and convincingly explained.

Since the wearing of motorcycle crash-helmets became compulsory in the UK about 30 years ago, the number of tetraplegic ex-motorcyclists has increased markedly --- both in absolute terms and as a fraction of the number of motorcyclists, of number of accidents, rider-miles and other such measures.

The reason is straightforward. Back in the good old days, many motorcycle accident victims would die of brain damage brought about by a fractured skull. The fact that they also had spinal cord damage from a broken neck was irrelevant in these circumstances. These days, they are about as likely as they ever were to break their necks but they are much less likely to die from brain damage and so go on to suvive the consequences of a damaged spinal cord.


Paul

Yes Xilman,

I can't really add much to Xilman's excelent reply.
Wearing crash helmets move a large number of people from the "dead" category to the "injured" category, thus increasing the number of people "injured" whilst wearing crash helmets.
To be sure there are also people who are "unharmed" instead of "injured" but this is more than made up for in lives saved.

Graeme

Re: Use and abuse of statistics II
 

[quote="graeme"]Here are the second lot of statistical "facts". The puzzle is what's wrong with them and can you give a better explanation.


5) 1 in 3 marriages end in divorce. (quoted almost endlessly - I think in the US the equivalent figure is 1 in 2)

6) Crash helmets cause head injuries. (This was actually used to avoid giving soldiers helmets in WWI)

7) 1 in 3 schoolkids have used drugs. (used on an anti-drug poster campaign)[/quote]

There is nothing "wrong" with any of these statements. They are all true, or at least reasonably close to accurate. The only "wrongness" comes from the implications that are made based on these observations.

Take for example the crash helmet statement. Crash helmets do decrease the ability of the wearer to observe their environment. They may also increase the wearer's risk taking because of the "I'm protected" mentality. Both of these effects are likely to have some marginal increase in the number of collisions.

However, the helmets also reduce more head injuries than they cause.
Although, as Paul points out, a significant number of those "reductions" are only in the way the incident gets reported and not really a reduction in the number of serious injuries.

I've had a small book on my shelf for over 50 years, "How to Lie With Statistics". It's a very good read.

One of my favorite abuses comes from using statistics to imply that certain locations/activities should be avoided because they are associated with physical harm.

The observation is that more people die in bed than any other location.

Wakerbath:

As I mentioned in Use and Abuse of Statistic I some, or most even, are literally true but are misleading like e.g. the crash helmets. As it happens the other two in this topic are widely reported but WRONG, i.e. completely unjustified statements not supported by the data they are allegedly summarising.

This is of course why they are here, your mission (should you choose to accept it) is to explain why they are wrong.

The 1/3 marriages end in divorce one is what actually what caused me to think about such well known, but, shall we say, dubious statistics. I didn't understand what this apparantly simple stat' meant.
Did it mean 1/3 of ALL marriages - but how do you know how my marriage is going to turn out, or my parents' marriage? So is it the number of divorces after say 5 years, or 10 years (or 20 or 30 or ...) It doesn't say. Of course the real answer is .... well I'll leave it a bit. I'll just say that it make a good headline, but take it with a large grain of salt.

Graeme

[quote="graeme"]Wackerbath:
The 1/3 marriages end in divorce one is what actually what caused me to think about such well known, but, shall we say, dubious statistics. I didn't understand what this apparantly simple stat' meant.
Did it mean 1/3 of ALL marriages - but how do you know how my marriage is going to turn out, or my parents' marriage? So is it the number of divorces after say 5 years, or 10 years (or 20 or 30 or ...) It doesn't say. Of course the real answer is .... well I'll leave it a bit. I'll just say that it make a good headline, but take it with a large grain of salt.
Graeme[/quote]

I don't know the "raw" data to which you refer. Without that data, I cannot draw any conclusion about the validity, or lack thereof, of the quoted statistic.

Some of the observations, like hair length, are intutively reasonable.
There is a negative correlation between height and hair length because there is a positive correlation between height and (male) sex and a negative correlation between (male) sex and hair length.

As for the marriages, no marriage lasts forever. Very few last 50 years. Short term fluctuations in demographics may affect the observations, but the long term averages would be correct.

There are three ways that a marriage can (officially) end. I think that we can reasonably ignore the very small number that are annulled. That leaves divorce and death. It is reasonable to categorize the deaths and count the number of divorces and deaths over a given period. That would give a statistic on "the marriages that ended between ... and ...".

Of course, the categorization must be done properly so that we count marriages and not individuals. The divorces are easy to count. In examining the deaths, we must eliminate singles, widow(er)s and divorcees since they are not married at the time of their death. We also need to exclude half of the concurrent deaths since there is only one marriage in that case of two deaths of a married person.

Whilst there's not much traffic here, I'll answer some of Wackerbath's points.



[quote]
I don't know the "raw" data to which you refer. Without that data, I cannot draw any conclusion about the validity, or lack thereof, of the quoted statistic.
.[/quote]

That's the problem isn't it ;) , but the "1 in 3" stat is thrown about regardless of its dubious provenance. You've gone down the sort of roads I did in trying to figure out what this 1in 3 thing actually was, and that it didn't mean what it was usually thought to mean.

In other news, you're spot on with the taller people have longer hair answer. To (slightly) restate it, men tend to be taller than women and men tend to have shorter hair than women, so taller people have shorter hair (statistically)

[quote="graeme"]That's the problem isn't it ;) , but the "1 in 3" stat is thrown about regardless of its dubious provenance. You've gone down the sort of roads I did in trying to figure out what this 1 in 3 thing actually was, and that it didn't mean what it was usually thought to mean.[/quote]

Well, I have more trouble with your claim that it is "wrong". Based on my personal experience, 1 in 3 is not an unreasonable estimate. In my view, the burden is on you to show that there is data to support a significantly different conclusion.

The statistics that I have seen lately are 50% of marriages end in divorce. Looking at the marriages of my friends out of college, that statistic appears to be pretty good. If the marriage lasts at least ten years, it seems to stick much better, but there were a lot after the first few years (a good reason to delay children).

My parents marriage ended with both a civil divorce and a religious annulment. How do you count that one? :rolleyes:

Answers to I & II
 

Hmm I tried posting a version of this earlier today but can't see it. Here goes again.

Here are the answers to Use and Abuse ... I & II, together will a few lines of discssion to make things clear (I hope). Feel free to comment. I hope everyone enjoyed them, especially those who gave answers.


1) Firemen cause fires. Well, where there are significant fires there are firemen and the bigger the fire the more firemen are present. Hence the conclusion. This is a straightforward confusion of correlation with causation. It's easily seen to be wrong in this case, but many real life errors are due to this problem.

2) Taller people have shorter hair. Men are taller than women, and have shorter hair so this is true. What's interesting is that taller men don't have shorter hair than small men, nor do taller women have shorter hair than small women, but taller people do have shorter hair than smaller people.

3) Taller people are more intelligent. Well adults are both taller and more intelligent than children. The problems with this are lack of precision in the terms. Tallness doesn't correlate with intelligence of people of the same age. (I.Q. tests suffer from this problem and have to be "corrected" for age groups)

4) There are more people aged 65 than 64. You'd expect this to be the other way round. The problem here is reporting. If you ask a person someone else's age, they are more likely to not know precisely, and will typically round it to the nearest multiple of 5. So all ages in the mid sixties will tend to be reported as 65, inflating that value and deflating the number of 64s reported. A better way in this case is to ask for birthdates.

5) 1 in 3 marriages end in divorce. This caused the most comment so I'll address it more than the others. Satistics like this are invariably calulated from a particular years figures, so that in a particular year X people get married and X/3 get divorced. This is then generalised into the 1 in 3 get divorced.
this is false for (at least) two reasons. It compares one statistic of one set of people against a different statistic of another set of people. Normally you'd have keep one of these factors constant (comparing different thngs of the same people or the same thing in different people) . there's no a priori reason to suppose any connection between the numbers of people getting married this year and the numbers of failed marriages from 2 5, 10 or more years ago.
Also there is no account taken of the large number of married people who didn't get married or divorced this year.
To illustrate, suppose the same number of people got divorced as married in a particular year. Could we say "Everyone gets divorced" ? Of course not, since there will be a substantial number of married people who are not divorced.

Now, it may be argued that in the long run, the average numbers will relect the divorce rate/marriage rate ratio, but this isn't the case either. Since during the lifetime of the average marriage (which I *guess* to be 10-20 years) both the marriage rate and the divorce rate have changed by a factor of two. Thus making any prediction based on this year's divorce/marriage ratio useless.

All this means that any similarity between this figure and the actual number of failed marriages is at best an estimate and at worst a coincidence.

6) Crach helmets cause head injuries. This has been well discused above.

7) 1 in 3 schoolkids have used drugs. This number was produced from a survery by some anti-drug campaign, primarily to produce a shocking figure so that Someone would Do Something.
The shocking thing was how badly the survery was done. It's hard to know where to start. What's a "drug", what's "use", what's "schoolkid" even. Presumably alcohol isn't included otherwise I would expect the number to be nearly 100%. I don't even think tobacco was included even though it's illegal for minor to buy or use it.
How did they get the info, did they hide behind the bike sheds with clipboards or what?
It turns out that they polled 1000 kids in 3 (3!) schools and of those who answered 1 in 3 said they'd used drugs. Now, is it beyond comprehension that teenagers would lie about using drugs - both ways?
I guess that "in our statistically insignificant survey about 30% of the kids who answered our questions said that they had used drugs of somekind at least once" lacks the punch of the original.

so what's the real ratio - I have no idea


Hope you enjoyed them,

Graeme

Re: Answers to I & II
 

[quote="graeme"]1) Firemen cause fires. Well, where there are significant fires there are firemen and the bigger the fire the more firemen are present. Hence the conclusion. This is a straightforward confusion of correlation with causation. It's easily seen to be wrong in this case, but many real life errors are due to this problem.[/quote]

But Firemen really do cause fires. That's a part of their job.

Haven't you read "Fahrenheit 451"? :)

Seriously, with all the high profile fires in the Western US, haven't you seen the pictures of the firemen with their torches lighting fires?

Starting a small fire in order to gain control of a big one is common practice. It is called a "backfire".