From: cmk@athena.mit.edu (Charles M Kozierok)
Subject: Re: Misleading stats
Organization: Massachusetts Institute of Technology
Date: Sat, 23 Jan 1993 04:31:48 GMT

In article <1jnvbh$s94@agate.berkeley.edu> delorme@garnet.berkeley.edu (Lisa DeLorme) writes:
>In article <C12HCG.HCw@ecf.toronto.edu> pelton@ecf.toronto.edu (PELTON MATTHEW ALAN) writes:
>>  On the "Facts (sic) & Arguments" page of the _Globe & Mail_ today,
>>there's a statement that "The majority of men who assault women in 
>>Canada are white (71.9 per cent) and Canadian-born (63.4 per cent)."
>(stuff deleted)
>>  Also -- what do you think of the statement?  My friend doesn't mind
>>it because he thinks it's supposed to show that white Canadians are
>>just as likely to beat their wives as are non-white immigrants.  I
>>think it's misleading because it implies (without stating) that white
>>Canadians are more likely to beat their wives (because they commit
>>the majority of the crimes), without actually stating it.  It was 
>>provided as a statistic on its own, without any context, so it 
>>seems patently misleading, even though it's not false.
>>
>
>
>I think the statistic is only misleading if you read things into it that it
>doesn't claim, in other words, if you confuse absolute numbers with rates.
>
>An example I often use with my students: The majority of people who are on
>welfare are white. African-Americans receive welfare at a higher rate than
>other groups. How can both statements be true? (They are). It is because
>there are more whites than anyone else. Say you have a population of 100,00
>people, 80% white (80,000) and 20% black (20,000) and no other races. Say
>10% of the whites were on welfare (rate), that's 8,000 people. Say 25% of
>the black people were on welfare (a rate), that,s  5,000 people. Blacks
>would have a higher *rate* of welfare membership, while more white people
>*in absolute numbers* would be on welfare.
>
>Thus, the statistic above is not misleading. It is refering to absolute
>numbers and stating accurately that the majority are white. To know if
>the rates differ, you would have to know the percentage of *each* race that
>beats their wives, or know their relative proportions of the population.
>If 79.9 percent of the offenders are white, but whites are only 20% of the
>population, then clearly they are offending way out of proportion to their
>numbers. If all groups offend equally, then we would expect their percentage
>in the offender pool to be roughly equal to their percentage in the population
>pool.
>
>Thus the statistic qouted in the paper is fine. Sometimes a rate is more
>appropriate, sometimes an absolute number, depending on what you are trying
>to state. From the above statement, it *would not* be appropriate to say that
>non-whites are *more likeley* to beat their wives because the data that would
>allow you to compute a rate is not there. But, the paper didn't make that
>assertion, the reader did.

i disagree. in order for it to be misleading, the statistic merely must
result in people having the wrong impression about reality, regardless
of what was said. if many people think one thing after reading the
statistic and many people think something else, it is misleading, even
if it is not incorrect. and the statistic in question most definitely is
misleading.  because a large number of the Globe's readers are concerned with
proportions, not absolute numbers. and they could have avoided the whole
thing by simply including the necessary demographic references.

--
charles