In article <3l6qro$f7e@physerver.phy.mtu.edu> cescript@mtu.edu (Charles Scripter) writes:
>On 26 Mar 1995 15:52:02 GMT, Tim Lambert (lambert@alboka.cse.unsw.edu.au) wrote:
>> Except that homicide rates in NSW did fall following the 1920 law:
>[...]
>> It is possible that the drop in homicide rates after 1920 may have
>> been caused by something other than the 1920 law, but to assert as
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> Ah, yes... Now Lambert asserts causality... Another example of
>the fallacies of logic by Tim:
Ah, yes. Another example of the fallacies of logic by Charles. This
one is a particularly crude form of the straw man fallacy:
STRAW MAN
The straw man fallacy is to misrepresent someone else's position so that it
can be attacked more easily, then to knock down that misrepresented position,
then to conclude that the original position has been demolished. It is a
fallacy because it fails to deal with the actual arguments that have been
made.
I did NOT assert causality. Anyone fooled by Charles'
misrepresentation of what I wrote should look again at what I actually
wrote.
>> Charles Scripter does above that "no such effect exists" seems like a
>> better example of "Another triumph of wishful thinking over reality :)"
> I have already shown that the "effect" is within the "quantum
>noise" limit; It is indistinguishable from the expected natural
>variations.
No you haven't shown that: You have presented three bogus analyses
that purport to show that the effect was not statistically
significant:
1. by assuming (incorrectly) that homicide _rates_ were Poisson.
2. by assuming (incorrectly) that the sample standard deviation was
the same as the standard deviation of mean.
3. by inappropriately using a test of extremely low power (essentially
discarding all the years after 1920 except for one)
When we correct the errors in each of the analyses we find a
statistically significant effect in each case:
1. The total number of homicides in NSW 1910-1920 was 474, while there
were 347 from 1921-30. If we assume that the numbers are Poisson
distributed we get the following standard deviations:
Before (1910-20): sqrt(474) = 22
Before (1921-30): sqrt(347) = 19
Converting these to rates we get
Annual homicide rate per 100k population
Before (1910-20): sqrt(474) = 2.3 +/- 0.11
Before (1921-30): sqrt(347) = 1.5 +/- 0.08
Difference = -0.8 +/- 0.14
The difference is almost six standard deviations, which is highly
significant in anyones book.
2. If we calculate the standard deviations of the means in the
conventional way (see an elementary stats book for details) we get:
1910-1920 rates (before) 2.33 +/- 0.13
1921-1930 rates (after) 1.49 +/- 0.11
Difference = 0.84 +/- 0.17
The difference is almost five standard deviations, which is highly
significant in anyones book.
3. Charles claims that his simple model of no change in the homicide
rate fits the data well. Applying the conventional test for goodness
of fit, the chi-square test gives a chi-square value of 69.2 for his
model. This statistic has 20 degrees of freedom (21 observations -
one fitted parameter). The probability of a value this large occuring
by chance is 0.0000002. I think we can reject Charles' model.
In any case, even if Charles' was correct and the decrease was not
statistically significant, it is still incorrect to deny its existence.
> Similarly, your analysis _fails to show_ a significant
>deviation (your "deviation of the means" is incorrect; such can only be
>applied to UN-CORRELATED data. Your model has only a 1/4096 chance of
>the apparent correlation actually being due to random statistics).
I don't think Charles meant to say what he does above. The
statistical tests I have presented show a statistically significant
correlation between lower homicide rates and the gun law. He seems to
be saying that because there is a correlation, the methods used to
show the correlation are invalid. This is nonsense. He then goes on
to say that the correlation has a p value of 1/4096=0.00024, which is
a statistically significant correlation, contradicting what he stated
in the first sentence.
I assume that he was trying to say something else -- perhaps he would
care to try again?
Tim