Deltoid

In article fkk@leland.stanford.edu writes:

In a recent post Pim cites Tim Lambert as support for his position on the Florida data. I'm sorry but Lambert's analysis is flawed at its core.

No it isn't. It appears that you don't understand what statistical hypothesis testing is, or what it means.

Let's see what he says: First of all Rick is stating that

it is supportable only in the 'right' time span. Yet he fails to provide proof for such remarks. The time span is the same data as used by Kleck. It is Kleck however who is misleading the facts by carefully selecting his data. Yet even this is not going to help him since the data show no support for his thesis as well.

This is overstating things somewhat. The data does support his hypothesis, in that the reported rape rate did fall. However, this decrease was not statistically significant. This means that random variations in the reported rape rate provide an equally good explanation.

A crime rate two standard deviations from the mean would be statistically significant. However, The 67 rape rate was only 0.9 standard deviations less than the 58-66 mean, so this rate is not statistically significant. However the 66 rate was 1.7 standard deviations above the mean, so the change from 66 to 67 was 2.6 standard deviations (of the 58-66 rate). This is NOT significant because the standard deviation of the changes in the rates does not equal the standard deviation of the rates. For this data, the standard deviation of the rates from 58-66 is 12, and the standard deviation of the changes from one year to the next in the years 58-66 is 16. The change from 66 to 67 does NOT exceed 2 standard deviations (of the 58-66 changes in the rate).

In Kleck's statistical analysis of the Orlando data, he wrote:

"It might be suggested that Orlando had experienced erratic ups and downs in its rape trends before and that the 1967 experience just happened to reflect one of the brief, sharp downward swings in the rape rate, which it had experienced before, and that the downward swing was therefore unrelated to the gun training program. However, this suggestion too is unlikely, since Orlando had not experienced so large a one-year change in rape rates in its recent past, and the decrease exceeded two standard deviations, a measure of the variability in rape rates over the 1958-1966 period (1958 was the first year the FBI reported rape data for the Orlando SMSA). In other words, the rape decrease was considerably larger than would be expected on the basis of variation in the rate in the recent past."

This is mathematically incorrect. Kleck has confused "standard deviation of the rates" (a measure of the variability of the rates) with "standard deviation of the CHANGES in the rates" (a measure of the variability of the CHANGES). His conclusion about the decrease being considerably larger than expected is simply incorrect.

The notion that you can accurately assign a standard deviation to the data as Tim Lambert - and perhaps Kleck as well is fraught with hazards.

The problem is that there is no in this case there is no way to determine an accurate mean for the data - there is therefore no way to accurately determine a standard deviation.

In this case - the rape rate in each year is actually an INDEPENDENT and entirely different measurement - potentially reflecting entirely different conditions. An estimate of a mean and standard deviation when you really have only single data points to support a particular view is invalid in this case. You may make certain assumptions to arrive at a number but these assumptions can easily include observer bias.

This is confused. Statistical hypothesis testing works by DISPROVING hypotheses. In this case the null hypothesis is that the observations are drawn from the same normally distributed population. Under this hypothesis the sample mean and standard deviation are unbiased estimators of the underlying mean and standard deviation. The statistical test tells us that we cannot reject the null hypothesis. You are correct in that it might be false, but statistics can never prove it to be true.

Simply taking y number of years around any given data point and trying to calculate a mean and standard deviation is simply wrong without compelling reasons based in physical reality. One might make compelling reasons to select a particular time range but there are so many variables that can affect the rape rate in any given year it is easy to be wrong.

In this particular case 1958-66 was chosen by Kleck because it was all the UCR data available about rape rates in Orlando before the gun training.

Tim Lambert's comments should be entirely discounted - his numbers are meaningless - he could select the range of data any way he pleases to get his numbers.

Utter nonsense. I didn't select the range of data --- Kleck did. I merely corrected the error in his calculations.

I also note that by the same reasoning Frank could also have said that Kleck's numbers are meaningless, but he doesn't. Is this the pro-gun double standard at work again?