A particular state's murder rate per 100,000 for 1999 through 2010:
| 1999 | 6.6 | ||
| 2000 | 6.2 | ||
| 2001 | 6.6 | ||
| 2002 | 5.8 | ||
| 2003 | 5.1 | ||
| 2004 | 6.1 | ||
| 2005 | 6.9 | ||
| 2006 | 6.3 | ||
| 2007 | 6.2 | ||
| 2008 | 7.7 | ||
| 2009 | 6.5 | ||
| 2010 | 7.0 |
There was a change in state law for which the first full year was 2008. The average for 1999-2007 was 6.2; for 2008-2010: 7.1 (rounded). Std. dev. is 0.494 and 0.492, respectively. Using Student's T (appropriate because n is so small for both year ranges), for a 95% confidence interval, .380 and 1.222 respectively. This indicates that the 13.9% increase in murder rates for the years 2008-2010 is not statistically significant; the uncertainty range for 1999-2007 is 5.82 to 6.58; for 2008-2010, 5.84 to 12.91. In short, it is impossible to determine at the 95% confidence level if the change in law caused the changed the increase in murder rate. You have to get down to the 80% confidence level before you get statistical significance -- which isn't terribly impressive.
Interestingly: enough the firearms homicide rate, which may or may not include justifiable homicides, rose 25% -- far more than the murder rate.
Do I have this right?
UPDATE: I ran it by a nationally known economist who confirms that the methodology is right.
Clayton,
ReplyDeleteI haven't checked your means and std deviations, but taking them as you calculated them, I plugged them into a stat calculator and got this:
====================
Null hypothesis: Difference of means = 0
Sample 1:
n = 9, mean = 6.2, s.d. = 0.494
standard error of mean = 0.164667
95% confidence interval for mean: 5.82028 to 6.57972
Sample 2:
n = 3, mean = 7.1, s.d. = 0.493
standard error of mean = 0.284634
95% confidence interval for mean: 5.87532 to 8.32468
Test statistic: t(10) = (6.2 - 7.1)/0.3292 = -2.7339
Two-tailed p-value = 0.02105
(one-tailed = 0.01053)
============================
This is showing a statistically significant difference at 95 percent. Doing a little sensitivity analysis, the difference becomes statistically significant when the mean of sample 2 gets to 6.933. The critical t here is "2.228" and according to the above, we're in the tail at -2.733.
Basil