# Comparing difference in murder rate in dependent samples?

I have some mortality data and I am trying to determine if the mortality is different in one subpopulation compared to the total population. The problem is I am having trouble determining which statistical tests to run.

Data

Say I am comparing the number of deaths due to murder in these two populations in a single year. I have estimated the deaths due to murder in the subpopulation in this year based on a 10 year average (which is why it is a decimal <1).

                        Farmers    All occupations
Murders                   0.4           30
Total population          2800          8000000


I can calculate the murder rate per 100,000 people which is 14.3 for farmers and 0.38 for the general population. I can calculate the expected number of farmer murders based on the general population rate, which would be 0.01 murders. I can calculate ratios of the murder rates (14.3/0.38 = 37.6) or observed and expected rates.

I know this is really quite basic but I'm a novice at this and struggling. I am unsure if it is more meaningful to compare crude murder rates or calculate the rate ratio. How can I calculate a p-value and 95% confidence interval to determine whether the rate difference or rate ratio is statistically significant?

• Do you know what are the standard deviations? Is this a home work? – Aksakal Apr 13 '17 at 15:52
• No I don't know the standard deviations. And no it is not homework. – AEV Apr 13 '17 at 17:07

You want to know if being murdered is independent from being a farmer. Use a $\chi^2$ independence test. See : http://www.ling.upenn.edu/~clight/chisquared.htm

You must use real numbers of persons, not average (divided) values or whatsoever. The test mainly tells you if your statistics are strong enough (practically if you enough persons and deviation) to rule out the independent hypothesis. That's why real numbers of persons are required.

Write something like two variables:

• M=0 if not murdered (still living or dead another way), M=1 murdered

• F=0 if is/was not a farmer, F=1 is/was a farmer

Write the table as in the tutorial and just apply the test.

Assume that the farmers get murdered at the same rate as the population, which is $$\frac{300}{8000000}=3.75\times 10^{-5}$$ times in 10 years. Then for 2,800 farmers you expect $$3.75\times 10^{-5}\times 2800=0.105$$ murders in 10 years.

Now, you can calculate the CDF of Poisson with intensity 0.105 for $x=3$, subtract that from 1 and you'll get the probability to observe 4 or more murders in 10 years, which is $5\times 10^{-6}$. This is one tailed test under the assumption that you know the population distribution. Basically it's certainly the case that farmers get murdered way more often than the general population