America's Safest and Most Dangerous Cities

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The reason I question the assertion that poverty correlates with crime  is that when I plot poverty rates for states vs homicides rates I don't see a correlation. You can check the following data for yourself. When there is a correlation the data points should more or less follow a straight line or at least a curved line. But when I plot this data I get something that looks like a shotgun blast, points all over the place. Now it would probably be more accurate to look at city level or county level data. That takes much more time than even a retired geezer would care to spend. But at least at the state level I just don't see a correlation. Let me know if you disagree.

[data]

Points in statistical analysis very, very rarely follow anything that actually looks like a straight line.  You need a correlation coefficient (more on these in a bit) very close to either +1 or -1 for that to happen.  More often than not, it does look like a "shotgun blast", as you put it.  It often is not immediately obvious whether or not a correlation exists.  However, there are methods of analysis that attempt to find a method in the madness.

The first is the method of correlation coefficients, which I mentioned above.  A correlation coefficient, as I said above, is essentially a measure of how correlated two variables are.  Given random variables X and Y, the correlation coefficient r is given by



where E(X) is the expected value of random variable X, μ_X is the mean value of random variable X and σ_X is the standard deviation of random variable X (essentially, how far away from the mean most values of the random variable are).  It would take a while to get into all of the details, but it suffices to say that the correlation coefficient is a measure of how related X and Y are to each other.  It can be anywhere between -1 (a perfect negative correlation) and +1 (a perfect positive correlation).  A value r = 0 would indicate that there is no relation between the variables at all.

Now, we can't calculate r as above because that's applicable to two random variables, not to two sets of sample data.  However, if you go through the process of calculating the correlation coefficient for two sets of sample data (the formula is much like the one above), then you would get that r = 0.48: not a perfect correlation by any means, but certainly greater than 0, which is what one would expect the correlation coefficient to be close to were there no correlation between the variables at all.  Uncorrelated random variables very rarely yield sets of sample data with a sample correlation coefficient greater than 0.2 or less than -0.2.

Another method would be the process of hypothesis testing, but unfortunately, I really should be heading to bed, so I'll have to do this section at a later date.  It's safe to say, however, that those data are indeed, in fact, somewhat correlated.  It's not a perfect correlation by any means because there obviously would be other factors contributing to homicide rates (I should also note that homicide rates are also not all the crime that might occur due to poverty), but a correlation is actually there, even if it looks like one big mess.

I suppose you're assuming a lot of data points. If you have 2, you will always have a correlation of 1 or -1. If you have enough data points, then much smaller correlations will be statistically significant. Yes, J.J., a correlation of 94% can be statistically significant with enough data points.

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The reason I question the assertion that poverty correlates with crime  is that when I plot poverty rates for states vs homicides rates I don't see a correlation. You can check the following data for yourself. When there is a correlation the data points should more or less follow a straight line or at least a curved line. But when I plot this data I get something that looks like a shotgun blast, points all over the place. Now it would probably be more accurate to look at city level or county level data. That takes much more time than even a retired geezer would care to spend. But at least at the state level I just don't see a correlation. Let me know if you disagree.

[data]

Points in statistical analysis very, very rarely follow anything that actually looks like a straight line.  You need a correlation coefficient (more on these in a bit) very close to either +1 or -1 for that to happen.  More often than not, it does look like a "shotgun blast", as you put it.  It often is not immediately obvious whether or not a correlation exists.  However, there are methods of analysis that attempt to find a method in the madness.

The first is the method of correlation coefficients, which I mentioned above.  A correlation coefficient, as I said above, is essentially a measure of how correlated two variables are.  Given random variables X and Y, the correlation coefficient r is given by



where E(X) is the expected value of random variable X, μ_X is the mean value of random variable X and σ_X is the standard deviation of random variable X (essentially, how far away from the mean most values of the random variable are).  It would take a while to get into all of the details, but it suffices to say that the correlation coefficient is a measure of how related X and Y are to each other.  It can be anywhere between -1 (a perfect negative correlation) and +1 (a perfect positive correlation).  A value r = 0 would indicate that there is no relation between the variables at all.

Now, we can't calculate r as above because that's applicable to two random variables, not to two sets of sample data.  However, if you go through the process of calculating the correlation coefficient for two sets of sample data (the formula is much like the one above), then you would get that r = 0.48: not a perfect correlation by any means, but certainly greater than 0, which is what one would expect the correlation coefficient to be close to were there no correlation between the variables at all.  Uncorrelated random variables very rarely yield sets of sample data with a sample correlation coefficient greater than 0.2 or less than -0.2.

Another method would be the process of hypothesis testing, but unfortunately, I really should be heading to bed, so I'll have to do this section at a later date.  It's safe to say, however, that those data are indeed, in fact, somewhat correlated.  It's not a perfect correlation by any means because there obviously would be other factors contributing to homicide rates (I should also note that homicide rates are also not all the crime that might occur due to poverty), but a correlation is actually there, even if it looks like one big mess.

Gabu
I was hoping someone more talented at statistics than I am would step forward and do the analysis. Is the .48 number based on the data I posted? Can you use hypothesis testing to determine the probability that there is in fact a correlation? 

With regards to using homicide rates as a measure of crime, I feel that in high crime areas crime is under-reported because the residents have learned that reporting a crime does no good. Murders are a different story, because its hard to ignore a corpse. So in my opinion homicide is a more accurate indicator. Also it is probably the most feared crime.

An r correlation  of 0.48 would be statistically significant at the 95% confidence level, provided that you have 18 or more data points. However J.J. would disagree.

With 50 data points, it's even statistically significant at the 99% confidence level.

http://www.gifted.uconn.edu/siegle/research/Correlation/corrchrt.htm