Sociology 498: Homelessness

Interpreting correlations

Correlations are the central part of Burt's analysis and our 1990 Census analaysis of city differences in homelessness. A few guidelines help us interpret these numbers.

The question that we are trying to get an answer to is: What kinds of city characteristics distinguish high homelessness cities from low homelessness cities? For example,

• Do cities with higher rates of poverty also have higher rates of homelessness?
• Do cities with low welfare benefits have more homelessness?

All the numbers in the table are correlations. They report the strength of the relationship between two variables: in this case, homelessness and many other characteristics of the cities. Each row represents some other city characteristic that ranks cities from high to low.

Many of the correlations have no asterisks after them. That means they are not "statistically significant" -- in other words, they are ZERO for all we can tell. A zero correlation means that cities with more of that characteristic do not on average have high OR low rates of homelessness. For instance, the correlation with "% in poverty" is .051 with no asterisks. This means that cities with high poverty rates do not have any more homelessness than cities with low poverty rates. But high poverty cities don't have any less homelessness either.

A large positive number (with asterisks!) means that there is a correlation between the two variables. For instance, the correlation of homelessness with "% One-person households" is .459. This means that cities in which a large proportion of households are only one-person households tend to be cities with high homelessness rates.

A large negative number (with asterisks!) also means that there is a correlation between the two variables, but in this case that cities that are high on the variable tend to be low on homelessness. For instance, the correlation of homelessness with "% Owner-occupied, 1980" is -.329. This means that cities in which most homes and apartments are owned (as opposed to rented) tend to be cities with low homelessness rates. (Another way of saying this is cities in which most homes and apartments are rented are cities with high homelessness rates).

The bigger the correlation coefficient (in either a positive or negative direction), the stronger the relationship. So, for instance, the correlation of homelessness rates with % one-person households in 1980 (.459) is bigger than the correlation with the correlation with fair market rent of a 1 bedroom apartment in 1989 (.293). That means cities with high 1989 homelessness tend to be have many one-person households and tend to have high rents, but the household types are somewhat more important than high rents in determining homelessness rates.