As you work with data more, you'll find that basic descriptives don't always serve your purpose. In this way, data analysis is like home repair. I could use a screwdriver to do most of my projects, but it would be a lot more work and the results would not be as useful. With data, you may need to go beyond the basic and turn to social science or other disciplines for analysis tools as indices.
For example: When San Jose Mercury News economics reporter Scott Thurm wanted to look at the income gap in Silicon Valley to see if it fit with national trends, simply using percentage breakdowns did not show what he needed to know. So we turned to two tools to look at the data in a different way: percentiles and the Gini coefficient of income inequality.
The Gini coefficient
First of all, it's not every day that you get to use a big word like "coefficient." But other than impressing your nerdy friends, the Gini is a useful tool. This tool was developed by Mr. Gini (Italian economist Corrado Gini) in 1912 to estimate the inequality of incomes and wealth.
Special tools are needed to measure income inequality because standard income measurements, such as median, don't give you the whole picture.
Let's consider two income distributions. County 1 County 2 100 18000 888 19001 1000 19300 1200 20000 48800 30000 50000 31600 51800 32000 70000 34000
The median for both of these is $25,000. However, the range is significantly different. County 1 has incomes at extreme ends of the spectrum, while County 2 tends to be in the middle.
Because I didn't have time to come up with a good tool to measure inequality, and Mr. Gini had already done the work, I used a spreadsheet for the Gini formula, which J.J. Thompson had developed at the University of North Carolina.
The data used for the Gini is categorical income data such as that provided in Census figures. For example: 500 people in the $10,000 to $14,999 category, and so on. By multiplying the midpoints of each category by the number of people in the category, you can derive the weighted income, and therefore the other parameters.
According to J.J., the problem arises in determining the midpoint for the top category of income - the Census doesn't limit the income, nor does it give you the value of the top income. What it does do, however, is provide aggregate income for those $150,000 and higher, which can be divided by the number of people in that category to come up with a midpoint.
The result of the Gini is one number you can use to compare your county to other counties or to your county over time. Here's the formula:
Gini=1-SUM(Xi-Xi)(Yi+Yj)
Where:
X is the cumulative proportion of recipients Y is the cumulative proportion of income i is a particular income category j is i-1 (the previous category)
Income Midpts. 1250 Tot. Households 526 Weighted Inc. 657500 Total Inc. 113981250 Total Pop. 7734 PropPop 0.06801138 CumPropPop (PropInc X 0.06801138 PropInc 0.00576849 CumPropInc (Y) 0.00576849 (Xi- Xj)(Yi+Yj) 0.0003923
This is repeated for all the income categories and then totaled so you end up with one number for the county or whatever area you're calculating. You can calculate that same number for other counties to compare geographically or to other years to compare over time.
Jennifer LaFleur can be reached by email at jlafleur@sjmercury.com