Measuring Hayward’s diversity

We got an interesting e-mail on Monday from Hayward resident Chuck Purvis, who is also the official “Census Person” at the Metropolitan Transportation Commission. It was in response to a Sunday Review article on politics, ethnic segregation and at-large vs. district elections in Hayward, which itself was prompted by a talk that Cal State East Bay professor Melissa Michelson gave on the subject last week. (You can view Michelson’s detailed presentation here: District Elections for City Council)

Warning: If, like me, the word “entropy” causes you to stare blankly into space, or makes you think vaguely of Thomas Pynchon, you might want to refresh yourself with a quick crash course before reading Chuck’s email:


I was interested in your article in Sunday’s Daily Review: “Power in Numbers.”

In terms of calculating a “diversity index”, we have relied on an index based on “entropy.” For example, if there are five groups of things, and all groups are equally represented (20% each), then there is a “perfect” diversity, with an index, or score, of 1.000. If, on the other hand, there was 100% in one category and 0% in the other four categories, then we would have a perfectly un-diverse score of 0.000.

So, I checked the Census Bureau’s American Factfinder, and downloaded the data for all places in the U.S., using the bureau’s latest 2005 American Community Survey data. The data is in Excel format, including a summary table showing the 25 most racially diverse large cities (65,000-plus population) in the entire United States. You can view ranking here.

Vallejo is the most racially diverse large city in the United States, with a diversity index of 0.945. Hayward is the second most racially diverse large city in the U.S., with a diversity index of 0.926. Oakland is No. 3 in the U.S. (Matt’s note: Those three are followed by: Jersey City, N.J., at fourth; Sacramento fifth; Fairfield sixth; Richmond (Calif.) seventh; San Leandro eighth; Stockton ninth; and New York City comes in at 10th.)

In a nutshell:

Assume five groups (white, black, Asian, Hispanic, and other (other + American Indian + native Hawaiian + multi-racial).

1. Multiply each proportion by the natural logarithm of the proportion. So, if proportion is 0.25 (25%), then: 0.25 * ln(0.25) = -0.34657.

2. Sum the five values. The answer will be negative, and approaching -1.609.

3. Divide this sum of -1.609. The answer is the diversity (entropy) index. (Note: the -1.609 denominator is based on 5 * 0.20 * ln(0.20).)

Five years ago, we calculated the diversity index for all places in the Bay Area, using Census 2000 data. That data is available here (see Table A.3 in Data Summary #1).

Interestingly, in 2000, Hayward was the sixth most diverse place in the Bay Area, after #1 Vallejo, #2 Ashland!; #3 Suisun City; #4 Oakland; and #5 Pittsburg. (The 2005 survey data isn’t yet available for smaller cities, like Ashland, Suisun City or Pittsburg. Have to wait a couple of years.)

Don’t ask me to explain the difference between the entropy index and the dissimilarity index….

[Please feel free to share this info....]

Happy Holidays,

Chuck Purvis

We also noticed that along with being the second-most diverse U.S. city according to Chuck’s ranking, Hayward had the highest (6.8) percentage of “Other” among the top 25. Others, in this case, being anyone who doesn’t define themselves as black, white, Asian or Latino. (This, as Chuck noted, could include American Indians, Hawaiians and people who are multi-racial.) Go diversity!


  • Monica

    Good article; I will definetly share it.

  • Old Baldy

    the Bay area will always be the leaders in progressiveness, whether it be ethnic diversity, technology or education.