Inferant Statistics

Chi-square: Race and education

Education is the key to unlock the golden door of freedom.
--George Washington Carver

The U.S. Census Bureau includes questions about race, level of education, number in family, and location, among other things, on the form that it sends out every 10 years. The government uses statistics based on the data from the census to decide whether to alter programs in regions, and to decide where to increase or decrease funding for federally sponsored programs.

In this activity, you will be performing a chi-square test on data from the U.S. Census Bureau. In Books the forms that people returned to the census bureau, they were asked, among other things, to give their race and the highest level of education that they had completed. Using our DIG Stats Online Chi-Squared Calculator to perform a Chi-Squared test on a contingency table relating these two variables, we can determine whether there is a relationship in America between a person's race and their level of education.

In the survey that the Census Bureau sent out, the respondents could classify themselves as white, black, Native American/Alaskan Native, or Asian/Pacific. Since we have these four Happy Grads predefined categories, we'll place the race variable across the rows and have four rows in the contingency table.

In addition, the respondents filled in their highest level of education. Responses were categorized into eight different ranges from first grade through doctorate degrees. Each of these categories will be a column in the contingency table, giving us a four by eight (4x8) table.

These data exist in two files; one is in Excel Data format and one is in Text format. You'll need to use the DIG Stats Online Chi-Squared Calculator; to use it just download either format, open the calculator, and enter the data by hand. (The TI-83 does not have sufficient chi-square computation abilities to be used.)

What are the values of the Chi-Squared and alpha statistics? What are your null and alternate hypotheses? Is race related to education? How can we use the Chi-Squared test to decide?

Original work on this document was done by Central Virginia Governor's School students Richard Barnes, Kim Tibbs, and Ryan Nash (Class of '00).