## Example

PUBLIC SCHOOL TEACHERS' SALARIES BY GEOGRAPHICAL REGION

Table 9.1 gives data on average salary (in dollars) of public school teachers in 50 states and the District of Columbia for the year 1985. These 51 areas are classified into three geographical regions: (1) Northeast and North Central (21 states in all), (2) South (17 states in all), and (3) West (13 states in all). For the time being, do not worry about the format of the table and the other data given in the table.

Suppose we want to find out if the average annual salary (AAS) of public school teachers differs among the three geographical regions of the country. If you take the simple arithmetic average of the average salaries of the teachers in the three regions, you will find that these averages for the three regions are as follows: \$24,424.14 (Northeast and North Central), \$22,894 (South), and \$26,158.62 (West). These numbers look different, but are they

(Continued)

3It is not absolutely essential that dummy variables take the values of 0 and 1. The pair (0,1) can be transformed into any other pair by a linear function such that Z = a + bD (b = 0), where a and b are constants and where D = 1 or 0. When D = 1, we have Z = a + b, and when D = 0, we have Z = a. Thus the pair (0, 1) becomes (a, a + b). For example, if a = 1 and b = 2, the dummy variables will be (1,3). This expression shows that qualitative, or dummy, variables do not have a natural scale of measurement. That is why they are described as nominal scale variables.

4ANOVA models are used to assess the statistical significance of the relationship between a quantitative regressand and qualitative or dummy regressors. They are often used to compare the differences in the mean values of two or more groups or categories, and are therefore more general than the t test which can be used to compare the means of two groups or categories only.

CHAPTER NINE: DUMMY VARIABLE REGRESSION MODELS 299

EXAMPLE 9.1 (Continued)

 Salary Spending Ü2 Ü3 Salary Spending Ü2 Ü3 19,583 