TABLE 13.2 Project STAR: Differences Estimates with Additional Regressors for Kindergarten Regressor (1) (2) (3) (4) 13,90** (2.45) 15.93** (2.24) 15.89** (2.16) Small class 14.00** (2.45) Regular size with aide 1.22 (2.04) 1.79 (1.96) 0.31 -0.60 (2.27) (2.25) Teacher's years of experience 1,47** (0.17) 0.74** (0.17) 0.66** (0.17) -12.09** (1.67) Boy Free lunch eligible -34.70** (1.99) Black -25.43** (3.50) Race other than black or white -8,50 (12.52) Intercept 918.04** 904.72** (1.63) (2.22) School indicator variables? no no yes yes 0.01. 0.02 0.22 0.28 Number of observations 5786 5766 5766 5748 Note: The regressions were estimated using the Project STAR Public Access Data Set described in Appendix 13.1. The dependent variable is the combined test score on the math and reading portions of the Stanford Achievement Test. The number of observa- tions differ in the different regressions because of some missing data. Standard errors are given in parentheses under coefficients. The individual coefficient is statistically significant at the *5% level or **1% significance level using a two-sided test.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
For the following calculations, use the results in column (3) of Table 13.2.
Consider two classrooms, A and B, with identical values of the regressors
in column (3) of Table 13.2, except that:
a. Classroom A is a “small class,” and classroom B is a “regular class.”
Construct a 90% confidence interval for the expected difference in
average test scores.
b. Classroom A has a teacher with 6 years of experience, and classroom
B has a teacher with 12 years of experience. Construct a 95% confidence
interval for the expected difference in average test scores.
c. Classroom A is a small class with a teacher with 6 years of experience,
and classroom B is a regular class with a teacher with 12 years
of experience. Construct a 95% confidence interval for the expected
difference in average test scores.
d. Why is the intercept missing from column (4)?
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