Statistics Assignment

Statistics Assignment

I analyzed the data using ordinary least-squares regression in the SAS statistical analysis program. GPA and achievement test scores were convened to z scores for ease of interpretation and to facilitate comparisons. In addition, I adjusted the interpretation of the data for the design effect associated with the data. NELS: 88 is not a true random sample; it is a stratified probability cluster sample, which means that the resulting statistics are more variable than they would be if the data were from a simple random sample. The design effect was the ratio of the sampling variance on the basis of the complex design to the sampling variance according to a simple random sample; for NELS, the mean design effect was 2.5 (Ingels et al., 1994). SAS assumes a true random sample and does not adjust for complex sampling designs and, as a result, SAS-generated standard errors may be too large, and t statistics may be too small. To adjust for the design effect, I multiplied the square root by the critical t value for a random sample of this size (i.e., 1.96) to get a complex design critical t value of 3.0 (Haggerty et al., 1996); therefore, the results were interpreted conservatively with an implied t value of 3.0.

Procedure

As a first step, regressions were run with the full sample (n = 19,386 the three measures of achievement were each regressed on the 12 types of parent involvement (see Table 1). Racial effects were the strongest effects in the models. For both mathematics and reading, Blacks and Hispanics were at a substantial disadvantage compared with Whites, and Asians were at a disadvantage in reading. Those relationships were very different for grades, however. As prior research has indicated (Muller, 1993), Blacks were not at a significant disadvantage for grades, and both Hispanics and Asians earned better grades than Whites at every point on the test-score distribution.

To test for significant racial-ethnic and income differences in the relationship between parent involvement and achievement, I tested models that included interaction terms (results not shown) created by multiplying the income and racial--ethnic variables by the independent variables in the model. Many of the interaction terms were significant, and an F test indicated that the model with the interaction terms was significantly different from the main effects model.

Given the strong racial-ethnic effects in the full sample models and the presence of significant racial interaction effects, a more detailed analysis of effects by race-ethnicity and income level was justified. The data were partitioned into different income and racial-ethnic groups; grouped models were estimated. (see tables 2 and 3 in Apendix)

Results Model Fit

An F test indicated that the middle- and high-income models were not significantly different from each other, so only the middle- and low-income models were interpreted. Each of the racial-ethnic group models was significantly different from the other; therefore, results were reported for all four groups.

Parent-reported discussion predicted a .06 standard deviation decrease in mathematics test scores for students from middle-income families, and it approached ...