NOTE: Scores are in the two-digit format reported to universities; the last digit reported to students is always zero. Thus, a score of 55 here correponds to a score of 550 as reported to the student.

To see if students accurately report their SAT-Verbal scores, we compare these two models:

Model A: DIFFSATV = beta0 + error
Model C: DIFFSATV = 0 + error

The estimated models are

Model A: DIFFSATV = 1.03
Model C: DIFFSATV = 0

SAS/Insight provides everything we need for comparing these two models, except for PRE. However, it is easy to invert the conversion formula for PRE to F (=t^2) to get the formula for F (=t^2) to PRE. That is, PRE = t^2/(t^2 + N-PA). In this case, PRE = 4.2421^2/(4.2421^2 + 169) = .096.

Notes on the graphs: The boxplot identifies a number of potential outliers. However, in this context it is interesting to note that twice as many of these potential outliers are in the direction of overstating one's SAT-Verbal score. The histogram is not especially useful except that it does show the positive skew--students were more likely to report scores above rather than below their true scores. The normal QQ plot is not particularly bad. The flat area in the middle is because so many students did indeed correctly report their SAT-Verbal scores. The sharp drop in the normal QQ plot at the low end does suggest an extreme score that might adversely affect the analysis. This is the student whose difference is -10.5 (i.e., he reported his last digit as 5, which cannot be). When looking at this student's difference for the SAT-Math score, he is a positive outlier. It may be the case that he reversed his SAT-Verbal and SAT-Math scores. Although a frequency table is often not very useful for a continuous score such as this, in this case it is because so many students report their scores accurately.

Journal Summary