The SAT

(noun)

SAT Reasoning Test (formerly Scholastic Aptitude Test and Scholastic Assessment Test): a national exam taken annually by high school juniors and seniors.

Related Terms

Examples of The SAT in the following topics:

  • Exercises

    • For the following data, plot the theoretically expected z score as a function of the actual z score (a Q-Q plot).
    • For the data in problem 2, describe how the data differ from a normal distribution.
    • For the "SAT and College GPA" case study data, create a contour plot looking at College GPA as a function of Math SAT and High School GPA.
    • For the "SAT and College GPA" case study data, create a 3D plot using the variables College GPA, Math SAT, and High School GPA.

  • The Regression Method

    • The average SAT score is 560, with a standard deviation of 75.
    • If you know no information (you don't know the SAT score), it is best to make predictions using the average.
    • If the students admitted all had SAT scores within the range of 480 to 780, the regression model may not be a very good estimate for a student who only scored a 350 on the SAT.
    • For example, if no one before had received an exact SAT score of 650, we would predict his GPA by looking at the GPAs of those who scored 640 and 660 on the SAT.
    • Let's say the highest SAT score of a student the college admitted was 780.

  • Normal probability table

    • Ann's percentile is the percentage of people who earned a lower SAT score than Ann.
    • The total area under the normal curve is always equal to 1, and the proportion of people who scored below Ann on the SAT is equal to the area shaded in Figure 3.6: 0.8413.
    • In other words, Ann is in the 84th percentile of SAT takers.
    • Determine the proportion of SAT test takers who scored better than Ann on the SAT.
    • The normal model for SAT scores, shading the area of those individuals who scored below Ann.

  • Variance Sum Law I

    • where the first term is the variance of the sum, the second term is the variance of the males and the third term is the variance of the females.
    • Notice that the expression for the difference is the same as the formula for the sum.
    • Contrast this situation with one in which thousands of people are sampled and two measures (such as verbal and quantitative SAT) are taken from each.
    • In this case, there would be a relationship between the two variables since higher scores on the verbal SAT are associated with higher scores on the quantitative SAT (although there are many examples of people who score high on one test and low on the other).
    • Thus the two variables are not independent and the variance of the total SAT score would not be the sum of the variances of the verbal SAT and the quantitative SAT.

  • Statistical Literacy

    • The standard for an athlete's admission, as reflected in SAT scores alone, is lower than the standard for non-athletes by as much as 20 percent, with the weight of this difference being carried by the so-called "revenue sports" of football and basketball.
    • Based on what you have learned in this chapter about measurement scales, does it make sense to compare SAT scores using percentages?
    • As you may know, the SAT has an arbitrarily-determined lower limit on test scores of 200.
    • Therefore, SAT is measured on either an ordinal scale or, at most, an interval scale.
    • Therefore, it is not meaningful to report SAT score differences in terms of percentages.

  • Variance Sum Law II

    • Compute the variance of the sum of two variables if the variance of each and their correlation is known
    • which is read: "The variance of X plus or minus Y is equal to the variance of X plus the variance of Y."
    • For example, if the variance of verbal SAT were 10,000, the variance of quantitative SAT were 11,000 and the correlation between these two tests were 0.50, then the variance of total SAT (verbal + quantitative) would be:
    • The variance of the difference is:
    • If the variances and the correlation are computed in a sample, then the following notation is used to express the variance sum law:

  • Standardizing with Z scores

    • Table 3.4 shows the mean and standard deviation for total scores on the SAT and ACT.
    • The distribution of SAT and ACT scores are both nearly normal.
    • Ann is 1 standard deviation above average on the SAT: 1500 + 300 = 1800.
    • Using µSAT = 1500, σSAT = 300, and xAnn = 1800, we find Ann's Z score:
    • SAT score of 1500), then the Z score is 0.

  • Introduction to Multiple Regression

    • These residuals are referred to as HSGPA.SAT, which means they are the residuals in HSGPA after having been predicted by SAT.
    • The correlation between HSGPA.SAT and SAT is necessarily 0.
    • The following equation is used to predict HSGPA from SAT:
    • However, if you do not know the student's HSGPA, his or her SAT can aid in the prediction since the β weight in the simple regression predicting UGPA from SAT is 0.68.
    • The explanation is that HSGPA and SAT are highly correlated (r = .78) and therefore much of the variance in UGPA is confounded between HSGPA or SAT.

  • Normal probability examples

    • Shannon is a randomly selected SAT taker, and nothing is known about Shannon's SAT aptitude.
    • What is the probability Shannon scores at least 1630 on her SATs?
    • Edward earned a 1400 on his SAT.
    • (a) What is the 95th percentile for SAT scores?
    • The probability Shannon scores at least 1630 on the SAT is 0.3336.

  • Exercises

    • For the following data, how many ways could the data be arranged (including the original arrangement) so that the advantage of the Experimental Group mean over the Control Group mean is as large or larger then the original arrangement.
    • What is the one-tailed probability for a test of the difference.
    • (SG) Compute Spearman's ρ for the relationship between UGPA and SAT.
    • Give the Z and the p.
    • Give the Chi Square and the p.