# Correlation between SAT Scores, Graduation Rate, and SAT Participation Rates

Daniel

Peter

William

The SAT test has long been the standard by which universities and students measure readiness for university, and there is a large amount of data concerning it and the students taking it. There is a large amount of data concerning high school students, the main segment of the population that take the SAT. The SAT test is normally integral to the collegiate entrance process, and is the bane of many a student in high school. This test is an indicator of high performance and scholastic achievement, and, while varying numbers of students take this test, it provides an idea of the number of students looking at college. The SAT score of a high school measures the readiness of its students for college and can determine funding. However, the focus of the majority of private and public education studies involves the entire teenage population and the ever important graduation rate. This rate has been used as the benchmark of school performance by legislation and public perception, and this rate can elevate a school or force it into reorganization. The graduation rate, therefore, is the most important statistic regarding our primary education system, and translating this into enrollment in secondary education is a focus of legislative efforts. Combining both of these facets offers a large window into a segment of the population that is the focus of numerous social studies: the American teenager.

To find the SAT data go to www.mathforum.org/workshops/sum96/data.collections.  Afterwards click on The Data Library followed by Data Sets.  Once there look for the 14th link from the top titled "SAT Scores by State (1990-2004)" to download the Excel file of the data.  If you look at the download link directly below it titled "1984-1993 Teen Statistics" you will find the other data set we used.  The data collected on SAT statistics from 1990 through 2004 shows the participation rate, along with mean math and verbal scores, of students by state.  In addition, it has the national average scores and participation rate from 1991 through 2004.  Our other data set tabulates a variety of information by state such as high school graduation rate, juvenile violent crime rate and median income.  We hope to use the data of overlapping years in the two sets to find correlation between a subset of the variables.

The data suggests a correlation between the participation rate of high school students and the mean SAT I scores of both the verbal and the math portions of the SAT.  At first glance, there appears to be a negative correlation of participation rate to mean SAT score.  One theory for this alleged phenomenon is that only the very well prepared students in the low-participation states take the SAT, raising the average compared to states with high-participation rates, where more ill-prepared students take the SAT.  We will attempt to prove, with confidence intervals and hypothesis testing, that there is indeed a negative correlation of participation rate to mean SAT score that is not the result of random chance.

The data also suggests a correlation between the graduation rate of high school students to SAT scores.  It appears that there is a positive correlation between high school graduation rate to mean SAT score.  One theory for this apparent correlation is that the states with higher graduation rates produce more well-prepared students that will take the SAT exam.  We will again, with confidence intervals and hypothesis testing, attempt to prove that there is a positive correlation between graduation rate and SAT mean score that is not the result of random chance.

States in the U.S. will want to improve their mean SAT scores, since this reflects well on their education systems and encourages more funding.  If either of these correlations can be proven to not be the result of random chance, then the states will have a general idea of how to improve their mean scores (if the correlations are true, lower the students taking the test and raise the graduation rate of students.)  This knowledge would greatly aid the policymakers in the education departments across the U.S.

References:

Drexel University. (2008, August 19).  SAT Scores by State(1990-2004). Math Forum. Retrieved March 25, 2011, from http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html

Drexel University. (2008, August 19).  1984-1993 Teen Statistics. Math Forum. Retrieved March 25, 2011, from http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html