Average SAT Scores by U.S. State

Average SAT Scores by U.S. State Colleen Skinner

Introduction

The dataset I will be using ('Guber1999data.csv') includes average SAT (Scholastic Aptitude Test) scores by U.S. state. These scores are average Verbal scores, average Math scores, and average total scores. The dataset also includes some variables for each state that might impact the average SAT score. These variables include the amount of money spent on students, the student-teacher ratio, the salary of teachers, and the percent of students who take the SAT.

Data Found Here

I will be utilizing this SAT scores data to visualize the average SAT scores for the 50 U.S. states. I will also work to determine what variables (money spent on students, student-teacher ratio, the salary of teachers, and percent of students who take the SAT) can be used to help predict a state's average total SAT score based on this data.

The above three histograms help us to visualize the distribution of SAT scores (average Verbal, Math, and Total SAT scores) for the U.S. states. The first histogram (Verbal SAT Scores) shows that 26 states had average verbal SAT scores below 450 and that 20 states had average verbal scores above 475, with the remaining 4 states having scores between 450 and 475. The second histogram (Math SAT Scores) shows that many states (23 states) had average math SAT scores between 460 and 500. Also, despite both Verbal and Math SAT scores being out of 800 total, the states' average verbal scores range from around 400 to a bit under 525 while the states' average math scores range from around 440 to around to a bit under 600, meaning there is a much wider range for average math SAT scores than average verbal SAT scores. Finally, the third histogram (Total SAT Scores) shows that many states had combined/total scores around 900 and there were also many states who had scores above 1000 but with only one state getting above 1100. However, these histograms do not allow us to determine which state had which score. So, we can look at different visualizations of this same data to determine which state corresponds to which average SAT score.

The bar graph above shows the average total SAT score for each state. The bars have been reordered so the states are not in alphabetical order but rather are in order from highest total SAT score to the lowest total SAT score. This allows us to easily compare the scores of each state. Also, we can easily determine both the state with the highest average total SAT score and the state with the lowest average total SAT score. Here, we can see that North Dakota has the highest average total SAT score while South Carolina has the lowest. Unfortunately, this bar plot does not allow us to see the geography of these states. Are states with high SAT scores near each other or not? This question cannot be answered easily based on this chart alone (assuming no prior knowledge of America's geography).

The map above helps us better view the geography of U.S. states' average total SAT scores. Based on this map we can tell that North Dakota is the state with the highest average SAT score as it is the only state that falls in the 1101-1150 range of SAT scores. Similarly, South Dakota is the state with the lowest average SAT score as it is the only state pictured that falls in the 801-850 range for SAT scores. It is also interesting to note that states on the coast (both east coast and west coast) have lower average total SAT scores than states that are more in the middle of America. States that are near/surround North Dakota also have fairly high average SAT scores.

The map above shows the percent of students in each state that take the SAT. Interestingly, states that are on the east coast, as well as states on the west coast have much higher percentages of students who take the SAT while states that are more in the middle of the U.S. have much lower percentages of students who take the exam. Many states around the middle of America fall into the 1-15% range of students taking the exam. Massachusetts and Connecticut are the only two states that fall into the 75-90% range and they are both on the east coast of America. It is noteworthy that no state has greater than 90% of students taking the exam and there is also no state with 0% of students taking the SAT. Also, it is interesting to compare the previous map to this map. Upon comparing the two maps we find that the same states that had higher average total SAT scores also had a lower percentage of students who took the SAT while the same states that had lower average total SAT scores also had a higher percentage of students who took the SAT. There could potentially be a negative relationship between these two variables, but these maps alone are not quite enough to definitively say if there is or not.

To help determine the effects of the many variables on a state's average total SAT score I utilized a linear model. The dependent variable was the average total SAT score (SATT) and the independent variables were the amount spent (Spend), the student-teacher ratio (StuTeaRat), the salary of the teachers (Salary), and the percent of students who actually take the SAT exam (PrcntTake).

Based on the results of the model (which can be seen on the right), the percent of students who take the SAT is the most significant predictor for the average total SAT score. According to this linear model, a 1 unit increase in the percent of students who take the exam will decrease the average total SAT score by 2.904 points. This means that there is a negative relationship between the average total SAT score and the percent of students who take the SAT. Despite the other independent variables not being as significant, the model does show that the student-teacher ratio has a negative relationship with the average total SAT score while both the amount spent and teacher's salary have a positive relationship with the average total SAT score.

The four substantive effects plots above further prove the findings of the linear model from before. We can easily visualize the positive or negative relationships between the variables. The substantive effects plots show the slight positive linear relationship between the amount of money spent on students and the average total SAT score as well as the slight positive linear relationship between teacher salary on students and average total SAT score. The above plots also show the slight negative relationship between the student-teacher ratio and the average total SAT score. Finally, we can see that the percent of students who take the SAT exam in a state is the most significant predictor of that state's average total SAT score as well as the fact that the is a negative linear relationship between these two variables. This means that states with a higher percentage of students taking the SAT will have lower predicted average total SAT scores than states with a lower percentage of students taking the exam.

Conclusions

Average SAT scores vary in the United States from state to state, however, we can utilize data visualization to easily see which states have high average SAT scores and which have low average SAT scores. We can also visualize the percentage of students in the U.S. who actually take the SAT in order to determine which states have a large percentage of students taking the exam as having a large percentage of students taking the exam could impact the states’ average SAT scores. After running a linear model, it was determined that the percent of students in a state that take the SAT exam is a significant predictor for that state’s average total SAT score, while the other variables (amount of money spent on students, student-teacher ratio, and teach salary) are not significant predictors. The substantive effects plots further confirm the findings of the linear model and show the negative relationship between the percent of students that take the SAT and the average total SAT score. We can also see this on the maps. North Dakota is the only state with an average total SAT score above 1100, however, only 1-15% of students in the state actually took the exam. Similarly, South Carolina has an average total SAT score between 801 and 850, but had 46-60% of students take the SAT. Additionally, Massachusetts and Connecticut had 75-90% of students take the SAT, however, both states had average total SAT scores between 901 and 950. Overall, a state’s average total SAT score is related to the percent of students in that state that take the SAT. This may be because states with a lower percentage of students taking the SAT have a majority of students getting higher scores which would therefore lead to an overall higher average total SAT score for the state. States with a large percentage of students taking the exam have more potential for students to bring down the average SAT score of that state.

Created By

Colleen Skinner

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