Is there an association between GPA and extracurricular participation?

Robert Catlett

Andrew Alexander

Matt Proffitt

AP Statistics B2

Disclaimer:

This study was done in an AP Statistics course with relatively small sample sizes. The validity of such studies must always be questioned. Please keep this in mind if you use or report the results of this study.”

Abstract:

Our observational study was conducted to determine whether or not there is an association between a student’s grade point average and his or her extracurricular participation level. We expect that a higher GPA will be associated with higher extracurricular participation. Our population is all of the students at Tates Creek High School. All of our inferences will relate back to this population only. Students were given a survey sheet and asked to write their cumulative GPA and the number of extracurricular activities they had participated in this year. An extracurricular activity is defined as any club, sport, or activity a student participates in outside of the normal school day. The general perception is that students who are involved in many activities outside of school tend to do better in school. Students who are not as involved, tend to not be as focused in the classroom. The goal of this statistical survey is to determine whether or not there is a statistically significant relationship between grade point average and extracurricular participation. To do this we will use a T- Test for Regression. T is the test statistic and the distribution has n-2 degrees of freedom. T is calculated as b/SEb.

Methodology

The question we are trying to answer is whether of not grade point average is a good indicator of a student’s extracurricular involvement. We randomly selected 50 students from the entire population of Tates Creek High School. We did this by obtaining a list of every student in the school, assigning them numbers, and using a random number generator to select the students. Due to the time constraints we could not block by grade level. The experiment was single blind because the students were unaware of the purpose of the study we conducted.

This is a sample of a survey sheet we distributed to the randomly selected individuals:

Congratulations! You have been randomly selected to participate in our AP Statistics survey. The information you provide for us will remain completely confidential. Do not include your name. Please answer the following questions honestly. Thank you.

1. What is your cumulative GPA (grade point average)? __________

2. How many clubs, organizations, or sports teams do you actively participate in? _________

Raw Data

GPA	Extracurriculars
4	2
3.85	4
3.9	6
3	2
2.8	1
2	0
2.2	0
3.25	0
2.3	2
1.8	0
2	1
2.05	2
3.5	1
3.875	5
3.1	4
3.5	3
3.9	5
2	1
3.2	2
4	5
3.5	4
2.5	0
3.415	6
3.8	6
3.8	4
3.5	1
3.75	2
3.8	6
3.2	2
3.5	2
2.6	1
3.9	5
3.0	1
3.8	2
3.0	1
3.5	2
3.1	0
3.9	3
3.8	8
3.0	1
3.3	7
3.0	1
3.1	0
2.0	0
2.5	3
3	1
3.75	5
3.5	1
3.4	1
3.65	8

Inference

H-naught: β=0 (There is no relationship between GPA and extracurriculars)

H-a: β≠0 (There is a relationship between GPA and extracurriculars)

β is defined as the true slope of the relationship between GPA and extracurrculars

Assumptions

· Observations are independent

· True relationship is linear

· The standard deviation of the response variable is the same everywhere about the true line (see residual plot)

· Response variable varies normally

Residual plot:

Minitab Output:

The regression equation is

Extracuriculars = - 4.32 + 2.16 GPA

Predictor Coef SE Coef T P

Constant -4.318 1.319 -3.27 0.002

GPA 2.1648 0.4048 5.35 0.000

S = 1.81380 R-Sq = 37.3% R-Sq(adj) = 36.0%

Scatter plot with LSRL:

Conclusion

Because the p-value, .002, is less than α=.05, we reject H naught, there is no relationship between GPA and extracurriculars, in favor of H a, there is a relationship between the two variables.

By looking at the scatterplot and the LSRL, you can see that those students who have a high GPA are more likely to have a high participation in extracurricular activities. This inference only applies to our population of Tates Creek students. This does not mean that a high GPA causes high extracurricular participation because association does not mean causation. To prove causation a controlled experiment must be conducted.

Due to the time of year it was difficult to reach all of the randomly selected subjects. This may have negatively influenced our study. Also, keep in mind that our sample size was small and our results should not be published without replication.