Age, Gender, Alcohol Use and Academic Performance:

A Statistical Analysis

College students are faced with difficult choices, and choosing to drink responsibly is among the most important. A college campus may be one of the few places where underage students have access to alcohol, yet ironically a college curriculum is set up in such a way that problem drinkers are, due to minimum G.P.A. requirements, less likely to succeed. If male students are more likely to drink, then the underage male drinker may be more likely to face negative repercussions than other students. College administrators across the nation are concerned that alcohol abuse is a factor in other campus problems like sexual abuse, violence, vandalism, and a variety of mental and physical illnesses. This paper, using a small random sample of Hanover College students, sheds some light on the issues of underage drinking, gender differences, and academic performance.

The Data

A survey was administered to approximately 175 students via random distribution to their campus mailboxes, and 60 completed surveys were returned. The “Gender” variable indicates a female student with a one, a male student with a zero. The “Age” variable is expressed in years and months. The “Alcohol” variable is the response to the question of how many alcoholic beverages a student consumes in a typical week.

One survey left the “Age” question blank, and 16 surveys left the “G.P.A.” question blank. Because the survey was administered during the fall semester, when freshmen do not yet have a cumulative G.P.A., I assume that these blanks indicate a first year student. A quick check of the response for “Number of semesters on this campus” verifies that these responses are all from a student who indicates that this is their first semester at Hanover College. During analysis of these variables, all missing values will be deleted.

Summary Statistics

Summary statistics of the variables (see Table 1) used in this analysis indicate that 58.33% of the sample are female. The mean age of the students is 19.82 years, with a

Table 1: Summary Statistics

	Gender	Age	GPA	Alcohol
Mean	0.58	19.82	3.19	4.36
Median	1.00	19.75	3.10	1.00
Max	1.00	22.29	4.00	36.00
Min	0.00	17.25	2.50	0.00
Std. Dev	0.50	1.16	0.40	7.47
Count	60.00	59.00	44.00	60.00

standard deviation of 1.16 years, a maximum of 22.29 and a minimum of 17.25 years. The mean number of alcoholic beverages consumed in a typical week is 4.36 drinks, with a standard deviation of 7.47 drinks, and a maximum value of 36 drinks a week. The mean grade point average is 3.19, with a standard deviation of .40, a maximum value of 4 and a minimum of 2.5. I believe that the relatively high G.P.A. values are a result of the absence of first year students in the sample, a subset of students who typically earn lower cumulative grade point averages than the rest of the population.

Who is more likely to drink, men or women?

Table 2 summarizes drinking tendencies by men and women in the sample. There are 35 women and 25 men in the sample. In the sample of 60 students, 29 (48.33%) report that they drink zero alcoholic beverages in a typical week. This subset of the sample will be labeled “Non-Drinkers”; the rest (51.67%) are labeled “Drinkers”.

Table 2: Totals by Gender and Drinking Preference

	Male	Female	Totals
Non-Drinkers	10	19	29
Drinkers	15	16	31
Totals	25	35	60

Table 3 converts the above totals to joint and marginal probabilities. There are four possible outcomes in the table. The most likely is that a student is a non-drinking female (31.67% of all students), the least likely is a non-drinking male (16.67%).

Conditional probabilities shed additional light on gender differences and whether a student is a drinker or non-drinker. For example, 58.33% of the sample are female, but given a student is a drinker, the probability of a student being female falls to 51.61%. Given a student is a non-drinker, the probability that a student is female rises to 65.52%. In other words, females are overrepresented in the non-drinking subset and underrepresented in the drinking subset. The opposite is true of the male students. Although males constitute only 41.67% of the sample, the probability that a student is male, given they are a drinker rises to 48.39%. The probability that a student is male, given you know he is a non-drinker, falls to 34.48%. Thus males are overrepresented in the drinking subset and underrepresented in the non-drinking subset of the sample. These results are evidence that drinking and gender are dependent events.

Table 3: Joint and Marginal Probabilities

	Male	Female	Marginal Probabilities
Non-Drinkers	P(NDÇM) = 10/60 = .1667	P(NDÇF) = 19/60 = .3167	P(ND) = .4833
Drinkers	P(DÇM) = 15/60 = .2500	P(DÇF) = 16/60 = .2667	P(D) = .5167
Marginal Probabilities	P(M) = .4167	P(F) = .5833	1.00

Who drinks more, men or women?

The above analysis indicates that the probability of a student being a drinker rises if that student is a male, and falls if the student is a female, but does not address the issue of who drinks the most alcohol. Table 4 summarizes the difference in mean number of drinks consumed in a typical week. Although it appears that men drink more in a typical week (7.2 drinks) than women (2.33 drinks) do, further analysis is necessary to determine whether these differences are statistically significant.

Table 4: Weekly Drinking by Gender

	Male Students	Female Students
Sample Mean	7.20	2.33
Sample Std. Deviation	10.24	3.56
Maximum	36	12
Sample Size	25	35

A one-tailed hypothesis test would test a null hypothesis that the mean number of drinks is greater for the population of men than for women students. Since one of our samples is less than 30 in size, we will use the t-distribution to test the hypothesis:

Ho: m_m - m_f £ 0

Ha: m_m - m_f > 0

At the 95% level of confidence, and with 58 degrees of freedom, the critical (one-tailed) t-value is approximately 1.672. Assuming equal variances for both populations, a pooled estimate of the standard error of the sampling distribution is calculated and used to calculate a test statistic of 2.61. Since the test statistic is greater than the critical value with 58 degrees of freedom we reject the null hypothesis and conclude that men drink more than women do at Hanover College.

Do students over the age of 21 drink more than those under the legal drinking age?

Students above the age of 21 drink 6.2 alcoholic beverages in a typical week, while underage students consume an average of 4.1 per week. A one-tailed hypothesis test is used to determine whether these differences are statistically significant. Using similar small-sample techniques, I test the hypothesis:

Ho: m_over - m_under £ 0

Ha: m_over - m_under > 0

At the 95% level of confidence, and with 57 degrees of freedom, the critical (one-tailed) t-value is approximately 1.672. Assuming equal variances for both populations, a pooled estimate of the standard error of the sampling distribution is calculated and used to calculate a test statistic of .821. Since the test statistic is less than the critical value with 57 degrees of freedom we fail to reject the null hypothesis and conclude that students above the age of 21 do not drink more than students below the legal drinking age.

An Empirical Model of G.P.A. as a function of studying and drinking

A common assumption is that more studying outside of class will increase a student’s cumulative grade point average, while more drinking outside of class will decrease the G.P.A. Thus a simple empirical model of grade point average would be:

Thus we should expect a positive coefficient on the Study variable while observing a negative coefficient on the Drink variable.

After removing all observations with missing data, we are left with a sample size of 44 students. Table 5 below summarizes the results of the multiple regression estimation. The adjusted R2 is extremely low, indicating that this model does a poor job of explaining the variation in cumulative G.P.A. The constant term means that if you consume zero alcoholic beverages and study zero hours outside of class, your G.P.A. would be 2.96. This seems extremely high, and is probably a result of the omission of the first year students from the sample. However, we should not put too much emphasis on the intercept anyway because it absorbs the effects of many omitted variables.

The slope coefficient for Drink is .001, which means that 10 more drinks in a week will actually increase your cumulative grade point average by .01 points. However, this coefficient is statistically insignificant from zero with a t-statistic of only .12.

The coefficient for Study is .013, which means that 10 additional hours of study per week would increase your G.P.A. by .13 points. With a t-statistic of 1.867, this coefficient is statistically different from zero at the 90% degree of confidence. In other words, additional hours of study will increase your G.P.A., while additional drinking will have statistically no affect on your G.P.A.

Table 5: Multiple Regression Output

Regression Statistics
Multiple R	0.284084116
R Square	0.080703785
Adjusted R Square	0.035860067
Standard Error	0.396661634
Observations	44
	Coefficients	Standard Error	t Stat	P-value
Intercept	2.968064495	0.145517	20.39667	4.42E-23
Alcohol	0.001105538	0.008949	0.123532	0.90229
Study	0.013209365	0.007074	1.867321	0.069017

Conclusion:

Hanover College, like many institutions of higher learning, is forced to accept the fact that, on a weekly basis, many students consume alcohol while trying to maintain acceptable levels of academic performance. Based upon this sample of 60 students, it appears that men are more likely to consume alcohol than are women, and that men on average consume more alcoholic beverages in a typical week than do women. Although law requires that a person be over 21 years old to consume alcohol, this does not imply that legal college students drink more alcohol than those underage students do. Finally, drinking alcohol does not significantly affect cumulative grade point averages, but additional studying outside of class has a small, significantly positive effect on a student’s G.P.A. The anomalous finding that excessive drinking does not lower G.P.A. is probably due to the nature of our sample and future studies that include first year students would perhaps shed more light on this issue.