**Pepperdine
University**

Graziadio School of Business and Management

Rick Marriner

MBA 671.41

Statistics and Research Methods

Summer 1998

Questions regarding Golf Ability and Alcohol Consumption

**I. Introduction**

*A. Purpose of Study*

The subject of this research study is a golfer's ability with regard to power and accuracy as it relates to alcohol consumption. The purpose of the study is to test the validity of claims that alcohol consumption somehow increases the ability of a player in his or her pursuit of ever-better scores.

Specifically, the researcher suspects that the rumor that alcohol consumption increases a player's ability with regard to power and accuracy is a malicious conspiracy started by the golf club to increase sales of alcohol. The research will test this rumor with empirical evidence collected.

*B. Background of Subject*

In a general search for ways to improve a golf game, the researcher came across numerous devices that propose the miracle cure for a persons golf game. The psychological strategies of relaxation are the closest to what the purpose of this study is. More accurately, professional trainers have taught the art of relaxation as a way to improve a golf game. The researcher believes that it is for this reason that people who are convinced alcohol relaxes them also believe that alcohol will improve their game.

The researcher, however, could not document any statistical analysis or research previously conducted on the effects of alcohol on a player's golf ability with regard to power or accuracy. There is a sub-culture of amateur golfers on the Internet who postulate on the beneficial effects of alcohol on their golf ability. The most representative home page of which was "The Golf Guzzler" which can be found by visiting : http://guzzler.cybertude.com/guzzler/guzzbuzz.html.

The topic itself is worthy of this study due to the potential benefits to amateur golfers who currently spend money and damage their health in pursuit of a longer drive or more accurate iron shot. In fact, they could be spending their money and ruining their health on often, uncomfortable or embarrassing non-alcoholic devices to improve their wretched golf ability.

*C. Participants*

The researcher is Rick Marriner an MBA Candidate at Pepperdine University, CA. He is a 23-year-old amateur golfer with a handicap of 16. The researcher's interest in this study is biased by the skepticism of any tactic other than hard work and training to improve the golf ability of the average player.

The population directly affected by this research is all male amateur golfers between the ages of 23-29 with handicaps between 13 and 20.

**II. Hypothesis/Methodology**

*A. Definitions of concepts common to
both hypothesis.*

**Experimental Golfers (Wishing
to remain anonymous)**

__Age Sex Handicap Occupation__

Golfer A 29 male 13 Valve Sales

Golfer B 23 male 16 Shipping

Golfer C 26 male 20 US Navy

**Driver** - the instrument in
the game of golf that is used to hit the golf ball the farthest.

**Pitching Wedge** - An
instrument used in golf by the player to hit the ball short
distances with significant loft to reduce the effect of rolling
once the ball has landed. This club is used for high accuracy.

**Alcohol consumption** - Four
16 fluid ounce draft beers (Budweiser) consumed over a period of
one half-hour without any other food or beverage.

**Golf Ability** - Measured in
both power and accuracy with various types of clubs over various
types of courses. Golf ability is inversely related to the score
on a given course.

**Accuracy** - Measured by
observing if the ball landed on the target green.

**Distance** - Measured from
the where the player hit the ball to where it landed in yards.

**Score** - The number of
strokes (swings and hits) taken by a player from the beginning of
the course to the end. This score includes penalties, which are
not actual swings and hits.

**Par** - The average number of
strokes a professional golfer would use to finish a course.
Usually par is 72 strokes for 18 holes.

**Handicap **- The average
number of strokes above par a player has accumulated over the
last seven games.

**Driving Range** - This is a
simulated golf course with nets and platforms such that a golfer
can hit the ball repeatedly and practice distance and accuracy.

**Hypothesis # 1 - Power Question**

**Research Question:** Is a
player's golf ability with regard to power improved with the
consumption of alcohol?

**Null Hypothesis:** There is
no improvement in a player's golf ability with regard to power
due to the consumption of alcohol.

**Alternative Hypothesis:**
There is an improvement in a player's golf ability with regard to
power due to the consumption of alcohol.

*A. Further definitions of concepts
and variables. - Hypothesis #1*

The independent variable in this test of the hypothesis is whether the player has consumed alcohol or has not. It is based on the intake of alcoholic beverages over a period of one half hour between samples. The dependent variable in this test of the hypothesis is the golf ability with regard to power.

Alcohol consumption level is defined in this test as the consumption of four 16 Fluid ounce glasses of cold draft Budweiser over a period of 1/2 hour between samples. At the driving range, each of the three players in the test will hit a control group of 10 balls for power (distance) with their driver. These balls will be measured for distance by the researcher observing from an elevated observation deck and measuring in 10-yard intervals between markers of the driving range.

After the consumption of the alcohol the players will wait 15 minutes and hit 10 additional balls for power (distance) with their driver. The researcher will take measurements in the same manner as above.

*B. Data Collection Plan - Hypothesis
#1*

The basis for data collection is a small sample field experiment. On July 5, 1998 at the Rio Hondo Golf Course driving range three similar golfers hit 10 balls first without any alcohol consumption and then hit 10 balls after alcohol consumption. The distance each shot goes is measured the researcher out of direct site of the golfer. The elevated height gives the observer a better view of where the ball actually landed in respect to the yardage markers on the driving range.

*C. Sampling Plan - Hypothesis #1*

A judgment sample from a convenient pool of available players was obtained according to the discretion of the researcher. This combination is defined as the most convenient group of elementary unit's (players known by the researcher) representative of the population (Male amateur golfers between ages 23-29 with handicaps between 13 and 20). The convenience pool of available golfers was then culled to size by the researcher who use judgmental sampling techniques to chose three players relatively similar in golf ability with regard to power.

This system of data collection is defended on cost and because the population in question is extremely heterogeneous. It is most importantly defended on the fact that the sample size is to be relatively small. This data collection plan maximizes the ability of the researcher to make the most out of the resources available for direct experimentation of this hypothesis. There has been serious concern regarding the error based on researcher bias in judgmental sampling. However, the researcher feels only approximate information about the population is needed to service the hypothesis at this stage or research.

*D. Data analysis Procedure.
Hypothesis #1*

The null hypothesis was tested with the paired Students T Test, specifically a small sample test sample, less than 30, about a difference between two dependent means. The data satisfies all assumptions of normalcy and equal variances for this test. The researcher used this method of testing specifically because the data lost its independence because the same players were used in the first data set as the second.

The sample is three means taken before the consumption of alcohol and three means taken after alcohol consumption. Each "before" mean is paired with its corresponding "after" mean and the three differences are calculated.

*E. Level of Significance - Hypothesis
#1*

In order to reduce the chance of a type I error, that is the probability that the null hypothesis will be rejected when in fact the null is actually correct, the researcher tested at the .01 level of significance. This level was chosen because, as a skeptic of the rumor, the researcher does not want to give the impression that alcohol consumption will lead to a better golf score. The false rejection of null would substantiate the rumor allowing golf club owners to grow rich at the expense of a golfer's health.

**Hypothesis II: The accuracy
question**

**Research Question:** Is a
player's golf ability with regard to accuracy improved with the
consumption of alcohol?

**Null Hypothesis:** There is
no improvement in a player's golf ability with regard to power
due to the consumption of alcohol.

**Alternative Hypothesis:**
There is an improvement in a player's golf ability with regard to
power due to the consumption of alcohol.

*A. Further definitions of concepts
and variables. - Hypothesis #2*

The independent variable in this test of the hypothesis is the Blood Alcohol Content and whether the player has consumed alcohol or has not. It is based on the intake of alcoholic beverages over a period of one half hour between samples. The dependent variable in this test of the hypothesis is the golf ability with regard to accuracy.

Alcohol consumption level is defined in this test as the consumption of four 16 Fluid ounce glasses of cold draft Budweiser over a period of 1/2 hour between samples. At the driving range, each of the three players in the test will hit a control group of 10 balls for accuracy (at target greens) with their pitching wedge. These balls will be measured for accuracy by the researcher observing from an elevated observation deck. The measure of accuracy will be either "yes" the ball landed on the target green 75 yards away or "no" the ball did not land on the target green 75 yards away.

After the consumption of the alcohol, the players will wait 15 minutes and hit 10 additional balls for accuracy (at target greens) with their pitching wedge. Again, the researcher will take measurements in the same manner as above.

*B. Data Collection Plan - Hypothesis
#2*

The basis for data collection is a large sample field experiment. On July 5th, 1998 at the Rio Hondo Golf Course driving range three similar golfers will hit a total of 30 balls between them first without any alcohol consumption and then hit a total of 30 balls between them after alcohol consumption. The researcher, out of direct site of the golfer, measures the accuracy of each shot. The elevated height gives the observer a better view of where the ball actually landed in respect to the target green on the driving range.

*C. Sampling Plan - Hypothesis #2*

As with hypothesis #1, a judgment sample from a convenient pool of available players was obtained according to the discretion of the researcher. This combination is defined as the most convenient group of elementary unit's (players known by the researcher) representative of the population (Male amateur golfers between ages 23-29 with handicaps between 13 and 20). The convenience pool of available golfers was then culled to size by the researcher who use judgmental sampling techniques to chose three players very similar in golf ability with regard to accuracy.

This system of data collection is defended on cost and because the population in question is extremely heterogeneous. This data collection plan maximizes the ability of the researcher to make the most out of the resources available for direct experimentation of this hypothesis. There has been serious concern regarding the error based on researcher bias in judgmental sampling. However, the researcher feels only approximate information about the population is needed to service the hypothesis at this stage or research.

*D. Data analysis Procedure -
Hypothesis #2*

The null hypothesis was tested with the Chi-squared test of independence. The researcher used this method of testing specifically because the data is qualitative bi-modal nominal data.

The sample is the combination of 30 "yes" and "no" scores recorded from the hits golf balls taken before the consumption of alcohol and the combination of 30 "yes" and "no" scores recorded from the hits golf balls taken after alcohol consumption.

*E. Level of Significance - Hypothesis
#2*

In order to reduce the chance of a type I error, that is the probability that the null hypothesis will be rejected when in fact the null is actually correct, the researcher tested at the .01 level of significance. This level was chosen because, as a skeptic of the rumor, the researcher does not want to give the impression that alcohol consumption will lead to a better golf score. The false rejection of null would substantiate the rumor allowing golf club owners to grow rich at the expense of golfer's health.

**III. Presentation of Findings -
Hypothesis 1**

A.

1. Research
Question: Is µ_{D} > 0
?

2. Null
Hypothesis: µ_{D }= 0 ?

3. Alternative
Hypothesis: µ_{D} > 0
?

- Statistical Test:
Paired Student's t test of a hypothesis about the value
of µ
_{D}.One tailed test Degrees of Freedom (df) = n

_{D}- 1 = 2a = .01 t ³ 6.965

- __________________________________________
n

_{D }= 3 golfersx-bar = 37 yards µ

_{D}= 0 4.129s

_{D}= 15.52 yards - Examination of Null Hypothesis: Retain the null hypothesis of no significant difference at the .01 level of significance because the Student's t test statistic of 4.129 is less that the critical value of 6.965.

P Value: Between .05 and .025

Administrative Decision: The data tend to suggest that the true population mean difference between pairs of data is not significantly greater than the hypothesized mean difference of zero. Therefore, it would appear as if the consumption of alcohol does not significantly effect the power aspect of golf ability.

**III. Presentation of Findings -
Hypothesis 1**

*B. Discussion of Results*

Any observed difference in this experiment is best explained by chance error in sampling. According to the P value (the observed level of significance) the probability of this difference happening again if the experiment were repeated is only between 90% and 95%. This chance of repeatability is too low to reject null. The researcher can therefor only consider this test to yield a retention of the null hypothesis of no significant difference between the distance balls traveled before the golfer's alcohol consumption and the distance traveled after the golfer's alcohol consumption.

Specifically, the true population mean difference between pairs of data is not significantly greater than the hypothesized mean difference of zero. Therefore, the consumption of alcohol does not significantly effect the power aspect of golf ability.

**III. Presentation of
Findings - Hypothesis 2**

C.

1. Research Question: Is there a statistically significant relationship between golf ability with regard to accuracy and whether or not the golfer has consumed alcohol.

2. Null Hypothesis: There is no significant relationship between golf ability with regard to accuracy and whether or not the golfer has consumed alcohol.

3. Alternative Hypothesis: There is no significant relationship between golf ability with regard to accuracy and whether or not the golfer has consumed alcohol.

4. Statistical Statement:

Statistical Test: Chi-squared Test of Independence

Degrees of Freedom (df) = (r-1)(c-1) = (2-1)(2-1) = 1

a = .01 t ³ 6.635

5. Presentation of Data: Table 2-1

Cell fo fe (fo-fe) (fo-fe)^{2 }(fo-fe)^{2}/fe

A 15 17.5 -2.5 6.25 .357

B 15 12.5 2.5 6.25 .500

C 20 17.5 2.5 6.25 .357

D 10 12.5 -2.5 6.25 .500

**Sum = 1.714**

6. Examination of Null Hypothesis: Retain the null hypothesis independence at the .01 level of significance because the Chi-squared test statistic of 1.714 is less that the critical value of 6.635

P Value: 0.19

Administrative Decision: The data tend to suggest that there is no statistically significant relationship between golf ability with regard to accuracy and whether or not the golfer has consumed alcohol. Furthermore, by studying table 2-1 above, it would appear that although there are proportionately more accurate golf shots after alcohol consumption than before this difference in proportions is not statistically significant.

**III. Presentation of Findings -
Hypothesis 2**

*D. Discussion of Results*

Consulting the Chi-square test statistic, the researcher converted the test statistic to a Z score, which allowed the researcher to calculate an exact observed level of significance, P Value. Given the P Value of .19, there is only an 81% chance that, given repeated samples for the same hypothesis, this outcome would occur again. This is not close enough for consideration for any exceptions to be made in terms of rejecting the null hypothesis in favor of the alternative.

There is no significant relationship between golf ability with regard to accuracy and whether or not the golfer has consumed alcohol. Furthermore, by studying table 2-1 on page 11, there are proportionately more accurate golf shots after alcohol consumption than before. This difference is not statistically significant. This is determined by comparing what actually did happen as a result of alcohol consumption (the frequency observed values, fo) with what should have happened with alcohol consumption (the frequency expected values, fe).

**IV. Interpretation and
Conclusions**

*A. Interpretations*

In testing the two hypotheses for golf ability there were three important interpretation factors that became evident from the data and the data collection. These substantive interpretations stem from a more general view of the experiment.

The first is the importance of the difference in the mean distance for hypothesis #1. The distance seemed substantial, and failed because the critical value was high. This was caused by the degrees of freedom only being 2, which forces a higher critical value for the rejection of the null. It is important to note that had there been 2 additional golfers in the experiments with a similar mean difference then there is a strong likelihood that the difference would have bordered on a significant difference in means.

The second important interpretation comes from hypothesis #2. The chi-square test is a good measure of independence. However, the experiment forced the nominal data sample. Had the researcher chosen to measure the distance off target in yards as a measure of accuracy the results might have been different. It is important to consider this because the accuracy looks to increase with the consumption of alcohol when only the descriptive statistics are observed. Had a different statistical test been available then there is a chance the results would be in favor of the alternative hypothesis.

The third important factor was not tested, but could have been. That is the fact that after alcohol consumption the golfers engaged in the experiment tended to care less how well they did in the measurements of the golf ability with regard to power and the golf ability with regard to accuracy.

*B. Conclusions*

Given the extreme retention of the tested null hypothesis the researcher can conclude that the rumor that alcohol consumption increases a average handicap male golfer between the ages of 23-29 ability with regard to power and accuracy is in fact false. The researcher can further conclude that the developers of the rumor may have had intentions that were not in the best interest of the golfer. Specifically, golfers who spend money on alcohol to increase their golfing ability do not, on average, gain a significant amount of additional golf ability.

*C. Recommendations*

The researcher's recommendation for further research includes larger sample tests and a test regarding attitude towards personal golf performance in relation to alcohol consumption.

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