Introduction

This is a research paper looking at the affects of alcohol on aerobic exercise. To be more specific the population parameter of interest in this study is the effect of consuming two standard drinks of alcohol within one minute before starting aerobic exercise on immediate aerobic capabilities, measured as the speed of a 100-meter indoor run. The research question that I chose was: Does drinking alcohol affect immediate aerobic capabilities? Before seeing any data, My initial conjecture for this question is that consuming alcohol before aerobic exercise will impair aerobic capabilities, resulting in slower running speeds. I suspected that the actual parameter value would be lower than the conjectured value, indicating a negative effect of alcohol on aerobic capabilities.

The initial conjecture was inspired by looking at similar studies and looking at their results. There was no study that looked at the same variables as mine but the general evidence pointed to no correlation or a negative correlation between alcohol and aerobic exercise. Specifically, one paper written by Leasure et al. talked about the base affects of alcohol on exercise and another by McNaughton et al. talked about alcohols general effect on sprinting. This second one was much closer the research question for this study.

Data Collection Methods and Problems

The observational units used in this study were individuals randomly selected from households in a random city. The variables measured were whether alcohol was consumed and the performance on the 100-meter run were measured for each individual. I collected this data by randomly selecting houses in a city via a dice roll and choosing the eldest individual from each household. If the selected individual declined to participate, I moved on to the next house. Those who consented were asked to complete a 100-meter indoor run for the control group. For the treatment group, participants were given two shots of vodka (30ml) and asked to wait for one minute before completing the run. I recorded the run times for each group 40 times.

A potential bias may have been introduced in this process by selecting the oldest individual from each household may limit the generalizability of the study’s findings to a younger population. While the sampling method ensures that participants are of safe/legal drinking age, the potential bias introduced by selecting the oldest individual from each household should be acknowledged when interpreting the results and generalizing them to the broader population. Also more data could be collected to reduce any variation in the data.

Descriptive Statistics

The data collected for the study is shown below.

Data <- read_csv("Mini Project - Data Collection - Canty - Sheet1 (1).csv")
bwplot(Alcohol ~ Time, 
       horizontal = TRUE, 
       main="Side-by-side boxplots",
       data = Data)

t_test_result <- t.test(Time ~ Alcohol, data = Data)
t_test_result$statistic
##         t 
## -1.274033
t_test_result$p.value
## [1] 0.2068418

The data is presented in a side by side box plot above. Some important statistics that we can look at were the average values of 17.8 seconds for the sober group and 19.17 seconds for the treatment group giving a t-test result of -1.27. Looking at the box plot, both sets of data had a relatively normal distribution but the treatment group had a few outliers at the larger times. On a first glance, it doesn’t look like there is much of an association between the two variables.

Analysis of Results

The population of interest for this study is individuals who engage in aerobic exercise. The parameter of interest is the effect of consuming two standard drinks of alcohol within one minute before starting aerobic exercise on immediate aerobic capabilities, specifically measured as the speed of a 100-meter indoor run. The null hypothesis is \(H_0: \mu_{\text{Control}} = \mu_{\text{Treatment}}\), where \(\mu_{\text{Control}}\) is the population mean speed of the control group (no alcohol consumed) and \(\mu_{\text{Treatment}}\) is the population mean speed of the treatment group (alcohol consumed). Whereas the alternative hypothesis \(H_a: \mu_{\text{Sober}} \neq \mu_{\text{Treatment}}\), indicating that there is a significant difference in mean aerobic capabilities between the control and treatment groups.

Next, I will look at some error analysis. In this setting, a Type I error would represent concluding that there is a significant difference in mean aerobic capabilities between the control and treatment groups when there isn’t one (i.e., rejecting the null hypothesis when it is true). A Type II error would represent failing to detect a significant difference in mean aerobic capabilities between the groups when there actually is one (i.e., failing to reject the null hypothesis when it is false). Another possible error with this study is that the sample collected may not be fully representative of the broader population, as it only includes individuals from a specific city and selects the oldest individual from each household. This could introduce bias, particularly if older individuals differ systematically from younger ones in their response to alcohol consumption and aerobic exercise. However, efforts were made to randomly select participants and ensure they were of legal drinking age, enhancing the sample’s representativeness to some extent.

Looking at some statistics, the appropriate standardized statistic for comparing the means of two independent groups is the two-sample t-test witch had a value of -1.27, which is the difference in means between the two groups. Validity conditions for this test include random sampling, independence, normality of distributions, and equal variances. The p-value corresponding to the alternative hypothesis is 0.2068. This means that assuming there is a true difference in mean aerobic capabilities between the control and treatment groups, there is a 20.68% probability of observing a difference as extreme as, or more extreme than, what was observed. Since the p-value (0.2068) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that there is a significant difference in mean aerobic capabilities between the control and treatment groups. Since the validity conditions for the theory-based test are satisfied, we do not need to resort to a simulation-based approach in this case.

conf_interval <- t_test_result$conf.int
conf_interval
## [1] -3.5336956  0.7786956
## attr(,"conf.level")
## [1] 0.95

Now looking at a confidence interval (as shown in the r code above), an appropriate confidence interval for the difference in means between the control and treatment groups is -3.5337 to 0.7787 as shown in the r code above. The 95% confidence interval indicates that I am 95% confident that the true difference in mean aerobic capabilities between the control and treatment groups falls within the range of -3.5337 to 0.7787 seconds. Since zero is included in the confidence interval, it further supports the conclusion from the hypothesis test that there is no significant difference in mean aerobic capabilities between the two groups.

Conclusion

In summary, the results of the study suggest that alcohol consumption, as described in the study, does not have a significant effect on immediate aerobic capabilities during a 100-meter indoor run. The data did not align with the initial expectation of a significant difference in aerobic capabilities between the control and treatment groups. Both the p-value (0.2068) and the 95% confidence interval (-3.5337 to 0.7787) suggest that there is insufficient statistical support for a significant difference between these groups. Generalizing the findings to broader populations or processes may be slightly limited due to potential biases in the sampling method and a small sample size. For future research, I would suggest larger sample sizes and would explore whether different dosages or types of alcohol have varying effects on a wider range of aerobic capabilities.

Bibliography: references to literature mentioned in the introduction

Leasure JL, Neighbors C, Henderson CE, Young CM. Exercise and Alcohol Consumption: What We Know, What We Need to Know, and Why it is Important. Front Psychiatry. 2015 Nov 2;6:156. doi: 10.3389/fpsyt.2015.00156. PMID: 26578988; PMCID: PMC4629692.

McNaughton L, Preece D. Alcohol and its effects on sprint and middle distance running. Br J Sports Med. 1986 Jun;20(2):56-9. doi: 10.1136/bjsm.20.2.56. PMID: 3730755; PMCID: PMC1478291.