Introduction:

To test the effects of alcohol on reaction time, in this study we explored the question: does consuming 3 drinks in succession negatively affect an individual’s reaction time 30 minutes later for individuals 21 and older on Providence island? We had a tequila treatment group as well as a water treatment group to act as a control. Hence in this study, the population parameters we are interested in are the mean change-from-baseline ruler test scores 30 minutes after consuming either tequila or water (for adults 21+ on Providence island). Our single parameter of interest is the difference in mean ruler test change-from-baseline score between the tequila group and the water group (mean tequila group - mean of water group). A positive value for this parameter would indicate larger decreases in reaction time among adults drinking tequila, as a higher score is associated with a greater decrease in reaction time. Our initial conjecture is that subjects consuming tequila will have larger decreases in reaction times compared to subjects consuming water. This study was inspired by other research demonstrating an association between alcohol consumption and decreased reaction times. In one blind study, researchers gave participant a drink with 40mL vodka or a placebo drink, asking subjects to judge which one of two lines was shortest, emphasizing accurate and not rapid responding (Tzambazis et. al). The study demonstrated that alcohol significantly slowed total information processing. In another study, researchers similarly demonstrated that alcohol slowed premotor reaction times (Hernandez et. al). In this study, we test how 3 shots (90 mL) of tequila (40% alcohol) affects individuals reaction times 30 minutes later. We chose the amount of 3 standard drinks because it puts most adults very close to, or above the legal limit for driving (0.08 BAC), according to a chart presented by the University of Toledo (see references). The university also presents a chart suggesting that at BAC level 0.8, reaction time starts to be impaired. Hence in this study, we intend to demonstrate why the legal BAC limit for operating a motor vehicle is set at 0.08. In other words, we hope to demonstrate how just a few drinks can negatively impair adults reaction times 30 minutes later.

                        Data Collection Methods:

Sampling methods:

The observational units in this study were adults aged 21 from the various towns of Providence island. We randomly selected 60 legal aged individuals from the island’s towns, using town population sizes to select proportional amounts of subjects from each town in order to eliminate ‘town’ as a confounding variable. We assumed that the proportion of individuals 21+ years old is the same for all the towns in order to calculate the number of subjects selected from each town. In other words, we assumed the relative number of adults age 21+ is equal to the relative population sizes of the towns on the island (rather than calculating the relative proportions of legal adults/minors in each town). By taking representative sample numbers from each town we can better generalize our results to the entirety of Providence Island, rather than one town having a disproportionate number of subjects contributing to the data.

Sampling continued:

Within each town, we counted the houses, using the google random number generator to randomly select which houses we found subjects at. If we were denied consent, if the house was abandoned, or if the house had no individuals of legal drinking age, we moved on to the next randomly selected house. A list of randomly generated house number for each town was created ahead of time, so we could move on to the next randomly generated house number without repeating the process of randomization. This list contained extra house numbers to account for inability to gather subjects, so we could continue down the list rather than generating new numbers when houses didn’t have participants. Within each house, we used a google coin flip applet to randomly select the subject, depending on the number of individuals aged 21+ residing within the home (2 legal adults = 0.5 chance of selection).

Experimental Methods:

We started by recording all initial scores of the ruler test for subjects across all treatment groups. We randomly assigned subjects into treatment groups based on the first letter of their last name, though it is important to note that we added more subjects to the control group part of the way through the study, polluting this random assignment by last name. Once we had 30 subjects assigned to each treatment, we administered respective treatments to subjects. In the treatment group, subjects drank a 90mL of tequila within the span of two minutes. In the control group, subjects consumed 60mL of water. We recorded follow-up scores on the ruler test 30 minutes following consumption of liquids. Unfortunately, data gathering happened second for the control group, at which point a few of the subjects had fallen asleep. This meant we had to recollect the data on a following day. We repeated the whole process, collecting a new baseline score for these individuals, waiting 30 minutes, then collecting a final ruler test score. While the process of data collection remained constant, it is important to note the possible effect that collecting measurements on separate day (and at a different time) could have on the data. Overall, we made 3 repeat visits to subjects within the same day: first collecting baseline scores, then giving the treatment, and finally collecting another ruler test score.

                        Descriptive Statistics:

The chart below is a five-number summary of the data produced by the favstats code. From the summary, we can see that \(\bar{x}_{Tequila}\) = 3.87, whereas for the water group, \(\bar{x}_{water}\)= 0.25. The statistic of interest \(\bar{x}_{Tequila} - \bar{x}_{water}\) is equal to 3.62. This means that in our sample, subjects in the tequila group did an average of 3.62 inches worse on the second round of ruler testing compared to subjects who drank water. It appears there may be an association among variables, as this difference in means is large in the context of this study. Furthermore, we can see from the five-number summary that the variation in the tequila group (SD = 1.86) is notably larger than the variation in the water group (SD = 1.28). This notable difference in standard deviations among the two groups is alarming, and may suggest the large effects that alcohol is having on the reaction times of some subjects in the alcohol group.

#Loads the data set into R
Tequila_Data <- read_csv("SWAUsableData - Sheet3.csv")

#Produces a five-number summary of the dataset
favstats(Difference ~ Treatment, data = Tequila_Data)

Below is a side-by-side box plot of the sample data. The x axis represents inches, with a positive value indicating decreased ruler score tests by a given number of inches. We can see that the medians between treatment groups are almost 4 inches apart, with no overlap between middle quartiles. Furthermore, we can see from the whiskers in the tequila group that there is considerably more variation within the sample, likely due to the varying effects of alcohol on subjects in this group (which is also represented by the two outliers lying outside these whiskers). The differences in sample data displayed in this boxplot give visual evidence of an apparent association between alcohol and decreased reaction time.

#Creates a side-by-side box plot for two quantitative response variables.
bwplot(Treatment ~ Difference,
       horizontal = TRUE,
       main = "Side-by-side boxplots",
       data = Tequila_Data)

                          Analysis of Results:

The respective population parameters are the change-from-baseline ruler test scores (final-initial) for Providence Island adults 21 and older who consume either 90mL tequila or 60mL water. Once again, initial scores are measured before consumption, and final scores are measures thirty minutes after consumption for each of the two groups. The single parameter of interest is the difference in mean ruler test change-from-baseline score between the tequila group and the water group (mean tequila group - mean of water group).

The null hypothesis is that there is no difference in reaction time scores between Providence Island adults who consume 90mL tequila and 60mL water. \(H_0: \mu_{Tequila} -\mu_{water} = 0\)

The alternative hypothesis is that Providence Island adults who consume 90mL tequila will have greater decreases in reaction time than those who drink 60mL water. \(H_A: \mu_{tequila} - \mu_{water} > 0\)

In the context of this study, type I error would represent wrongfully rejecting the null hypothesis, finding a significant negative association between consumption of 90mL alcohol and reaction times, when in reality the association is not significant. If we increase the level of our significance level, there is a greater chance of making a type I error. Type II error in the context of this study would represent wrongfully failing to reject the null hypothesis, when there is actually an association between consumption of 90mL of alcohol and decreased reaction time. We might commit type II error when the true association between variables is relatively small, or if we decrease our significance level. For context, in this study the significance level, \(\alpha\), is 0.05.

The sample in this study can be considered representative of the the population of interest: adults 21 and older on Providence Island. Houses and individuals within each house were randomized, making our sample representative of adults 21 and older on Providence Island. We also took representative sample numbers from each town depending on the population size relative to the total population of the island. While our random sampling should make findings generalizable to adults on Providence Island, it’s important to note that alcohol’s effect have been shown to vary depending on variables like age, sex, and weight. Hence, results should be taken with a grain of salt.

  Using a theory-based approach to test for a significant association:

The value of the t statistic is 8.558, which is significant. The validity conditions for running this theory-based t-test are met, as there are at least 20 subjects in each treatment group (n = 27 for each of our treatment groups). Furthermore, the sample distributions are relatively unskewed, which can be seen in the stacked histograms below.

#Runs a two-sample t-test
stat(t.test(Difference ~ Treatment, data = Tequila_Data))
##        t 
## 8.558296
#creates a stacked histogram of the sample data 
histogram(~Difference | Treatment, data = Tequila_Data, width = 1, layout = c(1, 2))

The R code below calculates a p-value that corresponds to the above t-test. The p-value, 6.71e-11, is practically zero. This means the probability of observing a decreases in reaction time scores as large as the observed statistic is 6.71e-11, assuming the null hypothesis is true: there is no difference in reaction time scores depending on whether an adult drinks water or tequila. This p-value provides very strong evidence to reject this null hypothesis. In the context of alternative hypothesis, we have strong evidence to support the hypothesis that drinking 90mL of tequila negatively affects Providence Island adults’ reaction times 30 minutes later, compared to drinking 60mL of water.

#Calculates the p-value from the two-sample t-test
pval(t.test(Difference ~ Treatment, data = Tequila_Data))
##      p.value 
## 6.710564e-11

Confidence Interval:

The confidence interval calculated for data has a lower bound of 2.77 and an upper bound of 4.48. We are 95% confident that true difference in mean change-from-baseline scores on the ruler test between adults on Providence Island who consume three tequila shots and adults who consume 60mL water is between 2.77 and 4.48 inches. Furthermore, 0 does not fall within this confidence interval, meaning that there is strong evidence to support the hypothesis consumption of thee shots of tequila decreases reaction times. This conclusion of significance aligns with the conclusions drawn from the significant p-value.

#Produces a confidence interval of plausible population parameters
confint(t.test(Difference ~ Treatment, data = Tequila_Data))
                             Conclusion:

In this study we found strong evidence to support the hypothesis that consuming three shots of tequila negatively impacts Providence Island adults’ reaction times 30 minutes later, compared to when drinking water (p = 6.71e-11). We randomly sampled 54 adults aged 21+ from the towns of Providence Island, splitting subjects into two treatment groups: consumption of 90mL tequila or consumption of 60mL water. We found that median change-from-baseline ruler test scores was ~4 inches worse in the tequila treatment group than in the water treatment group, which is a very significant difference in the context of this study. When analyzing the data with a theory-based approach, we found a very significant value of the t-statistic (8.55) and p-value (p = 6.71e-11), which supports the alternative hypothesis that 90mL of tequila negatively impacts reaction times 30 minutes later. Furthermore, the confidence interval we calculated (2.77, 4.48) does not contain 0 within the interval, which further supports the hypothesis that three shots of tequila decreases adults’ reaction times compared to 60mL of water. The population of interest in this study is adults aged 21+ on Providence Island. Due to the random sampling methods, the results of this study are theoretically generalizable to this population. However, this population is very large and not constricted by any other variables other than age. Even still, there is a large range of ages of subjects in this study. The reality is that the effects of alcohol have been shown to vary with things like age, sex, weight, and activity level. As our population of interest is broad and does not account for variables like sex and weight, the results of this study should be generalized cautiously to sub-populations within our population of interest. It is probably valid to make the generalization that alcohol is negatively affecting ruler-test reaction times to our entire population of interest. However, the extent that alcohol is decreasing reaction times (as indicated by the confidence interval) may not be the same for certain sub-populations within the population of interest. Hence, in future study, the population of interest could be narrow in scope, maybe by a certain age range, weight range, or by sex. This would yield data that is more generalizable to the sub-population of study. If I were to repeat this study, I would do data collection during the day, so no subjects would fall asleep during collection. Furthermore, subjects might be getting sleepy at night, which could exacerbate the effects of alcohol on reaction time. Hence, doing the study during the day after subjects have rested would eliminate this possible confounding variable. I would also limit the population of interest to a certain age range of a certain sex. I’ll admit it was easier to collect subjects with a broader population of interest, though next time I would spend more time randomly collecting subjects from a more specific population. Future studies might also want to explore how the amount or type of alcohol affects reaction times. Furthermore, the ruler text could be given at a different time after consumption (in this study final tests happened 30 minutes after consumption). Or, subjects might consume the alcohol over a longer time period, rather than taking shots in succession.

                            Bibliography:

Hernández, O. H., Vogel-Sprott, M., & Ke-Aznar, V. I. (2007). Alcohol impairs the cognitive component of reaction time to an omitted stimulus: a replication and an extension. Journal of studies on alcohol and drugs, 68(2), 276–281. https://doi.org/10.15288/jsad.2007.68.276

Katherine Tzambazis, Con Stough, Alcohol Impairs Speed of Information Processing and Simple and Choice Reaction Time and Differentially Impairs Higher-Order Cognitive Abilities. Alcohol and Alcoholism, Volume 35, Issue 2, March 2000, Pages 197–201, https://doi.org/10.1093/alcalc/35.2.197

Blood alcohol content. University of Toledo. https://www.utoledo.edu/studentaffairs/counseling/selfhelp/substanceuse/bac.html