Introduction

As we approach finals season, students are being told more than ever to making sure they are getting enough sleep and to stay hydrated in order to do well on exams. So, for my final project, I wanted to see if drinking sufficient water for an extended period of time actually benefits the working memory speed of young adult residents of the Islands, a “virtual human population” created by a team at the University of Queensland to simulate statistical research.
I confirmed that a body water deficit as low as 1-2% can have a negative impact on cognitive function, according to measurements of memory as well as critical thinking and attentiveness (Riebl & Davy, 2013). Other studies looked at the impacts of increased hydration. One study found a positive association between a greater amount of water supplementation and cognition function and mood after a period of dehydration (Zhang et al., 2020), and another concluded that acute water drinking interventions were positively associated with enhanced working memory (Edmonds et al., 1970).
These conclusions were a good basis to have, but I wanted to look more specifically at how working memory is associated with different levels of consistent daily hydration, rather than how cognition is impacted while restoring water after a period of dehydration. I formed the research question, “Is a higher level of daily water consumption associated with better working memory performance in young- and middle-aged adults?”. I suspected that individuals with higher daily water intake would have faster working memory than those with lower daily water intake.

Data Collection Methods

Since I wanted to be able generalize data to a broad population, it was important for me to include individuals from across all three virtual islands. I randomly selected two cities from each of the three islands to sample from. At each island, I assigned each city a number 1-n, then used a random number generate to pick two numbers. The cities they corresponded to became part of my study. Thus, the adult residents of Helvig, Vardo, Nelson, Akkeshi, Mahuti, and Colmar made up my sampling frame. Going through the cities one by one, I used a random number generator to randomly select six houses to sample from. If there was only one adult between 20-60 years of age in a household, and they consented to be in the study, they were selected be part of my sample. If there were multiple adults in the age range in the household, I randomly selected one (by assigning them numbers 1-n, then using a random number generator) to be a part of my sample. If there was no one in the age range in the household, or if none of them consented to be in the study, I would randomly select a different household to replace it.
After consenting to be in the study, each participant was first asked how much water they drink per day, in cups. They were then asked to complete the Memory Game, which involved pairing 30 cards as quickly as possible. The time it took to finish this task was measured in seconds. This data was recorded according to their answer to the water consumption question: 6 or fewer cups per day meant they were part of the “Less Water” category, and greater than 6 cups placed them in the “More Water” group. This data was stored in the Water.Memory Google Sheet in the tidy format.
In each city, I randomly selected 6 houses to participate in the study. However, every city required at least 1 house to be replaced, whether due to the people living there all being outside of the age range (there was even a 120 year old living alone on Akkeshi!), people not consenting to be in the study, and even one house on Helvig being completely unoccupied. Occasionally, I would come across a house with two eligable residents, where the first one picked refused to be in the study. In this case, I just included the other individual in the house instead of randomly choosing another household. The first island, Ironbard, required the least amount of subject reselection for any of these reasons (1 on Helvig, 2 on Vardo). Nelson and Akkeshi, the cities on Providence, were more problematic, with the most subject reselection needed (4 and 3, respectively). Some of these had to be reselected multiple times when the replacements were also too old or did not consent to the study. On Bonne Santé, nearly every house had to be reselected (5 on Mahuti, 4 on Colmar), but not as many required multiple reselction attempts as the cities on Providence did. This comes out to an overall response rate of 65%.

Descriptive Statistics

Since my study had a binary categorical explanatory variable (water consumed on a daily basis, self-reported, divided into “less” (<=6 cups) and “more” (>6 cups)) and a quantitative response variable (time to complete memory test, in seconds), I used a side-by-side boxplot to visualize my data.

bwplot(Water ~ Time,
horizontal = TRUE,
main="Side-by-side boxplots",
data = WaterMemory)

The entire box-and-whisker plot for the “more water” group, including the mean, had lower values than the “less water” group. This indicates that, overall, the individuals in the “more water” group, who reported a daily water consumption greater than 6 cups, took less time to complete the working memory test when compared to the individuals in the “less water” group, who reported a daily water intake of 6 or fewer cups. This aligns with my alternative hypothesis that greater daily hydration is correlated with faster working memory. However, there is still overlap between the response variable outcomes of the two groups, with the top ~75/% of data in the “more water” group overlapping with the bottom ~75/% of the “less water” group. In other words, about 25/% of individuals observed who reported drinking greater than 6 cups of water per day had faster memory test times than any of the observed individuals who reported drinking 6 or fewer cups of water per day. Conversely, about 25/% of observed individuals who reported drinking 6 or fewer cups of water per day took longer to complete the memory test than any of the observed individuals who reported drinking more than 6 cups of water on a daily basis. From this visual data representation, I predicted that statistical methods would provide some evidence against the null hypothesis that there is no difference in the mean working memory speed of people who drink more or less water.

Analysis of Results

The goal of this study was to draw conclusions about the true difference in average working memory speed between adults on all three islands, aged 20-60, who drink greater than 6 cups of water per day and those who drink 6 or fewer cups of water per day. The null hypothesis was that there is no difference in the working memory speed of those with higher or lower daily water intake, represented as $ H0: {more} - {less} = 0 $. The alternative hypothesis was that the working memory speed of those who consume more water on a daily basis is faster than the working memory speed of those who consume less water on a daily basis, represented as $ HA: {more} - {less} < 0 $.

In this study, a type I error would occur if there truly was no significant difference in the average working memory speed of adults on the islands aged 20-60 who drink more water and those who drink less water, but our data allowed us to reject the null hypothesis and conclude that there is a significant difference. A type II error would occur if, from our data, we did not reject the null hypothesis when, in actuality, there is a significant difference in the working memory speed of adults on the islands aged 20-60 who drink more water and those who drink less water.

We took a random sample from across the population of interest, but with how large the population was, I don’t feel that a sample size of 36 was truly representative of all adults ages 20-60 from across all three islands. However, a larger sample size would not have been realistic given the time constraints and the fairly low response rate. In the future, I would choose a more limited population of interest (for example, just one island instead of all three, or shrinking the age range) in order to have a more representative sample.

stat(t.test(Time ~ Water, data = WaterMemory))
##        t 
## 1.685071
two.sided.p.value<-pval(t.test(Time ~ Water, data = WaterMemory))
cat("the one-sided p-value is",two.sided.p.value/2)
## the one-sided p-value is 0.05235846

Using a theory-based approach, I obtained a standardized t statistic of 1.69 and a one-sided p-value of 0.052. According to our textbook, this would give us moderate evidence against the null hypothesis that the working memory speed of islanders who drink more water on a daily basis does not differ from the working memory speed of islanders who drink less water. However, there were fewer than 20 individuals in the “more water” as well as the “less water” group, so the validity conditions for a theory-based approach were not met. For this reason, I decided to use a simulation-based approach for my conclusion.

set.rseed(498)
Water.null <- do(1000) * diffmean(shuffle(Time) ~ Water, data = WaterMemory)
p_value<-prop(~(diffmean <= -7.207), data = Water.null)
cat("simulation-based p-value is",p_value)
## simulation-based p-value is 0.048

Using this, I found a one-sided p-value of 0.048, which is slightly lower than the value found using a theory-based approach. The p-value of 0.048 provides strong evidence against the null hypothesis, according to our textbook, that the working memory speed of islanders who drink more water on a daily basis does not differ from the working memory speed of islanders who drink less water. In other words: the probability of observing a difference in working memory speed of subjects who drink more water and working memory speed of speed of subjects who drink less water as extreme as, or more negative than, -7.21 seconds is 0.048 assuming there is no difference in the true average working memory speed of these two groups in the population. We can conclude that islanders ages 20-60 who drink greater than 6 cups of water per day have a faster working memory, on average, than those who drink 6 or fewer cups of water per day.

confint(t.test(Time~Water, data = WaterMemory))

The theory-based 95% confidence interval was (-16.03, 1.61). In context, this means we are 95% confident that the time to complete a working memory test for young and middle-aged adults who drink more than 6 cups of water per day is, on average, faster than for those who drink 6 or fewer cups of water per day, by between -16.03 and 1.612 seconds. The interval includes 0, meaning it is plausible that there is no difference in population means, which matches our conclusion from the theory-based p-value but is different from the strong evidence against the null hypothesis that we got from the simulation-based p-value. However, because the interval is very skewed and close to not including 0, and because the data does not meet the criteria for the theory-based method, I do not feel comfortable confidently failing to reject the null hypothesis based on this confidence interval.

Conclusion

Based on the simulation based p-value of 0.048 and the 95% confidence interval, which includes 0, we have conflicting evidence about whether or not higher daily water consumption is correlated with an improved working memory speed in young and middle-aged adults. From my background research, which touted the benefits of increased water intake on short- and long-term memory, this is not the result that I expected. I thought the study would reveal clear and strong benefits of higher daily hydration levels on memory, which would be indicated by a very small p-value and a strongly negative confidence interval. Although the random sampling across all three islands means we are able to generalize our sample to the larger population, I do not think that this is reasonable due to the small sample size and conflicting statistical results. In the future, I would take a larger random sample and focus just on one island in order to get more conclusive evidence, even if it means the population that the conclusion could be generalized to would be smaller. Similar questions that would expand on this research which include performing an experiment with random assignment rather than just a study in order to better control for confounding variables, and/or to treat the amount of water consumed as a quantitative variable instead of a categorical one and performing linear regression to test for association.

Bibliography

Zhang, Jianfen, et al. Different Amounts of Water Supplementation Improved Cogni- tive Performance and Mood among Young Adults after 12 h Water Restriction in Baod- ing, China: A Randomized Controlled Trial (RCT), International Journal of Environ- mental Research and Public Health, U.S. National Library of Medicine, 24 Oct. 2020, https://pmc.ncbi.nlm.nih.gov/articles/PMC7662706/

Edmonds, C., et al., Drinking Water Enhances Cognitive Performance: Positive Effects on Working Memory but Not Long-Term Memory, UEL Research Repository, Springer Nature, 1 Jan. 1970 https://repository.uel.ac.uk/item/89q72

Riebl SK, Davy BM. The Hydration Equation: Update on Water Balance and Cognitive Performance. ACSMs Health Fit J. 17 Nov. 2013 https://pubmed.ncbi.nlm.nih.gov/25346594