Introduction

In this study, I investigated whether there is a statistically significant difference in average liver size between individuals who regularly consume alcohol and those who abstain entirely. This question emerged from a broader interest in how lifestyle behaviors-particularly alcohol consumption-might influence measurable physiological outcomes, such as liver size. I focused on virtual residents of the Vardos community, specifically adults between the ages of 35 and 45. The population parameter of interest was the difference in mean liver size, measured in centimeters, between two distinct groups: those who drank alcohol (drinkers) and those who did not (non-drinkers). Formally, I defined this as the average liver size of non-drinkers minus the average liver size of drinkers.

My interest in this topic was shaped by earlier scientific studies that examined the relationship between alcohol consumption and liver size. Sherlock (1982) discussed how sustained alcohol intake could cause liver cells to enlarge, leading to visible physiological changes and signaling potential liver dysfunction. Van Thiel et al. (1983) similarly explored alcohol-induced liver enlargement and highlighted its clinical relevance. These studies not only led me to hypothesize that drinkers would have larger livers than non-drinkers but also guided my decision to use liver size as the response variable and to compare groups based on drinking status in my simulated dataset.

Going into the study, I expected that drinkers would have larger livers than non-drinkers. Based on the literature and widely accepted health claims about alcohol’s impact on the liver, I hypothesized that the true difference in mean liver size would be negative-indicating that the average liver size for drinkers exceeds that of non-drinkers. This initial assumption shaped both the structure of my analysis and the interpretation of my results.

Data Collection Methods

The observational units in my study were forty-two virtual residents from the simulated community of Vardos, specifically adults aged between 35 and 45 years. My primary objective was to determine whether there was a statistically significant difference in liver size between residents who consumed alcohol regularly and those who didn’t. I divided participants evenly into two groups, each with twenty-one individuals. One group consisted of drinkers who I randomly assigned to consume between one and three servings of alcohol per day, with each serving being 250 mL of light beer. The control group, which I labeled non-drinkers, received no alcohol.

I followed a structured and systematic procedure for collecting data. First, I reviewed the first 122 households in Vardos and selected residents within the targeted age bracket. Then, I used an online random name generator to assign participants to either the drinker or non-drinker group in an unbiased way. After simulating alcohol exposure for the drinkers, I measured each participant’s liver size using the “Physiology” tab at the end of the exposure period. For non-drinkers, I took the measurement at the corresponding point in time.

During the process, I came across several limitations that could have affected the validity of my results. One major issue was that the alcohol exposure only lasted for a single day, which might not reflect the chronic effects of regular alcohol consumption. I also measured each participant’s liver size only once, which might have introduced more variability in the results. On top of that, I didn’t collect demographic information like gender or body mass index, even though those could be important confounding factors.

The way I sampled participants also came with potential risks. By selecting from only the first 122 households, I might have introduced selection bias if that subset wasn’t representative of the broader community. And since everything was conducted in a virtual environment, there are questions about how accurate or reliable the measurements from the “Physiology” tab actually are.

If someone wanted to replicate this study exactly, they would need to follow the same steps I did: select forty-two virtual residents aged 35 to 45 from the first 122 households in Vardos, assign them randomly to either the drinker or non-drinker group, expose the drinkers to one day of alcohol simulation, and then measure liver size using the same tool. If I were to do this again, I’d definitely want to simulate a longer period of alcohol use, take repeated measurements, and collect more background information from each participant. These improvements would make the findings more robust and potentially more applicable to real-world scenarios beyond the simulation.

Descriptive Statistics

data <- read_csv("CopyOfStats Proj Data - Complete Data.csv", skip = 1)
colnames(data)
## [1] "Participant Name"                 "House No."                       
## [3] "Age"                              "Alcohol Consumption (Drinks/Day)"
## [5] "Drinking Category"                "Liver size (cm)"
library(ggplot2)

# Create boxplot
ggplot(data, aes(x = `Drinking Category`, y = `Liver size (cm)`, fill = `Drinking Category`)) +
  geom_boxplot(alpha = 0.7, width = 0.5, outlier.color = "red") +
  labs(
    title = "Liver Size by Drinking Status",
    x = "Drinking Category",
    y = "Liver Size (cm)"
  ) +
  theme_minimal() +
  theme(legend.position = "none")

Non-drinkers:

library(readr)
Exploration_2_3_Data_Collection <- 
  read_csv("~/Stats Proj Data - Non-drinkers.csv")
head(Exploration_2_3_Data_Collection, n=2)
favstats(~`Liver size (cm)`,
data=Exploration_2_3_Data_Collection)

Drinkers:

library(readr)
Exploration_2_3_Data_Collection <- 
  read_csv("~/Stats Proj Data - Drinkers (1).csv")
head(Exploration_2_3_Data_Collection, n=2)
favstats(~`Liver size (cm)`,
data=Exploration_2_3_Data_Collection)
#sample sizes
n.nondrinkers<- 21
n.drinkers<- 21

x.bar.nondrinkers<- 15.30
x.bar.drinkers<- 15.69
  
SD.nondrinkers<- 1.23
SD.drinkers<- 0.73
  
# difference between the sample proportions of nondrinkers vs drinkers
x.bar.diff<-x.bar.nondrinkers-x.bar.drinkers
cat("difference in sample means is",x.bar.diff)
## difference in sample means is -0.39

In my study, the quantitative response variable was liver size, measured in centimeters, and the binary categorical explanatory variable was drinking status, which I categorized as either “Drinker” or “Non-Drinker.” I used a side-by-side boxplot to visualize the distribution of liver sizes for each group.

From the boxplot, I noticed that drinkers had slightly larger liver sizes compared to non-drinkers. The median liver size was higher for drinkers, and their interquartile range was more compact, suggesting less variability in that group. In contrast, liver sizes among non-drinkers were more spread out, with a few extreme values stretching the distribution upward.

The summary statistics I calculated supported these visual impressions. Drinkers had an average liver size of about 15.69 cm with a standard deviation of approximately 0.73 cm, while non-drinkers had a slightly lower mean of around 15.30 cm and a higher standard deviation of about 1.23 cm. This resulted in a difference in sample means of -0.39 cm (non-drinkers minus drinkers), indicating that drinkers, on average, had somewhat larger livers.

The higher variability among non-drinkers made me wonder whether factors beyond alcohol consumption-such as gender or body composition-might be influencing liver size. Overall, while the boxplot and summary statistics suggest a slight association between drinking status and liver size, the overlap in the distributions, especially within the middle 50% of values, indicates that the relationship is weak. To determine whether this observed difference is meaningful or simply due to chance, I knew I would need to perform further statistical testing.

Analysis of Results

In analyzing the results of my study, I focused on a simulated population of virtual adult residents from the Vardos community, all between the ages of 35 and 45. The parameter I investigated was the difference in mean liver size, measured in centimeters, between individuals who regularly consumed alcohol and those who did not. My goal was to determine whether drinkers had significantly different liver sizes compared to non-drinkers.

To test this, I conducted a theory-based two-sample t-test. The hypotheses I used were as follows:

Null Hypothesis (\(H_{0}\)): \(\mu_{1}\) = \(\mu_{2}\)
(The average liver size of drinkers is equal to that of non-drinkers.)

Alternative Hypothesis (\(H_{A}\)): \(\mu_{1}\)\(\neq\)\(\mu_{2}\)
(The average liver size of drinkers is not equal to that of non-drinkers.)

To better understand the results of my hypothesis test, I considered the possible errors. A Type I error in this context would mean concluding that there’s a difference in liver size between the two groups when, in fact, no such difference exists. That would lead me to falsely claim that drinking affects liver size. A Type II error, on the other hand, would mean failing to detect a real difference if one is actually there-so I’d be incorrectly concluding that drinking has no effect on liver size when it really does.

In interpreting these results, I also considered the risk of error. A Type I error in this context would have meant concluding that alcohol consumption affects liver size when it actually does not. A Type II error would involve failing to detect a true difference when one really exists. Given my results, I cannot rule out a small true effect, but I do not have enough evidence to confidently claim one either.

To ensure some consistency in the sampling frame, I selected participants from the first 122 households in the Vardos simulation and applied age restrictions to control for variability. While I used random assignment to place individuals into the drinker and non-drinker groups, the initial selection of households was not random, which may limit how representative the sample is of the broader simulated community. This affects the extent to which my results can be generalized. Still, the random assignment process helped reduce selection bias within the sample and supported the internal validity of the study. Several additional limitations also make generalization difficult. The data reflect only one day of alcohol exposure, which likely fails to capture the long-term physiological effects of regular drinking. Furthermore, I did not account for other potentially important variables such as gender, body composition, or medical history, all of which could influence liver size and weaken the external validity of the findings.

curve(dt(x, df = 40), from = -5, to = 5,
      main = "t Distribution (df = 40)",
      ylab = "Density",
      xlab = "t",
      lwd = 2,
      col = 'steelblue')

# Calculate Standard Error
SE.x.bar.diff <- sqrt(SD.nondrinkers^2 / n.nondrinkers + SD.drinkers^2 / n.drinkers)
cat("Standard error of the difference in sample means is", round(SE.x.bar.diff, 2))
## Standard error of the difference in sample means is 0.31
# Calculate t-statistic
t.stat <- x.bar.diff / SE.x.bar.diff
cat("Standardized statistic t is", round(t.stat, 2))
## Standardized statistic t is -1.25

To compare the mean liver sizes of drinkers and non-drinkers, I used a two-sample t-statistic, which measures how far the observed difference in sample means is from the hypothesized difference of zero, in units of standard error. In my study, the calculated t-statistic was approximately -1.25. The negative sign reflects that the mean liver size for non-drinkers was smaller than that for drinkers, and the magnitude indicates that the observed difference lies 1.25 standard errors below what I would expect if the null hypothesis were true.

For the t-test to be valid, certain conditions needed to be met. First, the samples had to be independent, which I ensured through random assignment to the drinker and non-drinker groups. Second, the sample sizes had to be sufficiently large to justify the use of the t-distribution, especially since the population standard deviations were unknown. With 21 participants in each group, this condition was satisfied, as it meets the commonly accepted threshold of 20 observations per group. Third, the distribution of the data should be roughly symmetric with no severe outliers. My visual inspection of the side-by-side boxplots suggested that both groups were reasonably symmetric and free of extreme values, supporting this assumption.

Since these validity conditions were reasonably satisfied, I felt confident that the use of a t-test was appropriate for this analysis. In that context, the standardized statistic of -1.25 provides a useful benchmark for interpreting how far my observed result is from what would be expected under the assumption of no true difference.

two.sided.p.value <- pval(t.test(`Liver size (cm)` ~ `Drinking Category`, data = data))
cat("The two-sided p-value is", two.sided.p.value)
## The two-sided p-value is 0.2226571

The p-value corresponding to my alternative hypothesis was approximately 0.223. This indicates that, assuming there is truly no difference in average liver size between drinkers and non-drinkers, there is a 22.3% probability of observing a difference in sample means as extreme or more extreme than the one I found in my study. Since this p-value is greater than the commonly used significance level of 0.05, I failed to reject the null hypothesis. In other words, the observed difference in liver size between the two groups was not statistically significant.

In the context of my research question, this result suggests that there is not enough evidence to conclude that alcohol consumption is associated with a difference in average liver size among virtual residents of the Vardos population. The small difference I observed is likely due to random variation rather than a true underlying effect.

confint(t.test(`Liver size (cm)` ~ `Drinking Category`, data = data))

I calculated a 95% confidence interval for the difference in average liver size between non-drinkers and drinkers, which ranged from -0.247 cm to 1.022 cm. Because this interval includes zero, it suggests that no difference in liver size is a plausible value for the true population parameter. In other words, the data are consistent with the possibility that drinking status has no real effect on liver size. This interpretation aligns with the results of my hypothesis test, where I failed to reject the null hypothesis. Together, the p-value and the confidence interval both point to the same conclusion: the difference observed in my sample is not strong enough to provide convincing evidence of a real association between alcohol consumption and liver size.

Conclusion

In this study, I set out to determine whether there is a statistically significant difference in average liver size between individuals who drink alcohol and those who abstain. Based on prior research-such as Sherlock (1982) and Van Thiel et al. (1983), which showed that long-term alcohol use can lead to liver enlargement-I expected drinkers to have larger livers than non-drinkers. My simulation data did show a small difference in the expected direction: the average liver size was 15.69 cm for drinkers and 15.30 cm for non-drinkers. However, this difference was not statistically significant. The p-value was 0.223, and the 95% confidence interval ranged from -0.247 cm to 1.022 cm, which includes zero. As a result, I could not confidently conclude that alcohol consumption had a real effect on liver size.

Through this project, I learned that even when prior research provides a strong theoretical expectation, short-term and simulated data may not clearly reflect those effects. Although the trend in my results supported my hypothesis, the observed difference was too small and variable to reject the null hypothesis. This process also highlighted the importance of understanding the limitations of one’s data. In hindsight, I recognize that the findings are not easily generalizable to real-world populations. The study was based on a single day of alcohol exposure and lacked important demographic variables like gender, body composition, and health history-all of which could meaningfully influence liver size.

If I were to run this study again, I would simulate a longer period of alcohol consumption and include repeated measurements to better account for variation. I would also collect more detailed participant data to improve the realism and generalizability of the results. Future studies could build on this work by looking at chronic drinking behaviors or comparing effects across different demographic groups. There’s clearly more to explore when it comes to understanding how alcohol consumption influences liver size over time.

Bibliography: references to literature mentioned in the introduction

Sherlock, D. H. Liver cell enlargement induced by chronic alcohol consumption: studies on its causes and consequences. The Journal of Pathology, Volume 138, Issue 3, 1982, pp. 255–270. https://doi.org/10.1002/path.1711380306

Van Thiel, D. H., Lester, J. M., & Gavaler, R. On the characteristics of alcohol-induced liver enlargement and its pathophysiological significance. Biochemical Pharmacology, Volume 32, Issue 21, 1983, pp. 3255–3261. https://doi.org/10.1016/0006-2952(83)90213-7