Introduction

What role does gender play in life on the Islands? Do men and women on the Islands face the same gender roles as men and women in our world? In order to explore this area of interest, I chose to focus specifically on the relationship between gender and dietary habits. I began by investigating the number of servings of vegetables eaten in a day by randomly selected female and male islanders. I was interested in finding the difference in mean number of servings of vegetables consumed in a day by female and male Islanders. The literature that inspired my research, “Eating Meat Makes You Sexy” by Susanna Timeo and Caterina Suitner from volume 19 of the Psychology of Men & Masculinity, is based upon three studies that were conducted surrounding the relationships between men, meat, masculinity, and mating. The first study examined “the meat–masculinity stereotype from the female perspective” in order to identify the role that females play in exacerbating existing gender roles that relate meat consumption with levels of masculinity and create an expectation of men to be meat-eaters; it was found that amongst the Italian women who participated in this study, “participants not only endorsed the gender stereotypes about food consumption but also conformed to it in their eating habits” (Timeo & Suitner, 2018).The second study was designed to reinforce the results of the first study, it followed the same map with improvements in the way the study was worded and in the measurements of masculinity used, and it was seen that “participants still preferred omnivorous over vegetarian men, even when they were not labeled as such” (Timeo & Suitner, 2018). The third study used the information regarding female perception of masculinity in relation to food to examine the male response to this perception. The results of this study suggested that “gender-norm endorsement is an additional and critical element for the meat-masculinity phenomenon” (Timeo & Suitner, 2018). Though these studies were performed specifically using a sample of Italian volunteers and the results may not be able to be generalized globally, I think the research that was done is very interesting and reflects a pattern that I have noticed in my life as an American, as well as observed more generally in media that is consumed worldwide. I am intrigued by gender roles in different areas of the world and whether they differ strongly, as well as gender roles on the Islands, whether they mimic those of our world, and if they do I am intrigued as to whether it is because the Islands are man-made and we have inherently created them to face these gender roles. Before I began my research I suspected that the mean numbers of vegetables consumed by female and male Islanders would be different as everyone faces varying eating habits, and I expected that, because the Islands program was developed to behave like a virtual human population, the female Islanders would consume the greater mean number of servings of vegetables than the male Islanders, as is observed in our world.

Data Collection

The observational units in this study are the islanders that consented, or were given guardian consent, to participate in my study. I collected data on 60 males and 60 females from across the Islands for my study. In order to mitigate bias in my selection of islanders, I collected males and females separately, but under the same process. I began with the males, first by selecting the towns that I would search for my male participants in. To do this, I used a random generator with the names of all of the towns on one of the three islands to randomly select four towns from which to seek participants. I repeated this random generation of four town names for each of the three islands, Ironbard, Providence, and Bonne Sante, and then I began searching for male participants in each of the towns. The towns from which I selected my male participants are Hofn, Vardo, Bjurholm, and Helluland on Ironbard Island, Arcadia, Shinobi, Akkeshi, and Hayarano on Providence Island, and Nidoma, Riroua, Pauma, and Gordes on Bonne Sante Island. I sought five male participants from each town, and I did so one-by-one using a random number generator to select the house numbers that I would visit. There were many possible outcomes of using this process: some houses were vacant, some did not house any males, and any males housed in them had the agency to decline to participate in my study. If the house was vacant or did not house any males, I generated a new house number. If the house contained males, I first asked the eldest to participate in my study. If he declined to participate, I asked the next-eldest male, and so on. If all males in a household declined to participate, I generated a new house number. Once I had gathered five male participants from the town I was visiting, I would move on to the next town on my list until I had gathered data on a total of 60 male participants from across the Islands. Once I had collected my male participants, I repeated the same process with the females. I randomly generated names of four towns on each island, and randomly generated houses to visit in search of female participants. The towns from which I selected my female participants are Hofn, Bjurholm, Vardo, and Helvig on Ironbard Island, Takazaki, Kiyobico, Shinobi, and Akkeshi on Providence Island, and Colmar, Mahuti, Gordes, and Valais on Bonne Sante Island. Once again, I asked the eldest female in the house to participate first, if she declined to participate I asked the next-eldest female and so on. If all females in a household declined to participate, I generated a new house number. If a house was vacant or did not house any females, I generated a new house number. I again collected five females from each of the four towns on each of the three islands, until I had a total of 60 female participants. This collection method was quite tedious at times, the random number generator seemed prone to finding houses that were vacant or did not contain any members of the gender for which I was searching, and I faced a lot of rejection in the process as well. In the end I had a fairly large sample that should be representative of the towns on the Islands from which I gathered my data. I also believe it could be argued that this sample is representative of the Islands as a whole. Islanders seem to move around a lot and many Islanders who participated in my study have since moved towns. To make this claim would require research into how often and how far Islanders tend to move. I have not performed this research and therefore will only generalize the results of my study to Islanders living in the towns I gathered data from. Once I had gathered all my participants, data collection was quite simple and required having each of my participants fill out a survey with only two questions: “Are you male or female?” and “How many serves of vegetables do you usually eat each day?”. This collection was only as difficult as it was time-consuming, as each islander must be individually tasked with completing the survey. Once they had all completed the survey, all of my data was collected and I did not have to make any repeat visits to any islanders. A potential source of sampling error is my selection of a new group of towns for my search for male and female participants. If the different towns on the islands have their own cultural systems or differing access to food resources, this could potentially cause differences in the eating habits of people who live in specific towns, and selecting men and women from different towns could unknowingly introduce this potential confounding variable.

Descriptive Statistics

Of the two variables (gender and number of servings of vegetables consumed in a day) I was studying, gender is the binary categorical variable, as Islanders can be either male or female. Gender is also the explanatory variable in my study. Number of servings of vegetables consumed in a day by Islanders is the quantitative variable, it is measured numerically to the nearest whole number and is the response variable in my study. I read the data I collected into R, as displayed using the head command. I used the favstats function to produce a numerical summary of the two groups of data, which are number of servings of vegetables consumed in a day by male Islanders and number of servings of vegetables consumed in a day by female Islanders. I also produced a side-by-side boxplot to visually compare the two groups of data.

library(readr)
vegdata<-
  read_csv("~/Downloads/csv files/Mini Project 3 - Sheet1-2.csv")
head(vegdata,3)
favstats(Number ~ Gender, data = vegdata)

The numerical summary of the two groups of data indicates that the distribution of number of servings of vegetables consumed in a day by male Islanders has a minimum value of zero servings, while the distribution of number of servings of vegetables consumed in a day by female Islanders has a minimum value of one serving. The two groups also face different Q1 values (one serving for the male group and two servings for the female group), different medians (two servings for the male group and three servings for the female group), and different means (2.87 servings for the male group and 3.20 servings for the female group). The male group also has a greater standard deviation of 1.85 servings compared to the standard deviation of 1.44 servings for the female group. The Q3 values are the same for each group at four servings, and the maximum values are also the same for each group at six servings. This data summarized using symbols is as follows:

\(\bar{x}_{male}= 2.87\)

\(SD_{male}= 1.85\)

\(\bar{x}_{female}= 3.20\)

\(SD_{female}= 1.44\)

The side-by-side boxplots below visualize the numerical summary of the two groups of data.

bwplot(Gender ~ Number, 
       horizontal = TRUE, 
       main="Side-by-side boxplots",
       data = vegdata)

It can be seen using the side-by-side boxplots that the male group has a wider range of values than the female group, and that both groups face right-skewness. The male group appears to be more strongly right-skewed than the female group, while still having a lower median number of servings of vegetables consumed in a day. In order to get a clearer picture of how the data is distributed, and specifically the significance of the skewness in each group, I used R to produce parallel histograms as well.

histogram(~Number | Gender, data = vegdata, 
        main="Parallel Histograms",
        cex = 0.1, width = 1, layout = c(1, 2))

It can be seen using the parallel histograms that the distribution of number of servings consumed in a day by male Islanders is neither symmetrical nor bell-shaped, it is significantly right-skewed with a high density of data points at six servings, the maximum value of the dataset. The distribution of number of servings consumed in a day by female Islanders, however, does appear relatively symmetrical and bell-shaped, with only a slight bit of right-skewness. At this point in my analysis, there does not seem to be an obvious association between the two variables.

The next step in my analysis is to perform a theory-based test of significance in regard to my population parameter, the difference in mean number of servings of vegetables consumed in a day by females and males across the Islands. My null hypothesis is that there is no difference in mean number of servings of vegetables eaten by men and women on the Islands. My alternative hypothesis is that female Islanders consume a greater mean number of servings of vegetables in a day than male Islanders.

\[H_0:\mu_{female}-\mu_{male}=0\]

\[H_a:\mu_{female}-\mu_{male}>0\]

In my study, a type I error would represent a ‘false alarm’ in which I reject my null hypothesis (that the difference in mean number of servings of vegetables consumed in a day by female and male Islanders is equal to zero) despite it being true, and falsely claim that female Islanders eat a greater mean number of servings of vegetables in a day than male Islanders. A type II error in my study would represent a ‘missed opportunity’ in which I failed to reject my null hypothesis despite it being false, and incorrectly claim that male and female Islanders eat the same mean number of servings of vegetables in a day. Due to my method of data collection, in which I randomly selected male and female participants from varying towns, I must be careful not to generalize the results of my analysis too broadly. It is possible that the results will not be representative of the entire population of the Islands because I sought my participants from a limited number of towns across the Islands. The results of my analysis can reasonably be considered representative of the populations of the towns from which my participants of each gender were randomly selected, but it is unclear whether they can reasonably be generalized to the population of the Islands as a whole. As mentioned previously, I believe further research could be conducted into the movement of Islanders across the Islands in their lifetimes and how this movement influences the representation of results of studies, but at this point in time I am unable to reasonably generalize the results to my population of interest, all Islanders.

Analysis of Results

The first step in my analysis was to perform a theory-based test of significance of the difference in mean number of servings consumed in a day by female and male Islanders. I used R to calculate the observed difference in means between the two groups.

diff(rev(mean(Number~Gender, data = vegdata)))
##         F 
## 0.3333333

This result indicates that the difference in mean number of servings consumed in a day by female and male Islanders in my sample is equal to 0.333 servings. The value is positive, indicating that the mean number of servings of vegetables consumed by female Islanders is 0.333 servings greater than the mean number of servings of vegetables consumed in a day by male Islanders within my sample.

\[\bar{x}_{female}-\bar{x}_{male}=0.333\]

I next performed a two-sample t-test on the data in order to determine how far this difference in means lies from the hypothesized value under my null hypothesis, which is equal to zero. The two-sample t-test takes the observed statistic, \(\bar{x}_{female}-\bar{x}_{male}=0.333\), and subtracts the hypothesized value (in this case, zero) from it, and then divides by the standard deviation of the statistic. The result is a standardized statistic which indicates the likelihood of the observed statistic within my sample occurring while assuming my null hypothesis to be true.

stat(t.test(Number ~ Gender, data = vegdata))
##        t 
## 1.104315

The resulting standardized t-statistic is equal to 1.10, which indicates that the observed difference in mean number of servings of vegetables consumed in a day by female and male Islanders lies 1.10 standard deviations above the value of zero that is expected under my null hypothesis. A standardized t-statistic of 1.10 does not indicate high levels of significance. I next used R to calculate the p-value that corresponds to the standardized t-statistic, and divided by two as I am using a one-sided test. A p-value here indicates the probability under my null hypothesis that a statistic equal to or more extreme than I have observed will occur. A smaller p-value indicates greater statistical significance.

pval(t.test(Number ~ Gender, data = vegdata))/2
##   p.value 
## 0.1359194

The resulting p-value from this calculation is equal to 0.136. This indicates that the probability of observing a difference in means equal to 0.333 or greater assuming that my null hypothesis is true is equal to 0.136, or it will occur 13.6% of the time. This p-value is moderately small but much greater than significance level alpha, 0.05, and like the value of the standardized t-statistic does not indicate statistical significance.

Based on my calculations and analysis thus far, I fail to reject my null hypothesis. A standardized t-statistic of 1.10 indicates that my observed statistic, \(\bar{x}_{female}-\bar{x}_{male}=0.333\), the difference in mean number of servings of vegetables consumed in a day by female and male Islanders, is 1.10 standard deviations away from the expected value of zero under my null hypothesis. This standardized t-statistic does not indicate evidence that female Islanders consume a greater mean number of servings of vegetables in a day than male Islanders. The theory-based p-value that corresponds to this standardized t-statistic is equal to 0.136, which indicates a 13.6% probability of my observed statistic occurring under my null hypothesis. This theory-based p-value agrees with the standardized t-statistic in that it does not indicate evidence that female Islanders consume a greater mean number of servings of vegetables in a day than male Islanders.

The validity conditions for a two-sample t-test are that the quantitative variable has a symmetric distribution in both groups or that there are at least 20 observations in each group and the sample distributions are not strongly skewed. While the data has more than 20 observations in each group, the quantitative variable of number of servings of vegetables consumed in a day, does not have a symmetric distribution in both male and female groups, and the male sample distribution is strongly skewed, indicating that validity conditions for a two-sample t-test are not met. Due to the failure of the data to meet the validity conditions for the theory-based tests that I performed, my next step was to perform a simulation-based test, which faces no validity conditions, and compare the results of each test.

I began my simulation-based testing using R to simulate my null distribution, which assumes no relationship between the explanatory (gender) and response (number of servings of vegetables consumed in a day) variables. I had R simulate this distribution by repeatedly shuffling the values of the response variable (number of servings of vegetables consumed in a day) and redistributing them at random to the explanatory variable (gender) groups, and then plotting the distribution of the simulated differences in sample means. I also had R highlight all data points in the simulated null distribution that represented a difference in sample means equal to my observed statistic, \(\bar{x}_{female}-\bar{x}_{male}=0.333\), or a more extreme value.

set.rseed(654) 
veg.null <- do(1000) * diffmean(shuffle(Number) ~ Gender, data = vegdata)
dotPlot(~ diffmean, data = veg.null,
        main="Simulated Null Distribution of the Difference in Sample Means",
        xlab="Difference in Sample Means",
        width = 0.01, cex = 1,
group = (diffmean >= 0.333))

It can be seen using the simulated null distribution that the highlighted portion, representing data points equivalent to or more extreme than my observed statistic \(\bar{x}_{female}-\bar{x}_{male}=0.333\), is quite large and begins in the body of the distribution as opposed to the tail. This indicates that outcomes equal to my observed statistic can reasonably occur under my null hypothesis, leading me to expect a large corresponding p-value.

p_value<-prop(~(diffmean >= 0.333), data = veg.null)
cat("right-sided p-value is",p_value)
## right-sided p-value is 0.157

Calculating the corresponding p-value to my null distribution using R produces a simulation-based p-value of 0.157. This signifies that the probability of a statistic occurring that is equal to or more extreme than my observed statistic, \(\bar{x}_{female}-\bar{x}_{male}=0.333\), assuming my null hypothesis to be true is equal to 0.157. This means that if my null hypothesis is true, my observed statistic of 0.333 will occur 15.7% of the time. This simulation based p-value is slightly larger than the theory-based p-value of 0.136, and also fails to suggest evidence against my null hypothesis.

The final step of my calculations is to use R to produce a simulation-based confidence interval using my observed statistic, \(\bar{x}_{female}-\bar{x}_{male}=0.333\), and the standard error of my null distribution to calculate a margin of error with which to define a 95% confidence interval.

 x.bar.diff <- 0.333
SE.x.bar.diff <- sd(~ diffmean, data = veg.null)
MoE <- 2 * SE.x.bar.diff
LB<-x.bar.diff - MoE 
UB<-x.bar.diff + MoE
round(cbind(LB,UB),3)
##          LB    UB
## [1,] -0.265 0.931

The simulation-based 95% confidence interval is (-0.265, 0.931). This means that there is 95% confidence that the difference in mean number of servings of vegetables consumed in a day by female and male Islanders lies between -0.265 servings and 0.931 servings. Zero is a value included in the simulation-based 95% confidence interval, which indicates that zero is a possible value of the difference in means. This simulation-based confidence interval agrees with the simulation-based p-value of 0.157 in suggesting that I should fail to reject my null hypothesis at this time.

Conclusion

Interested in the role that gender plays in life on the Islands, specifically its relationship to food and diet, I conducted an observational study using a sample of 120 randomly selected Islanders, 60 male and 60 female, from a handful of towns across the Islands. I was searching for the difference in mean number of servings of vegetables consumed in a day by female and male Islanders. I expected that female islanders may eat a greater mean number of servings of vegetables than male Islanders, and the data did appear to potentially be behaving as such in the visual and numerical summaries. Within my sample, I observed the difference in mean number of servings to be 0.333 servings greater in the female group. To determine the significance of the results, I performed a theory-based investigation. The theory-based investigation produced a standardized t-statistic of 1.10 and a corresponding p-value of 0.136. While neither of these values suggest evidence against my null hypothesis, I also performed a simulation-based investigation. My sample did not satisfy the validity conditions for a theory-based two-sample t-test as the distribution of the male group was severely right-skewed. My simulation-based investigation produced a p-value of 0.157, a slightly greater value than produced in the theory-based investigation, and again not a value that suggests my observed statistic holds statistical significance. I calculated a simulation-based confidence interval, which is (-0.295, 0.931). This interval includes the value zero, reinforcing the idea that my null hypothesis may be true. Overall, my calculations did not suggest evidence to support my alternative hypothesis that female Islanders consume a greater mean number of servings of vegetables in a day than male Islanders.

In the end, the data did not behave as I expected it would. If I, or someone else, were to replicate this study in the future, I would suggest taking a larger sample size and either using the same group of towns for both gender groups or selecting a lesser number of participants from each town and visiting all towns across the Islands in order to make these results representative of a broader population. Because of my method of selecting towns, these results could only be generalized to the female populations of Hofn, Bjurholm, Vardo, and Helvig on Ironbard Island, Takazaki, Kiyobico, Shinobi, and Akkeshi on Providence Island, and Colmar, Mahuti, Gordes, and Valais on Bonne Sante Island, and the male populations of Hofn, Vardo, Bjurholm, and Helluland on Ironbard Island, Arcadia, Shinobi, Akkeshi, and Hayarano on Providence Island, and Nidoma, Riroua, Pauma, and Gordes on Bonne Sante Island. If someone were looking to further this research, there are some other interesting tasks and survey questions within the Islands that could be interesting to study. Particularly, the “Vegetarian Diet 14 days” intervention task and the “On a scale from 1 to 10, how attractive do you think you are to members of the opposite sex?” survey question. These two features used in conjunction could produce interesting results in regard to gender roles and their behavior on the islands (whether men feel less attractive to the opposite sex after eating a vegetarian diet or whether females feel more attractive to the opposite sex). Furthermore, use of this task rather than only survey questions would allow for an experiment rather than an observational study, and the researcher could make claims about potential cause-and-effect relationships between the variables.

Bibliography

Timeo, Susanna, and Caterina Suitner. “Eating Meat Makes You Sexy”. Psychology of Men & Masculinity, vol. 19, no. 3, July 2018, pp. 418-429, (https://doi.org/10.1037/men0000119).