library(readr)
Final_Project_Data <- 
  read_csv("~/R/Math 247 Spring 2024/Homework/Islanders Data  - Sheet1 .csv")
head(Final_Project_Data, n=2)

Pets and Stress: Introduction

Does owning a pet contribute to lower salivary cortisol levels? Our research on the Islands was looking at a comparison between the mean salivary cortisol levels (SCLs) of Islanders who own pets and Islanders who do not. Whether an islander owns a pet is a binary categorical variable. This is the explanatory variable. An islander having a pet is a very easy variable to measure- it can be confirmed just by looking at an individual islander’s profile. The SCL is a quantitative variable that can be easily measured using a test of the islander’s saliva. Salivary cortisol is a biomarkerof the amount of stress that the human body experiences. This variable is the response variable.

The presence of animals, especially dogs, in people’s lives has been linked to lower stress levels, measurable through the concentration of SCLs (Krause-Parello et al. 2012). Interaction with animals notably lowers SCLs in college students, a highly stress prone group (Jimenez et al 2023, Pendry and Vandagriff 2019). The Pendry study also includes cats as an effective SCL reducer after only 10 minutes of visitation. In a study with healthcare professionals, the stress reduction via interaction with dogs was notable after only five minutes, and continued decreasing for up to 45 minutes post-encounter (Barker et al. 2005). Altogether, it seems that animals are impactful on SCLs across many groups of adults. Given this, we thought that the SCLs would be lower among Islanders who are pet owners than among those who are not.

Pets and Stress: Data Collection

We chose to study a medium-large sized town on the Island of Providence, called Reading. The observational units are adults from Reading, Providence. The data was collected by first having a random number generator output numbers between 1 and 697 (the number of houses in Reading), and asking the first person from the household to participate in the study. We did this until we had 75 participants in the study, then we went through each one and recorded whether or not they had a pet and started their salivary cortisol test. Once we had finished this, we went back through and recorded the values for each Islander’s salivary cortisol test. At this point, one of the Islanders withdrew from the study, so there were only 74 data pairs in the end. All of the data was entered into a spreadsheet arranged alphabetically. The response rate was approximately 65-70%. The data is sufficient because there are at least 20 of each of the explanatory variable categories.

Pets and Stress: Descriptive Statistics

After collecting all of the data, there did not seem to be a strong correlation between the presence or absence of a pet and the SCLs, measured in μg/dL. The numerical data summary shows a similar distribution for both groups. The Islanders group who are not pet owners had a wider range of values, but also more individuals in the group.

bwplot(Pet ~ Cortisol, 
       horizontal = TRUE, 
       main="Side-by-side boxplots",
       data = Final_Project_Data)

data(Final_Project_Data)
favstats(Cortisol ~ Pet, data = Final_Project_Data)

Pets and Stress: Analysis of Results

Further investigating the data requires assurance of a few validity conditions. We are studying the parameter of the difference in means of SCLs between Islanders who own pets and Islanders who do not, in the population of adult Islanders. The hypotheses would be:

\(H_A: μ_{pet}- μ_{no pet} = 0\) The null hypothesis is that there is no difference in mean salivary cortisol levels between pet owners and non-pet owners.

\(H_A: μ_{pet}- μ_{no pet} < 0\)

The alternative hypothesis is that the mean salivary cortisol levels of pet owners is lower than non-pet owners

In this situation, a type I error would be rejecting the null hypothesis when there actually was no difference in means. A type II error would be failing to reject the null hypothesis when there is actually a significant difference in the means of the groups. The sample represented by this data set is not a representative sample of the Islands, but it is a representative sample of the town of Reading, if we are interested in that.

The standardized statistic in this case would be the t-statistic. The validity conditions are met since each group has more than 20 observations, each group is independent from the other, and the distribution and variance is similar in both groups The t-statistic from this data set is

stat(t.test(Cortisol ~ Pet, data = Final_Project_Data))
##          t 
## -0.1580253

This is much lower than the value of 2 which generally indicates significance. The corresponding p-value is

two.sided.p.value<-pval(t.test(Cortisol ~ Pet, data = Final_Project_Data))
cat("the two-sided p-value is",two.sided.p.value)
## the two-sided p-value is 0.874905

This means that the probability of observing a difference in means such as the one we got assuming the null hypothesis is true is 87%. This is quite high, leading us to fail to reject the null hypothesis. In this case that means that there is no significant difference in means between the pet owner SCLs and the non-pet owner SCLS. The confidence interval for this is:

confint(t.test(Cortisol ~ Pet, data = Final_Project_Data))

This means that we are 95% confident that the true value of the difference in SCLs between pet owners and non-pet owners is between -0.02618 and 0.02234. This range includes 0, so that is a plausible value, meaning that is it plausible that there is no difference between the means of the groups. This conclusion agrees with the one derived from the p-value, that the null hypothesis is plausible in this case.

Pets and Stress: Conclusion

Based on the very high probability of observing the value of our difference in means within the null model, as demonstrated by a p-value of 0.875, and the confidence interval which includes 0, we can reasonably fail to reject the null hypothesis. We conclude that there is no significant difference in means in SCLs between Islanders from Reading with pets versus without pets. This is different than what we expected before, based on previous studies. However, there is not a lot of research on the SCLs of pet owners and non-pet owners without immediate animal exposure in the study. Since these data cannot be generalized to a wider population of Islanders, our first step moving forward would be to collect a more representative random sample and see if that has significance. In another future study we could investigate whether there is a difference in SCLs between people who have dogs and people who do not have dogs, since a lot of the prior research involves canine companions.

Bibliography: references to literature mentioned in the introduction

Barker, S. B., Knisely, J. S., McCain, N. L., & Best, A. M. Measuring Stress and Immune Response in Healthcare Professionals following Interaction with a Therapy Dog: A Pilot Study. Psychological Reports, 96(3), 713-729. 2005 https://doi-org.ezproxy.whitman.edu/10.2466/pr0.96.3.713-729

Krause-Parello CA, Tychowski J, Gonzalez A, Boyd Z. Human-canine interaction: exploring stress indicator response patterns of salivary cortisol and immunoglobulin A. Res Theory Nurs Pract. 2012;26(1):25-40. doi: 10.1891/1541-6577.26.1.25. PMID: 22866562.

Jimenez, Ana Gabriela , Luke Calderaro, Sophia Clark, David Elacqua, Emily Hazen, Vanessa Lam, Grace S. Leightheiser, Can dogs serve as stress mediators to decrease salivary cortisol levels in a population of liberal arts college undergraduate students?, EXPLORE, Volume 19, Issue 3, 2023, Pages 283-289, ISSN 1550-8307, https://doi.org/10.1016/j.explore.2022.08.007.

Pendry, P., & Vandagriff, J. L. Animal Visitation Program (AVP) Reduces Cortisol Levels of University Students: A Randomized Controlled Trial. AERA Open, 5(2). 2019. https://doi-org.ezproxy.whitman.edu/10.1177/2332858419852592