library(readr)
MiniProject3 <- read_csv("Mini Project 3 Data - Sheet1 (1).csv")

By analyzing the question “Do pet and non pet owners differ in levels of anxiety?” this study focused on animals and how or if they effect a person’s level of anxiety. To answer this question the study looked at the mean difference between the average level of stress among adult pet owners and the average level of stress among adult non-pet owners. In other words the parameter of interest looked at through this study is \(\mu_{non-pet owners} - \mu_{pet owners}\) or if the anxiety people feel is affected by owning an animal. A previous study was done on the relationship between owning a pet and how that was related to anxiety and depression symptoms in people. This study limited its participants to older aged adults, 70 years old to 91 years old. They found through this study that owning a pet later on in your life reduced the feelings of anxiety and depression an person feels on average compared to non pet owning individuals (Bolstad, Courtney J et al). I wanted to expand off of this study and did so by including a wider range of ages, 18 years old to 91 years old. I also focused the study on anxiety and did not look at depression symptoms among participants. Based on this previous study and general information I know about how pets are used for therapy I suspected that there would be a difference between the mean of pet owning individuals’ anxiety and the mean of non-pet owning individuals’ anxiety. I suspected that individuals without a pet would have higher levels of anxiety than individuals with a pet.

For my observational study the observational units were the people participating. Each variable was measured through a survey or questionnaire. The survey consisted of one question: “Do you own a pet?” which the participants answered yes or no to. The questionnaire consisted of another question: “On a scale from 1-10, how anxious are you right now?” which the participants would answer with a number 1-10. When acquiring participants random sampling was implemented as much as possible. Participants were spread across multiple islands and towns with no two participants from the same household or town to make sure that each participant was independent of each other. Each island and town was visited as well as scientific stations to obtain participates. In each town a house was randomly chosen by closing ones eyes, scrolling and picking at random. This was done over and over until 20 participants with a pet and 20 participants without a pet had their level of anxiety recorded. The participants covered a wide range of ages, gender, and jobs. The interviewer only had to visit each participant once to obtain the necessary data. This process of gaining participants led to as much random sampling as was possible with actually using a randomization tool. I had no trouble finding participants for my study. Very few people rejected to participate in the observational study and nothing went wrong while conducting the study.

The first variable that I tested in this observational study was if a participant owned a pet or not. This was a binary categorical variable measured on a yes or no basis. This was also the explanatory variable in the study. The second variable that I measured was the level of anxiety an individual was feeling right at that moment. This was a quantitative response that participant answered on a scale from 1 to 10 and the response variable in the study. The data from the two variables is:

data(MiniProject3)
favstats(Anxiety ~ Pet, data = MiniProject3)

The mean of the pet owning individuals was 4.100 and the mean of the non-pet owning individuals was 4.125. These means are very close together and both groups have a median of 4. The standard deviations of pet owning individuals is 1.804 and the standard deviation of non-pet owning individuals is 1.326. This tells us that there is very little variation between either of the groups. Another way to analyze the data from the two groups is to look at a side-by-side box plot:

bwplot(Anxiety ~ Pet, 
       horizontal = FALSE, 
       main="Side-by-side boxplots",
       data = MiniProject3)

The side-by-side box plot made is very symmetric with a lot of overlap between pet and non-pet owning anxiety levels. This tells us that there is little association between the two variables and helps visualize that the two groups do not have a lot of difference in their data.

The population that these results are related to are the adults on the islands. The parameter of interest that this study deals with is if the mean difference between the average level of stress among adult pet owners and non-pet owners is the same or different. My null hypothesis in this study to test this parameter and population is: \[H_0: \mu_{non-pet owner} = \mu_{pet owner}\]In words that means that there is no association between the level of stress an individual feels and whether or not they own an animal. My alternative hypothesis on the other hand for this study is: \[H_A: \mu_{non-pet owners} \neq \mu_{pet owners}\]In words that means that there is an association between the level of stress an individual feels and whether or not they own an animal. If a type I error, rejecting the null hypothesis without there actually being a significant difference between the groups, was made then there would be false information out about how pets relate to a person’s stress. A type I error would be stating that owning an animal has a significant effect on your anxiety when in reality it does not have any significant effect. If a type II error, failing to reject the null hypothesis when there is sufficient data to support a difference between two groups, was made it would also result in false information being given to the public about the relation between anxiety and pets. A type II error in regards to this study would be stating that owning or not owning a pet has no effect on the level of anxiety you feel when there was sufficient data to prove that your level of anxiety is affected by having a pet in the household. In the process of conducting this study the validity conditions were met for the sample to me a reasonable representation for the adults on the islands. There were 40 individuals that were randomly selected to participate in the study with 20 being pet owners and 20 non-pet owners. Having a bigger sample size would make it an even better representative sample but they are still reasonably the way they are.

I used a theory-based approach to calculate the necessary information to prove if the null hypothesis needed to be rejected or not. I ran a t-statistic:

stat(t.test(Anxiety ~ Pet, data = MiniProject3))
##          t 
## 0.04993762

and found that t = 0.0499. This t-statistic is very low telling us that there is little to no evidence against the null hypothesis. The validity conditions to conduct the t-statistic were met because there were at least 20 individuals in each group in the study and the sample distributions were not strongly skewed, small standard deviations. I calculated the two-sided p-value for the study:

two.sided.p.value<-pval(t.test(Anxiety ~ Pet, data = MiniProject3))
cat("the two-sided p-value is",two.sided.p.value)
## the two-sided p-value is 0.9604568

and found that the two-sided p-value = 0.960. This p-value is high and gives little to no evidence against the null hypothesis. Based off of the t-statistic and two-sided p-value I fail to reject the null hypothesis in this study believe that there is no association between the level of anxiety an individual feels and whether or not they own an animal. Lastly I calculated the confidence interval of the data:

confint(t.test(Anxiety ~ Pet, data = MiniProject3))

and found that the lower limit of the confidence interval is -0.991 and the upper limit is 1.04. This confidence interval tells me that we are 95% confident that the difference between the mean level of anxiety for non-pet owners and the mean level of anxiety for pet owners is between -0.991 and 1.041. This confidence interval contains zero implying that a difference of zero between the two means of pet and no pet is plausible. This is in line with my previous conclusions that I would fail to reject the null hypothesis and that there is no sufficient evidence to support the alternative hypothesis.

This observational study dealing with animals and the level of anxiety of individuals found that there is no association between the level of stress an individual feels and whether or not they own an animal. I failed to reject my null hypothesis from the data found in the study. With a t-statistic of 0.0499 and a two-sided p-value of 0.960 they both prove that there is little to no evidence against the null hypothesis and support the conclusion of this study. My data in this study went against how I thought it would behave and contradicted my original hypothesis that there would be a difference in means between pet owning individuals and non-pet owning individuals anxiety level with individuals without a pet would having higher levels of anxiety than individuals with a pet. I believe that it is reasonable to generalize my sample to all adults on the islands but nothing beyond that because random sampling was used as much as possible and a wide range of ages, genders, and jobs were represented in the sample of test subjects. I would not say that there is direct causation between owning a pet and your level of anxiety because this was only an observational study and additional testing would need to be down to find if there is causation between the two variables. The level of anxiety in my study was self-reported so in future studies it would make more sense to find a more objective way to report the anxiety of an individual. It would also make sense to record the anxiety of subjects multiple times over a long period of time instead of just once like in this study. To build off of this study and research question future studies could look at if specific animals lead to different levels of stress or if pets have a larger effect on stress in certain age groups of people.

Bolstad, Courtney J et al. “The Relation Between Pet Ownership, Anxiety, and Depressive Symptoms in Late Life: Propensity Score Matched Analyses.” Anthrozoos vol. 34,5 (2021): 671-684. doi:10.1080/08927936.2021.1926707