Introduction

The goal of the research is to determine the effect of pet companionship on the level of energy experienced by individuals. Therefore, the research question that we want to work on is “Does pet companionship affect the level of energy experienced by individuals?”. The population parameter of interest is the difference in mean of the energy level of islanders in the Nelson Island. While working on the research and from the general beliefs from people, it is believed that having a pet create a better health benefits. One of the existing research provides an overview of the potential health benefits of owing a pet, particularly the relationship between domestic dogs and human health. Interactions with animals may provide optimistic effects on physical and emotional wellness. This aligns with the hypothesis that pet friendship could impact energy levels (Wells 2007). Moreover, human companions and pet canines in adjusting autonomic reactions to stress in ladies. It gives understanding into the potential pressure easing impacts of both human and creature fellowship, which could be applicable to comprehending the relationship between pet fellowship and energy levels (Allen 1991). Before seeing any data, I suspect that individuals with pet companionship have higher mean of energy level. However, I am not fully confident about the magnitude of this effect before seeing data since previous study is about having a pet and this research is more about testing the effect on exposure to pet during the short term period rather than having a pet.

Data Collection Methods

The observational units of the study are 120 islanders from Nelson Island who give consent to participate in the study. The variables are pet companionship which is a binary categorical variable and level of energy which is quantitative variable. To measure pet companionship, we create treatment and control groups. Participants in the treatment group are assigned to sit with a dog for 10 minutes, while participants in the control group do not sit with any pet. This binary variable is measured by observing whether the individual is assigned to the treatment group (1) or control group (0). To measure the level of energy, we use a quantitative scale from 1 to 10. After sitting with a pet or not assign to sit with any pet, participants rate how energetic they feel right now, with 1 being very low energy and 10 being very high energy. This continuous variable captures the subjective experience of energy levels.

For reporting data, I tried to create the random sample and follow strictly to it as much as I can. By using random number generator, I choose a random island and run a number and then come to the house, if there are more than two people, I will randomize once more time to choose the person. However, something that makes it hard for the study is that some individuals may choose not to participate in the study, leading to the potential non-response bias if those who decline to participate differ systematically from those who agree to participate. Moreover, the study’s findings may not generalize to other populations or setting beyond the islanders included in the study since the sample size solely come from Nelson island. There are also might be errors in the measurement of variables, such as participants inaccurately reporting their level of energy or misinterpreting the instructions for the study. Due to the random nature of sampling, there is sampling error, meaning that the characteristics of the sample may differ slightly from those of the population.

Descriptive Statistics

library(readr)
Report_Final <-
  read_csv("~/Math 247 Mini Project/PetandEnergy - Sheet1 (1).csv")
head(Report_Final, n=2)
## # A tibble: 2 × 3
##   `First Name` `Pet companionship` `Level energy`
##   <chr>                      <dbl>          <dbl>
## 1 Gabrielle                      1           10  
## 2 Geraldine                      0            4.5
bwplot(as.factor(Report_Final$`Pet companionship`) ~ Report_Final$`Level energy`, 
       horizontal = TRUE, 
       main="Side-by-side boxplots",
       data = Report_Final)

library(readr)
Final_Project <-
  read_csv("~/Math 247 Mini Project/PetandEnergy - Sheet9.csv")
head(Final_Project, n=2)
## # A tibble: 2 × 2
##   `Pet companionship` `Level energy`
##                 <dbl>          <dbl>
## 1                   1           10  
## 2                   0            4.5
favstats(`Level energy` ~ `Pet companionship`, data = Final_Project)
##   Pet companionship min Q1 median     Q3  max     mean        sd  n missing
## 1                 0   4  5      6  6.625  9.5 5.950000 1.1921352 60       0
## 2                 1   9 10     10 10.000 10.0 9.841667 0.3120689 60       0

For my research, pet companionship is the binary categorical explanatory variable and the level of energy is the quantitative response variable. Therefore, I used a side-by-side boxplot. As we can see from the boxplot, the difference in mean are visible and since the without pet are right skewed, the boxplot for the with pet show the left skewed. To be more specific, the mean for those without pet companionship is around 5.95 and the mean for those with pet companionship is around 9.84. We can see that there is association between the pet companionship and the level of energy.

Analysis of Results

The population of the study is the islanders in the Nelson Island the the parameter of interest that I want to study is the difference in mean of pet companionship on human level of energy.

The null hypothesis: There is no difference in the mean energy levels between individuals with pet companionship and those without. \[H_0:\mu_{withpet}-\mu_{withoutpet}=0\] The alternative hypothesis: Individuals with pet companionship have higher mean energy levels than those without. \[H_0:\mu_{withpet}-\mu_{withoutpet}>0\]

In this case, the type I and type II error might appear in difference ways. Type I error would represent when the data lead to reject the null hypothesis that there is no difference in the mean energy levels between individuals with pet companionship and those without. In this setting, a type I error might appear when I incorrectly conclude that there is a significant effect of pet companionship on level of energy when in reality, there is no effect on pet companionship influence the level of energy. It is a false alarm in this situation. Type II error would represent when the data do not lead to reject the null hypothesis that there is no difference in the mean energy levels between individuals with pet companionship and those without. In this setting, a type II error might appear when I do not reject the null hypothesis when the null hypothesis is actually false. It is a missed opportunity in this situation.

Before seeing the numerical value, the discussion about the measurements in this research will evaluate if the sample is a representative from the populations of interest or not. Firstly, considering the sampling methodology, I tried my best to use the random sampling method. To be more specific, I use the random number generator to choose the house, after that, I come to the house and if there are more than 2 people, I will randomize once more time to choose the person and ask for consent. However, the populations just represent the people who give consent to participate to the study, which might create the bias since it might be different with the people who are not choose to not be in the study. Moreover, as I have mentioned, even though I try to create the representativeness of the sample, I just collected the data from Nelson Island which might have some confounding variables that are not take into account. In terms of the sample size, with 120 observational units, it is adequate to capture the variability and diversity within the population. However, larger sample sizes with diversity still needed to provide more representative estimate of population parameters. In general, my measurements in this research can consider as representative for the populations of interest. However, more data should be collected from islanders from different islands as well as keep trach of the number of getting refusal from islanders in participating in the research.

Theory-based approach

The appropriate standardized statistic for my research is the t standardized statistic. Since we are comparing means between two independent groups (with and without pet companionship), and whether there is a difference in mean energy levels between these two groups, a t standardized statistic which measures the difference in means between the two groups relative to the variability within each group is appropriate.

Checking on the validity condition, since participants were randomly assigned to treatment and control groups, we can say that independence of observations is met. Each observation (participant’s energy level) is independent of the others. Moreover, the observation units are 120, which is 60 in each group (greater than 20), which qualify the validity condition for using the t-test. Moreover, even though the treatment group (individuals with pet) distribution is left skewed and the control group (individuals without pet) distribution is right skewed, it is not strongly skewed so the validity condition here is met. For the population variances of energy levels for individuals with and without pet companionship, it is not equal but the sample sizes are large enough for the t-test to run here. Overall, the validity condition is met for the t-test.

histogram(~`Level energy` | `Pet companionship`, data = Final_Project, width = 1, layout = c(1, 2))

Finding the standardized statistic t:

stat(t.test(`Level energy` ~ `Pet companionship`, data = Final_Project))
##         t 
## -24.46208

The standardized statistic t is -24.46208.

two.sided.p.value<-pval(t.test(`Level energy` ~ `Pet companionship`, data = Final_Project))
one.sided.p.value<-two.sided.p.value/2
cat("the one-sided p-value is", one.sided.p.value)
## the one-sided p-value is 1.968934e-35

The p-value corresponding to the alternative hypothesis is the right-tailed p-value which is 1.968934e-35. The p-value of observing a difference in mean energy levels as extreme as or more extreme than what was observed, assuming that there is truly a higher mean energy level among individuals with pet companionship compared to those without. This extremely small p-value (close to 0) leads us to strong evidence reject the null hypothesis in favor of the alternative hypothesis. In the context of the problem, this indicates that there is significant evidence to support the alternative hypothesis, we conclude that individuals with pet companionship indeed have significantly higher mean energy levels than those without. Thus, pet companionship appears to positively influence the energy levels of individuals on Nelson Island.

Confidence Interval

#sample sizes
n.withpet<- 60
n.nopet<- 60

x.bar.withpet<- 9.841667
x.bar.nopet<- 5.950000
  
SD.withpet<- 0.3120689
SD.nopet<- 1.1921352
  
# difference between the sample proportions of with pet and no pet
x.bar.diff<-x.bar.nopet-x.bar.withpet

#standard error of the difference in sample means
SE.x.bar.diff<-sqrt(SD.nopet^2/n.nopet + SD.withpet^2/n.withpet)

# margin of error for 95% CI
MoE <- 2 * SE.x.bar.diff

LB<-x.bar.diff - MoE # lower limit of 95% CI
UB<-x.bar.diff + MoE # upper limit of 95% CI
round(cbind(LB,UB),3)
##         LB     UB
## [1,] -4.21 -3.573

The confidence interval is (-4.21, -3.573). In the context of the problem, we are 95% confident that the difference in mean energy levels between individuals with pet companionship and those without pet companionship is between -4.21 to -3.573. Since the confidence interval does not include zero, it suggests that the difference in mean energy levels is statistically significant. This aligns with the conclusion we have from conclusion by using p-value, where we rejected the null hypothesis and found evidence to support the alternative hypothesis that individuals with pet companionship have higher mean energy levels than those without.

Conclusion

In this study, we investigated the impact of pet companionship on the energy levels of individuals on Nelson Island. Our research question centered around whether individuals with pet companionship experience higher levels of energy compared to those without by using the difference in mean of individuals with pet companionship and those without pet companionship. Before analyzing the data, we hypothesized that individuals with pet companionship would indeed exhibit higher mean energy levels. The data behave as I expected. We conducted hypothesis testing using a t-test for independent samples. The corresponding p-value of 1.968934e-35 provided strong evidence against the null hypothesis, leading us to reject it in favor of the alternative hypothesis. This suggests a significant difference in energy levels between individuals with and without pet companionship. Additionally, we constructed a 95% confidence interval for the difference in mean energy levels. With the confidence interval of (-4.21,-3.573), which is not included 0, further supported our conclusion.

While our study provides strong evidence about the relationship between pet companionship and energy levels, there is limitations in the study. The sample, consisting solely of Nelson Island residents, may not fully represent broader populations. Therefore, the generalization is suitable for Nelson Island but we need further study for broader population. Moreover, since the study is the answer from participants who give consent to the study, there might be non response bias potential if those who decline to participate differ systematically from those who agree to participate. There are also might be errors in the measurement of variables, such as participants inaccurately reporting their level of energy or misinterpreting the instructions for the study.

In the future studies, I would using the random sampling method to collect data from different islands and also explore additional variables could enrich our understanding of the relationship between pet companionship and energy levels. With that perspective, in the future studies, researchers might explore additional factors influencing energy levels, such as the type of pet or duration of pet interaction. Additionally, considering diverse populations and employing more robust sampling methods would strengthen the external validity of research findings.

Bibliography: references to literature mentioned in the introduction

  1. Deborah L Wells, Domestic Dogs and Human Health: An Overview, British Journal of Health Psychology, Volume 12, Number 1, 2007, Pages 145-156, (https://doi.org/10.1348/135910706X103284.)

  2. Karen M. Allen, et al, Presence of Human Friends and Pet Dogs as Moderators of Autonomic Responses to Stress in Women, Journal of Personality and Social Psychology, Volume 61, Number 4, 1991, pp. 582-589, (https://doi.org/10.1037/0022-3514.61.4.582.)

  3. Rpubs link: https://rpubs.com/soltran/1181829