The research question is ‘How do interactions with animals affect human mental well-being’. Base on this question, the population parameter is the mean difference in mental well-being scores between individuals who regularly interact with animals and those who do not. Inspiration is coming from the book “Animals and human society: changing perspectives”, by Aubrey Manning and James Serpell. In chapter 7 and 8, it discussed how animals are being used as an entertainment and it was unusual for people to have any emotional connections with them in the early centuries. From the sociologist’s perspective, human gives love to animals but kill them at the same time. The question that the sociologist came up was how does the society deal with balancing these two conflicts. And these led to my research question of “How do interactions with animals affect human mental well-being”. The initial conjecture is that interaction with animals would lead to an improvement in mental well-being and the actual parameter value might be higher than the conjectured value.

The observational units are the individual participants. The two variables are being measured are the response variable – mental well-being; and the independent variable – animal interaction, they are all categorical variables. During this study, nothing went wrong, everything goes smoothly. Random number generator are being used in this case to select participants randomly. The standard of measuring mental well-being is through participants mood scales, anxiety inventories and overall life satisfaction measurements. And animals interactions is participants’ frequency of their interactions with animals. The questions given to the participants are do you interact with animals, and do you think interactions with animals has improve your mental well-being? Some of the sampling errors might be selection bias in which the sample isn’t representative of the general population and non-response bias in which the response rate is low or if certain types of individuals are less likely to respond. And if other variables that affect both the likelihood of an individual interacting with animals and their mental well-being or the method being used is not accurate or reliable, these could be the Non-Sampling Errors.

Interaction with animals Improved well-being Not Improved well-being Total
Yes 25 10 35
No 10 5 15
Total 35 15 50 
interaction <- c("Yes", "No")
improved <- c(25, 10)
not_improved <- c(10, 5)

data_matrix <- rbind(improved, not_improved)

bar_colors <- c("orange", "red")


barplot(data_matrix, beside = TRUE, col = bar_colors,
        main = "Impact of Interaction with Animals on Well-being",
        xlab = "Interaction with Animals", ylab = "Number of Responses",
        names.arg = interaction, legend = c("Improved", "Not Improved"))

Based on the table and the side by side bar graph, it seems like they have a little association between these two variables. The population is the individual participants and the parameter are the type and frequency of interactions with animals.

The null hypotheses is the interaction with animals does not affect mental well-being.

H0: pi1=pi2

The alternative hypotheses is the interaction with animals affects mental well-being.

Ha: pi1=/pi2

In this setting, type I error would be incorrectly reject the null hypothesis, which means falsely asserting that animal interactions improve mental well-being. Type II error occurs when the research concludes that interactions with animals do not significantly improve human mental well-being when, in reality, there is a true effect. A representative sample would involve random selection from the entire population of interest, adequate sample size and diversity in participants that reflects the population. So in this case, it is a representative sample of the populations of interest since it meet all the factors.

interaction_with_animals <- matrix(c(25, 10, 10, 5), nrow = 2, byrow = TRUE,
                                   dimnames = list("Interaction with Animals" = c("Yes", "No"),
                                                   "Mental Well-being" = c("Improved", "Not Improved")))

chi_square_test <- chisq.test(interaction_with_animals)

chi_square_test
## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  interaction_with_animals
## X-squared = 0, df = 1, p-value = 1
data <- matrix(c(25, 10, 10, 5), nrow = 2, byrow = TRUE,
               dimnames = list("Interaction with Animals" = c("Yes", "No"),
                               "Mental Well-being" = c("Improved", "Not Improved")))

sample_mean_yes <- mean(c(25, 10)) 
sample_mean_no <- mean(c(10, 5))  

total_counts <- c(25, 10, 10, 5)
sample_mean_overall <- mean(total_counts)

population_mean <- mean(total_counts)

population_sd <- sd(total_counts)

list(
  sample_mean_yes = sample_mean_yes,
  sample_mean_no = sample_mean_no,
  sample_mean_overall = sample_mean_overall,
  population_mean = population_mean,
  population_sd = population_sd
)
## $sample_mean_yes
## [1] 17.5
## 
## $sample_mean_no
## [1] 7.5
## 
## $sample_mean_overall
## [1] 12.5
## 
## $population_mean
## [1] 12.5
## 
## $population_sd
## [1] 8.660254

An appropriate test statistic would be the two proportion z-test in this scenario, because it is designed to compare the proportions of two independent groups. In this case, we are comparing the proportion of individuals with improved well-being between those who interact with animals and those who do not.The Z-test allows us to determine if the observed difference in proportions is statistically significant, and helps to quantify the difference between the groups and provides a standardized way to evaluate the hypothesis.

x1 <- 25 
n1 <- 35 
x2 <- 10
n2 <- 15 

p1 <- x1 / n1
p2 <- x2 / n2

p_pool <- (x1 + x2) / (n1 + n2)

SE <- sqrt(p_pool * (1 - p_pool) * (1/n1 + 1/n2))

z <- (p1 - p2) / SE

p_value <- 2 * pnorm(-abs(z))

list(z_statistic = z, p_value = p_value)
## $z_statistic
## [1] 0.3367175
## 
## $p_value
## [1] 0.7363299

Based on the code above, we can tell that the p-value is 0.7363299. This value is much greater than 0.05, which means that we do not have enough evidence to reject the null hypothesis, and there is no statistically significant evidence to suggest that interaction with animals has an effect on mental well-being. We can conclude that the data does not provide sufficient evidence to claim that animal interaction has a significant impact on mental well-being.

p1 <- x1 / n1
p2 <- x2 / n2

diff_p <- p1 - p2

SE <- sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

z_value <- qnorm(0.975)

lower_bound <- diff_p - z_value * SE
upper_bound <- diff_p + z_value * SE

list(lower_bound = lower_bound, upper_bound = upper_bound)
## $lower_bound
## [1] -0.2340007
## 
## $upper_bound
## [1] 0.3292388

The confidence interval is -0.2340007 to 0.3292388. This is the plausible range of values for the difference in proportions of improved mental well-being between the two groups. The lower bound represent that at worst, the proportion of improved well-being could be 23.40007% lower in the “Yes” group compared to the “No” group.The upper bound suggests that, at best, the proportion of improved well-being could be 32.92388% higher in the “Yes” group compared to the “No” group. The interval includes zero, infer that there is a possibility that there is no difference between the two groups. For this section, we can conclude that we are 95% confidence interval for the difference in proportions ranges from -0.2340007 to 0.3292388, which represent that the effect of interacting with animals on improved well-being is not definitively positive or higher based on the data. Compare to the previews conclusion, both conclusions shows that there is no significant evidence of an effect of animal interaction on mental well-being.

As stated before, we can conclude that animal interaction would not improve on human mental well-being. From this observational research, I learned that small sample size can lead to a lack of statistical power, making it harder to detect a true effect if one exists. The final result didn’t went as I expected. I expected that with more interaction with animals, it can help people to improve on their mental well-being. According to my own experiences, I feel my mental well-being improved a lot after had some interaction with animal.

For this research, it would be reasonable to generalize the sample to the larger population for a more accurate result. And for next time, I would divide the sample into few categories base on their age and gender, and their stress level. Also, add in the observations of the longer-term effects of animal interaction. One similar question that someone might choose to investigate in the future is “How do cultural or environmental contexts influence the effects of animal interactions on mental well-being.

Manning, Aubrey, & Serpell, J. (1994). Animals and human society: changing perspectives, (https://sherlock.whitman.edu/permalink/01ALLIANCE_WHITC/1aivab7/alma9915750801867)