1. Introduction and Data Collection Methods

This study investigates the potential intergenerational transmission of pet ownership. Specifically, this research seeks to determine if an individual’s likelihood of owning a pet as a young adult is associated with whether their parents kept pets during their childhood. The population parameter of interest is the difference in the proportion of young adults who own pets between two groups, those groups being those whose parents owned pets during their childhood and those whose parents did not. Alternatively, we can consider this as investigating the association between parental pet ownership and child’s pet ownership in the population of islanders.

A review of related literature suggests a connection between childhood experiences with pets and attitudes or behaviors towards pet ownership in adulthood. For instance, Serpell (1981) found that adult attitudes towards pets can be influenced by childhood experiences with them, indicating that individuals who owned pets as children may be more inclined to own pets as adults. Further research by Paul and Serpell (1993) supports this, demonstrating that higher levels of childhood pet keeping were related to more positive attitudes towards pet animals in young adulthood. Their study also found that childhood pet keeping was positively correlated with adult pet ownership levels. Specifically, subjects who reported more pets owned during childhood also expressed a greater desire to own pets in the future. These findings lead us to believe, before examining the island’s dataset, individuals whose parents owned pets would be more likely to own pets themselves as adults. Therefore, we might expect the proportion of pet owners to be higher among young adults whose parents were pet owners compared to those whose parents were not. However, due to the poor implementation of displaying pet ownership on the island’s website, as well as a lack of proper records of pet ownership on individual islander’s histories, leaves me with doubts about whether the engineers behind The Islands considered this real world trend when implementing pets. Conformation or dispelling of my suspicions will be left up to the data and analysis of it.

The observational units for this study were pairs of a parent and their adult child, selected from the citizens of the island city Kiyobico. Data collection involved identifying the first 100 randomly selected valid pairs from the online city directory. A pair was considered valid if it consisted of a living parent and their adult child (aged 18 or older) who had moved into their own residence. This criterion was established to allow for clear observation of independent pet ownership statuses for both the parent and the adult child.

The primary variable measured for each individual (parent and child) was their pet ownership status, recorded as “yes” or “no” based on information listed in the city directory. No further details about the pets, such as type or number, were collected. The data for each pair were organized into a spreadsheet, documenting the pet ownership status of the child in relation to their parent. All data were collected on a single day to maintain consistency and minimize potential confounding factors such as changes in household status or deaths.

During the data collection process, some initially identified pairs had to be excluded. This occurred because the parent was deceased, and The Islands offers no historical records of pet ownership. This exclusion represents a potential source of non-sampling error, as it might inadvertently omit a segment of the population whose characteristics could differ. The response rate is effectively 100% for the selected valid pairs, as the data was obtained from a directory rather than through direct contact requiring a response. The strict criteria for “valid pair” and the single-day data collection aimed to enhance internal consistency, but future studies might consider strategies for including cases with deceased parents, should the engineers behind The Islands choose to include pet ownership status in the islander’s personal histories, or expanding the geographical scope to improve generalizability across all islands.

2. Initial Analysis of Data

This code here will allow us to first load the data and then when run in r studio allows us to verify if it is being loaded correctly.

# We first load our cleaned collected data. If you are doing this on your home
# computer, make sure to replace this path with your own path to the data.

pets_data <- read_csv("C:/Users/Louis/Downloads/pet_ownership_100.csv", show_col_types = FALSE)

# Change the names of the raw column names to be consistent for later
# manipulation
colnames(pets_data) <- c("Child_Pet_Ownership", "Parent_Pet_Ownership")

# Convert columns to factors with more descriptive levels if desired, and
# ensuring 'Yes' is the first level for easier interpretation of proportions
# later.
pets_data$Child_Pet_Ownership <- factor(pets_data$Child_Pet_Ownership, levels = c("Yes",
    "No"))
pets_data$Parent_Pet_Ownership <- factor(pets_data$Parent_Pet_Ownership, levels = c("Yes",
    "No"))

# Display the first few rows and summary of the data to confirm it's being
# loaded correctly
print(head(pets_data))
print(summary(pets_data))
print(str(pets_data))
# Now that the data is loaded, we'll create a table to see the relationship
# between child and parent pet ownership.
ownership_table <- tally(~Child_Pet_Ownership + Parent_Pet_Ownership, data = pets_data)
print("Raw counts of pet ownership combinations (Child vs. Parent):")
print(ownership_table)

# To better understand the influence, we calculate conditional proportions,
# specifically, what's the proportion of children owning pets, given that their
# parents did or did not own pets?  Margin = 2 calculates proportions down the
# columns (i.e., conditioned on Parent_Pet_Ownership).
child_given_parent_props <- prop.table(ownership_table, margin = 2)
print("Proportion of Children Owning Pets, given Parent's Pet Ownership:")
print(child_given_parent_props)
#To create a visual summary explore we'll first summarize the data into a contingency table.
pet_table <- table(pets_data$Parent_Pet_Ownership, pets_data$Child_Pet_Ownership)

# Now, we can create a mosaic plot from this table.
mosaicplot(pet_table,
           main = "Pet Ownership: Child vs. Parent",
           xlab = "Parent Pet Ownership",
           ylab = "Child Pet Ownership",
           color = c("skyblue", "lightcoral"))

The mosaic plot visually represents the counts and conditional proportions derived from our data. The width of the bars in such a plot corresponds to the marginal proportion of the x-axis variable (Parent Pet Ownership), and the height of the segments within each bar indicates the conditional proportion of the y-axis variable (Child Pet Ownership). A noticeable difference in the distribution of colors (representing child pet ownership) between the “Parent: Yes” and “Parent: No” columns would suggest a strong association.

We see that approximately 54.2% of children whose parents owned pets also own pets themselves. In contrast, approximately 55.8% of children whose parents did not own pets own pets. These proportions are quite similar, with a slightly higher percentage of pet ownership among children whose parents were not pet owners. This visual and numerical inspection suggests there might not be a strong association, or the association might be contrary to what some literature suggests (which often implies a positive link between parental pet ownership and a child’s likelihood to own pets).

3. Hypothesis

Given these initial observations, we aim to determine if there is a statistically significant association between parents’ pet ownership status and their adult children’s pet ownership status among the islanders sampled.

The population of interest consists of adult islanders from Kiyobico. We are comparing two groups within this population: adult islanders whose parents owned pets during their childhood, and adult islanders whose parents did not own pets during their childhood. The parameter of interest is the difference in proportions, \(p_1 - p_2\), where: * \(p_1\) = the true proportion of adult islanders from this population who own pets, whose parents owned pets during their childhood. * \(p_2\) = the true proportion of adult islanders from this population who own pets, whose parents did not own pets during their childhood. Alternatively, this can be framed as testing for the independence of parental and child pet ownership.

In terms of proportions: * Null Hypothesis (\(H_0\)): \(p_1 = p_2\) (The proportion of adult islanders who own pets is the same regardless of whether their parents owned pets. Equivalently, \(p_1 - p_2 = 0\).) * Alternative Hypothesis (\(H_a\)): \(p_1 \neq p_2\) (The proportion of adult islanders who own pets is different depending on whether their parents owned pets. Equivalently, \(p_1 - p_2 \neq 0\).)

Initially, based off of real world experiments, we would expect \(p_1 > p_2\). However, our descriptive statistics showed \(p_1 = 0.542\) (children of pet-owning parents) and \(p_2 \approx 0.558\) (children of non-pet-owning parents) in the sample. Given this observed direction in our sample (where \(p_1 < p_2\) slightly), additionally, a two-sided alternative hypothesis (\(H_a: p_1 \neq p_2\)) is the most appropriate approach, as it allows for a difference in either direction.

In terms of association: Null Hypothesis (\(H_0\)): There is no association between parental pet ownership and adult child’s pet ownership in the population of islanders. (Pet ownership of child and parent are independent). Alternative Hypothesis (\(H_a\)): There is an association between parental pet ownership and adult child’s pet ownership in the population of islanders. (Pet ownership of child and parent are dependent).

It is important to identify Type I and Type II errors and what they would mean in the context of this study.

Type I Error: We would conclude that there is an association between parental pet ownership and an adult child’s pet ownership (or that the proportions \(p_1\) and \(p_2\) are different), when, in reality, no such association or difference exists in the population. This means claiming a relationship that isn’t actually there. Type II Error: We would fail to conclude that there is an association between parental pet ownership and an adult child’s pet ownership (or that the proportions \(p_1\) and \(p_2\) are different), when, in reality, such an association or difference does exist in the population. This means missing a real relationship.

4. Theory-Based Analysis

To test our hypothesis, we will use a Chi-squared (\(\chi^2\)) test for independence. This test is suitable for determining if there’s a statistically significant association between two categorical variables like parent and child pet ownership.

The standardized statistic for this test is the Chi-squared (\(\chi^2\)) value. For this test to be reliable, certain conditions should be met:

  1. The data should consist of counts from a random sample or a randomized experiment.
  2. All expected cell counts in the contingency table should be at least 5.

We will check these using the output from our R code. We will primarily focus on the uncorrected Chi-squared test.

# Uncorrected test
chi_test_uncorrected <- chisq.test(ownership_table, correct = FALSE)
print("--- Pearson's Chi-squared test (NO Yates' correction) ---")
print(chi_test_uncorrected)

# Default corrected test
chi_test_corrected <- chisq.test(ownership_table)
print("--- Pearson's Chi-squared test (WITH Yates' correction - R Default) ---")
print(chi_test_corrected)

# Summary of key results
cat("\n--- Key Results Summary ---\n")
cat(paste("Uncorrected Chi-squared Test: X-squared =",
          round(chi_test_uncorrected$statistic, 4),
          ", df =", chi_test_uncorrected$parameter,
          ", p-value =", round(chi_test_uncorrected$p.value, 4), "\n"))
cat(paste("Corrected Chi-squared Test (Yates'): X-squared =",
          round(chi_test_corrected$statistic, 4),
          ", df =", chi_test_corrected$parameter,
          ", p-value =", round(chi_test_corrected$p.value, 4), "\n"))

cat("\nExpected Cell Counts (these apply to both tests):\n")
print(round(chi_test_uncorrected$expected, 2))

Our R code output gives us the followng output:

All expected counts are above 5, so the validity condition is satisfied. The uncorrected Chi-squared statistic (\(\chi^2\)) is 0.0259. The p-value from the uncorrected test is 0.8721 which means that, if \(H_0\) is true (no association), the probability of observing a \(\chi^2\) statistic of 0.0259 or more extreme is approximately 0.8721. Since the p-value (0.8721) is greater than \(0.05\), we fail to reject the null hypothesis (\(H_0\)). This indictes that there is not sufficient evidence to conclude an association between parental pet ownership and adult child pet ownership among islanders in Kiyobico.

To estimate the plausible range for the difference in proportions:

From the sample:
\(p_1 \approx 26/48 =0.5417\)
\(p_2 \approx 29/52 = 0.5577\)

Now we can calculate the confidence intervals using R code.

successes_counts <- c(26, 29)
total_counts <- c(48, 52)
ci_diff_props_test <- prop.test(x = successes_counts, n = total_counts, correct = FALSE)
print(ci_diff_props_test)

This yields a 95% confidence interval of (-0.211, 0.179) for \(p_1 - p_2\) indicating that we are 95% confident the true difference between \(p_1\) and \(p_2\) lies between -0.2113 and 0.1792. Since this includes 0, it supports the null hypothesis and suggests no statistically significant difference. This aligns with the result of our hypothesis test and indicates that, within this sample, there’s no clear evidence that parental pet ownership influences adult pet ownership.

5. Conclusion

This study examined whether adult pet ownership is associated with childhood exposure to parental pets among islanders in Kiyobico.

In a sample of 100 individuals: - 54.2% of children whose parents owned pets also owned pets. - 55.8% of children whose parents did not own pets also owned pets.

Contrary to initial expectations, the sample showed a slightly higher rate among those whose parents did not own pets. A Chi-squared test gave a p-value of 0.8721, indicating no statistically significant association. A 95% confidence interval for \(p_1 - p_2\) was (-0.2113, 0.1792), also suggesting no significant difference. While literature often reports a positive correlation between childhood pet exposure and later ownership, our results did not replicate that. It’s possible that other unmeasured factors (type of pet, quality of relationship, socioeconomic variables) play a stronger role. Future research with a broader, more diverse sample and more nuanced data collection (like, pet type, ownership duration) could explore further patterns. Due to the following factors, however, this study seems to add no value to furter understanding The Islands. Firstly, it seems likely that pets and pet ownership on the islands is chosen arbitrarily and there seems to be no explicitly defined connections between pet ownership and any other statistics you can take from the Islanders. Secondly, and this is a major flaw with this study, there is no way to determine whether or not the adults pet was present during their child’s life and I therefore had to assume that they were present during their childhood. For further, I would recommend gathering data on pet status across an entire year to properly understand what the code behind The Islands is actually doing here. Ultimately I would not recommend anyone repeat this study.

6. Bibliography

Paul, E. S., & Serpell, J. A. (1993). Childhood pet keeping and humane attitudes in young adulthood. Animal Welfare, 2(4), 321–337. https://doi.org/10.1017/S0962728600016109

Serpell, J. A. (1981). Childhood pets and their influence on adults’ attitudes. Psychological Reports, 49(2), 651–654. https://doi.org/10.2466/pr0.1981.49.2.651