RPubs link information

• RPubs link: https://rpubs.com/lekhanhtoan/1437073

Introduction

• Baby names can reflect social, cultural, and demographic patterns over time.
• This investigation uses open data from the U.S. Social Security Administration, accessed through Data.gov.
• The dataset records baby names from Social Security card applications.
• The focus of this analysis is California baby name popularity from 2000 to 2025.
• In this report, popularity means the number of babies given a specific name in a specific year and sex group.
• This question is interesting because name popularity is not evenly distributed: many names are uncommon, while a small number of names are very popular.

Problem Statement

• This investigation asks:

How does baby name popularity differ by sex in California from 2000 to 2025?

• To answer this question, this presentation will:
  • describe the data source and pre-processing steps;
  • summarise the main numerical and categorical variables;
  • visualise the distribution and yearly trends in name popularity;
  • test whether mean name popularity differs between female and male records;
  • test whether sex is associated with popularity category.

Data Source

• The data is open data from the U.S. Social Security Administration, accessed through Data.gov.
• Data.gov lists the access level as public and the licence as CC0 1.0 Public Domain.
• The full dataset contains baby name records by state, sex, year of birth, name, and number of babies.
• The sampling method is not random sampling. It is administrative data based on Social Security card applications.
• To keep the investigation manageable, this analysis only uses California records from 2000 to 2025.

baby_names_ca <- read_csv(
  "CA.TXT",
  col_names = c("state", "sex", "year", "name", "number"),
  show_col_types = FALSE
)

baby_names_ca <- baby_names_ca %>%
  filter(year >= 2000, year <= 2025)

head(baby_names_ca)

# Data Description and Pre-processing

Important variables:

- `state`: U.S. state abbreviation. This analysis uses California only.
- `sex`: sex recorded as `F` or `M`.
- `year`: year of birth.
- `name`: baby name.
- `number`: number of babies given that name in that year and sex group.

Pre-processing steps:

- Imported the California text file from the ZIP dataset.
- Added meaningful column names.
- Filtered the data to years 2000 to 2025.
- Converted `sex` into a labelled factor.
- Checked for missing values.
- Created a popularity category for the categorical association test.


``` r
baby_names_ca <- baby_names_ca %>%
  mutate(
    sex = factor(sex, levels = c("F", "M"), labels = c("Female", "Male")),
    popularity_category = case_when(
      number < quantile(number, 0.33, na.rm = TRUE) ~ "Low",
      number < quantile(number, 0.66, na.rm = TRUE) ~ "Medium",
      TRUE ~ "High"
    ),
    popularity_category = factor(popularity_category, levels = c("Low", "Medium", "High"))
  )

missing_table <- baby_names_ca %>%
  summarise(
    missing_state = sum(is.na(state)),
    missing_sex = sum(is.na(sex)),
    missing_year = sum(is.na(year)),
    missing_name = sum(is.na(name)),
    missing_number = sum(is.na(number))
  )

kable(missing_table)

Descriptive Statistics

• The main numerical variable is number.
• It measures how many babies were given a specific name in a specific year and sex group.
• Descriptive statistics summarise the centre, spread, and range of name popularity.

summary_table <- baby_names_ca %>%
  group_by(sex) %>%
  summarise(
    Min = min(number, na.rm = TRUE),
    Q1 = quantile(number, 0.25, na.rm = TRUE),
    Median = median(number, na.rm = TRUE),
    Mean = mean(number, na.rm = TRUE),
    Q3 = quantile(number, 0.75, na.rm = TRUE),
    Max = max(number, na.rm = TRUE),
    SD = sd(number, na.rm = TRUE),
    n = n(),
    Missing = sum(is.na(number)),
    .groups = "drop"
  )

kable(summary_table, digits = 2)

Descriptive Statistics Interpretation

• The mean number of babies per female name record is 52.38.
• The mean number of babies per male name record is 79.54.
• The median values are lower than the mean values for both groups.
• This suggests that the data is right-skewed: most names have relatively low counts, while a small number of names are very popular.
• The highest count for one name-year-sex record is 4344.

Visualisation 1: Distribution

ggplot(baby_names_ca, aes(x = number)) +
  geom_histogram(bins = 40) +
  labs(
    title = "Distribution of Baby Name Popularity in California, 2000-2025",
    x = "Number of babies with the name",
    y = "Frequency"
  )

• The histogram shows that the distribution is strongly right-skewed.
• Most name records have low counts.
• A small number of name records have much higher counts and may appear as outliers.

Visualisation 2: Sex Comparison

ggplot(baby_names_ca, aes(x = sex, y = number)) +
  geom_boxplot() +
  labs(
    title = "Baby Name Popularity by Sex in California, 2000-2025",
    x = "Sex",
    y = "Number of babies with the name"
  )

• The boxplot compares the distribution of name counts for female and male records.
• It shows the median, spread, and outliers for each sex group.
• Outliers are expected because some names are much more popular than most other names.

Visualisation 3: Yearly Trend

yearly_totals <- baby_names_ca %>%
  group_by(year, sex) %>%
  summarise(total_babies = sum(number, na.rm = TRUE), .groups = "drop")

ggplot(yearly_totals, aes(x = year, y = total_babies, colour = sex)) +
  geom_line() +
  labs(
    title = "Total Babies Recorded by Sex in California, 2000-2025",
    x = "Year",
    y = "Total number of babies",
    colour = "Sex"
  )

• This graph shows how the total number of babies recorded in the dataset changed over time.
• It also allows comparison between female and male records across years.

Task 5: Hypothesis Test and Confidence Interval

Research question:

Is the average baby name count different between female and male names in California from 2000 to 2025?

Hypotheses:

\[H_0: \mu_F = \mu_M\]

\[H_A: \mu_F \ne \mu_M\]

where:

• \(\mu_F\) is the mean number of babies per female name record.
• \(\mu_M\) is the mean number of babies per male name record.

Task 5: Assumptions

• The response variable number is numerical.
• The explanatory variable sex has two independent groups: Female and Male.
• Welch’s two-sample t-test is used because it does not require equal variances.
• The distribution is right-skewed, so the result should be interpreted carefully.
• The sample size is large, so the t-test is reasonably robust to non-normality.

t_test_result <- t.test(number ~ sex, data = baby_names_ca)
t_test_result

## 
##  Welch Two Sample t-test
## 
## data:  number by sex
## t = -25.176, df = 112769, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
## 95 percent confidence interval:
##  -29.27315 -25.04438
## sample estimates:
## mean in group Female   mean in group Male 
##             52.38224             79.54101

Task 5: Result Interpretation

• The p-value is less than 2.2 × 10^-16.
• The 95% confidence interval for the difference in means is from -29.27 to -25.04.
• At the 5% significance level, the p-value is less than 0.05, so H0 is rejected.
• This means there is statistically significant evidence that the mean baby name count differs between female and male records.
• The result should be understood as a difference in average count per name record, not a claim about every individual baby name.

Task 6: Categorical Association

Research question:

Is there an association between sex and popularity category?

Hypotheses:

\[H_0: \text{Sex and popularity category are independent.}\]

\[H_A: \text{Sex and popularity category are associated.}\]

• popularity_category was created from the number variable using approximate terciles.
• The categories are Low, Medium, and High popularity.

association_table <- table(baby_names_ca$sex, baby_names_ca$popularity_category)
association_table

##         
##            Low Medium  High
##   Female 31359  34895 35108
##   Male   22285  25025 26175

Task 6: Chi-square Test

chi_result <- chisq.test(association_table)
chi_result

## 
##  Pearson's Chi-squared test
## 
## data:  association_table
## X-squared = 18.663, df = 2, p-value = 8.86e-05

chi_result$expected

##         
##               Low   Medium     High
##   Female 31098.41 34736.72 35526.87
##   Male   22545.59 25183.28 25756.13

• The chi-square test checks whether sex and popularity category are independent.
• The expected counts are checked because the chi-square test requires expected cell counts to be sufficiently large.

Task 6: Result Interpretation

• The chi-square statistic is 18.66 with 2 degrees of freedom.
• The p-value is 8.86e-05.
• At the 5% significance level, the p-value is less than 0.05, so H0 is rejected.
• This means there is statistical evidence of an association between sex and popularity category.
• However, Cramer’s V is 0.01, which indicates that the association is very weak in practical strength.

Task 6: Association Plot

association_df <- baby_names_ca %>%
  count(sex, popularity_category) %>%
  group_by(sex) %>%
  mutate(percent = n / sum(n) * 100)

ggplot(association_df, aes(x = popularity_category, y = percent, fill = sex)) +
  geom_col(position = "dodge") +
  labs(
    title = "Popularity Category by Sex",
    x = "Popularity category",
    y = "Percentage of records",
    fill = "Sex"
  )

• This bar chart shows the percentage of records in each popularity category.
• It helps visually compare whether female and male names have similar or different popularity patterns.

Discussion

• This investigation found that baby name popularity in California from 2000 to 2025 is highly uneven.
• Most names appeared with low counts, while a smaller number of names were very popular.
• The descriptive statistics and histogram support this because the distribution is right-skewed.
• The hypothesis test found that there was statistically significant evidence of a difference in mean name count between female and male records.
• The chi-square test found that there was evidence of an association between sex and popularity category.

Strengths and Limitations

Strengths:

• The dataset is official, open, public, and clearly documented.
• It covers many years of data.
• It includes both numerical and categorical variables, making it suitable for descriptive statistics, hypothesis testing, and categorical association.

Limitations:

• The dataset only includes names with at least 5 occurrences, so very rare names are excluded.
• This analysis focuses only on California, so results may not represent the whole United States.
• The analysis shows statistical patterns but does not explain the cultural or social reasons why certain names became popular.
• Repeated yearly records mean observations are not completely independent in a real-world sense, so results should be interpreted as exploratory.

Final Conclusion

• The key take-home message is that baby name popularity in California is strongly uneven, with most names having low counts and a small number of names being highly popular. The analysis also found statistically significant sex-related differences, although the categorical association was very weak in practical strength.
• The results suggest that baby name popularity can be meaningfully analysed using numerical summaries, visualisations, a t-test, and a chi-square test.
• Overall, this dataset is suitable for the assignment because it is open, clearly documented, and supports the required statistical analyses.

References

• Social Security Administration. (2026). Baby Names from Social Security Card Applications - State and District of Columbia Data. Data.gov. https://catalog.data.gov/dataset/baby-names-from-social-security-card-applications-state-and-district-of-columbia-data
• Social Security Administration. (2026). State-specific baby names dataset. https://www.ssa.gov/oact/babynames/state/namesbystate.zip
• R Core Team. (2026). R: A language and environment for statistical computing. R Foundation for Statistical Computing.