stac33_a5
Jinminli-1008264361
2025-03-27
Q1 a load dataset
ucb_data <- read.csv("https://ritsokiguess.site/datafiles/berkeley.txt", sep = "\t")
ucb_data## Dept Males.admitted Males.rejected Females.admitted Females.rejected
## 1 A 512 313 89 19
## 2 B 353 207 17 8
## 3 C 120 205 202 391
## 4 D 139 279 131 244
## 5 E 53 138 94 299
## 6 F 22 351 24 317b
The dataset is not tidy because:It contains multiple variables in column names (e.g., “Males:admitted” and “Females:rejected” instead of separate “Gender” and “Admission Status” columns). It does not follow the structure where each row represents a single observation.
#install.packages("tidyverse","dplyr")
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(dplyr)
tidy_ucb_data <- ucb_data %>%
pivot_longer(
cols = -Dept,
names_to = c("Gender", "Admission_Status"),
names_sep = "\\.",
values_to = "Count"
)
tidy_ucb_data## # A tibble: 24 × 4
## Dept Gender Admission_Status Count
## <chr> <chr> <chr> <dbl>
## 1 "A " Males admitted 512
## 2 "A " Males rejected 313
## 3 "A " Females admitted 89
## 4 "A " Females rejected 19
## 5 "B " Males admitted 353
## 6 "B " Males rejected 207
## 7 "B " Females admitted 17
## 8 "B " Females rejected 8
## 9 "C " Males admitted 120
## 10 "C " Males rejected 205
## # ℹ 14 more rowsc
# Plot the number of admitted and rejected individuals for each gender
ggplot(tidy_ucb_data, aes(x = Admission_Status, y = Count, fill = Gender)) +
geom_col(position = "dodge") +
labs(title = "Number of Individuals Admitted and Rejected by Gender",
x = "Admission Status", y = "Count") +
theme_minimal()
This bar chart shows the number of individuals admitted and rejected at
UC Berkeley, separated by gender.
Higher Male Admissions and Higher Female Rejection Rate: More males were admitted compared to females. While the number of rejected males and females appears similar, fewer females were admitted, indicating that a larger proportion of female applicants were rejected.
Possible Gender Disparity: The difference in admissions could indicate bias in the admission process or differences in application numbers across genders and departments. Further analysis, such as looking at acceptance rates (proportions) instead of raw counts, would give a clearer picture.
· # d
# Compute proportion
tidy_ucb_data <- tidy_ucb_data %>%
group_by(Dept, Gender) %>%
mutate(Prop = Count / sum(Count))
# View updated data
head(tidy_ucb_data)## # A tibble: 6 × 5
## # Groups: Dept, Gender [3]
## Dept Gender Admission_Status Count Prop
## <chr> <chr> <chr> <dbl> <dbl>
## 1 "A " Males admitted 512 0.621
## 2 "A " Males rejected 313 0.379
## 3 "A " Females admitted 89 0.824
## 4 "A " Females rejected 19 0.176
## 5 "B " Males admitted 353 0.630
## 6 "B " Males rejected 207 0.370e
ggplot(tidy_ucb_data, aes(x = Admission_Status, y = Prop, fill = Gender)) +
geom_col(position = "dodge") +
labs(
title = "Admission Proportions by Gender",
subtitle = "Proportions account for differences in application numbers",
x = "Admission Status",
y = "Proportion"
) +
scale_y_continuous(labels = scales::percent) + # Format as %
scale_fill_brewer(palette = "Set1") +
theme_minimal()
Why Proportions Are Better: It controls for different application
numbers: Males and females may apply in different quantities Shows
actual admission rates: Shows what percentage of each group was admitted
Avoids Simpson’s Paradox: The famous UC Berkeley case showed that while
women had lower overall admission rates, they often had higher rates
within individual departments Proportions is better when analyzing
gender disparity because it accounts for different application pool
sizes. Count alone can be misleading—for example, if more males applied
overall, they might have more admissions, but that does not mean they
had a higher acceptance rate.
Proportion allows for a fairer comparison.
f
tidy_ucb_counts <- tidy_ucb_data %>%
select(-Prop)
original_ucb_data <- tidy_ucb_counts %>%
pivot_wider(
names_from = c(Gender, Admission_Status),
values_from = Count,
names_sep = "."
)
print(original_ucb_data)## # A tibble: 6 × 5
## # Groups: Dept [6]
## Dept Males.admitted Males.rejected Females.admitted Females.rejected
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 "A " 512 313 89 19
## 2 "B " 353 207 17 8
## 3 "C " 120 205 202 391
## 4 "D " 139 279 131 244
## 5 "E " 53 138 94 299
## 6 "F " 22 351 24 317q2 a
Cognition <- read_table("https://ritsokiguess.site/datafiles/cognition.txt")##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## id = col_double(),
## c1 = col_double(),
## c2 = col_double(),
## c3 = col_double(),
## c4 = col_double(),
## c5 = col_double(),
## c6 = col_double(),
## c7 = col_double(),
## c8 = col_double(),
## c9 = col_double(),
## c10 = col_double(),
## c11 = col_double(),
## c12 = col_double(),
## c13 = col_double(),
## c14 = col_double(),
## c15 = col_double(),
## c16 = col_double(),
## c17 = col_double(),
## c18 = col_double()
## )## Warning: 1 parsing failure.
## row col expected actual file
## 101 -- 19 columns 20 columns 'https://ritsokiguess.site/datafiles/cognition.txt'Cognition## # A tibble: 201 × 19
## id c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 3 4 4 3 4 3 4 4 3 4 3
## 2 2 2 4 1 1 2 1 4 2 2 4 4 3
## 3 3 4 4 1 1 1 3 1 3 2 4 5 1
## 4 4 3 1 4 5 4 3 3 3 5 1 1 2
## 5 5 4 4 2 2 1 4 2 2 1 4 5 1
## 6 6 5 5 1 1 1 5 1 3 1 5 5 1
## 7 7 3 3 1 2 2 1 4 3 2 4 4 2
## 8 8 3 4 1 1 1 3 2 3 3 4 5 1
## 9 9 4 4 1 2 2 4 4 3 1 5 5 2
## 10 10 4 4 2 2 1 3 5 2 2 4 5 1
## # ℹ 191 more rows
## # ℹ 6 more variables: c13 <dbl>, c14 <dbl>, c15 <dbl>, c16 <dbl>, c17 <dbl>,
## # c18 <dbl>b
Cognition %>% pivot_longer(-id, names_to = "test",
names_prefix
= "c",
values_to = "perform", values_drop_na = TRUE )## # A tibble: 3,604 × 3
## id test perform
## <dbl> <chr> <dbl>
## 1 1 1 1
## 2 1 2 3
## 3 1 3 4
## 4 1 4 4
## 5 1 5 3
## 6 1 6 4
## 7 1 7 3
## 8 1 8 4
## 9 1 9 4
## 10 1 10 3
## # ℹ 3,594 more rows