#Research Question: How do developmental disability support expenditures differ among ethnic groups?
#Dataset: https://www.openintro.org/data/index.php?data=dds.discr
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.2.1 ✔ readr 2.2.0
## ✔ forcats 1.0.1 ✔ stringr 1.6.0
## ✔ ggplot2 4.0.3 ✔ tibble 3.3.1
## ✔ lubridate 1.9.5 ✔ tidyr 1.3.2
## ✔ purrr 1.2.2
## ── 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 errors
dds_data <- read.csv("dds.discr.csv")
#Examining Dataset
dim(dds_data)
## [1] 1000 6
head(dds_data)
## id age.cohort age gender expenditures ethnicity
## 1 10210 13-17 17 Female 2113 White not Hispanic
## 2 10409 22-50 37 Male 41924 White not Hispanic
## 3 10486 0-5 3 Male 1454 Hispanic
## 4 10538 18-21 19 Female 6400 Hispanic
## 5 10568 13-17 13 Male 4412 White not Hispanic
## 6 10690 13-17 15 Female 4566 Hispanic
str(dds_data)
## 'data.frame': 1000 obs. of 6 variables:
## $ id : int 10210 10409 10486 10538 10568 10690 10711 10778 10820 10823 ...
## $ age.cohort : chr "13-17" "22-50" "0-5" "18-21" ...
## $ age : int 17 37 3 19 13 15 13 17 14 13 ...
## $ gender : chr "Female" "Male" "Male" "Female" ...
## $ expenditures: int 2113 41924 1454 6400 4412 4566 3915 3873 5021 2887 ...
## $ ethnicity : chr "White not Hispanic" "White not Hispanic" "Hispanic" "Hispanic" ...
#Dataset contains 1,000 observations and 6 variables. Each row represents one individual receiving developmental disability services,including their age, gender, expenditures, and ethnicity.
#Cleaning Dataset
dds_clean <- dds_data |>
select(ethnicity, expenditures) |>
filter(!is.na(ethnicity), !is.na(expenditures)) |>
mutate(ethnicity = as.factor(ethnicity))
#Data now includes variables of interest and removes missing observations.
dds_clean |>
group_by(ethnicity) |>
summarise(
count = n(),
mean_expenditures = mean(expenditures)
)
## # A tibble: 8 × 3
## ethnicity count mean_expenditures
## <fct> <int> <dbl>
## 1 American Indian 4 36438.
## 2 Asian 129 18392.
## 3 Black 59 20885.
## 4 Hispanic 376 11066.
## 5 Multi Race 26 4457.
## 6 Native Hawaiian 3 42782.
## 7 Other 2 3316.
## 8 White not Hispanic 401 24698.
#Summary of ethinicity counts and mean expenditures. Mean expenditures differ widely across ethnic groups, where White not Hispanic contain the highest observation count and Native Hawaiian having the lowest observation count of the listed ethnicities. Notably, several ethnicites have low observation counts but high mean expenditures, such as American Indian.
#ANOVA
anova <- aov(expenditures ~ ethnicity, data = dds_clean)
summary(anova)
## Df Sum Sq Mean Sq F value Pr(>F)
## ethnicity 7 4.498e+10 6.425e+09 18.94 <2e-16 ***
## Residuals 992 3.366e+11 3.393e+08
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#The demonstrated p-value is far less than the significanc level of 0.05 and is thus statistically significant, rejecting the null hypothesis.
#Tukey HSD
tukey <- TukeyHSD(anova) |>
sort( decreasing = TRUE)
#Ordering our Tukey HSD results by descending difference order
tukey_df <- as.data.frame(tukey$"ethnicity")
sorted_tukey <- tukey_df |>
arrange(desc(diff))
sorted_tukey
## diff lwr upr
## Native Hawaiian-Multi Race 38325.603 4211.8443 72439.361
## Native Hawaiian-Hispanic 31716.764 -712.9354 64146.464
## Native Hawaiian-Asian 24389.961 -8284.5690 57064.492
## Native Hawaiian-Black 21897.740 -11214.3871 55009.867
## White not Hispanic-Other 21381.049 -18278.0837 61040.181
## White not Hispanic-Multi Race 20240.818 8918.5625 31563.073
## White not Hispanic-Hispanic 13631.979 9615.7153 17648.244
## Native Hawaiian-American Indian 6344.083 -36386.2486 49074.415
## White not Hispanic-Asian 6305.177 642.1478 11968.205
## White not Hispanic-Black 3812.955 -3988.1940 11614.105
## Black-Asian 2492.221 -6300.7558 11285.198
## Other-Multi Race -1140.231 -42194.2058 39913.744
## Multi Race-Hispanic -6608.838 -17953.9899 4736.313
## Hispanic-Asian -7326.803 -13035.4709 -1618.135
## Other-Hispanic -7749.069 -47414.7442 31916.606
## Hispanic-Black -9819.024 -17653.3669 -1984.681
## White not Hispanic-American Indian -11740.701 -39853.4429 16372.040
## Multi Race-Asian -13935.641 -25962.7764 -1908.506
## Other-Asian -15075.872 -54941.9641 24790.220
## Black-American Indian -15553.657 -44459.9327 13352.619
## Multi Race-Black -16427.862 -29597.5252 -3258.200
## Other-Black -17568.093 -57793.6240 22657.438
## Asian-American Indian -18045.878 -46449.8345 10358.079
## White not Hispanic-Native Hawaiian -18084.785 -50506.4814 14336.912
## Hispanic-American Indian -25372.681 -53494.6515 2749.290
## Multi Race-American Indian -31981.519 -62029.9521 -1933.086
## Other-American Indian -33121.750 -81573.3922 15329.892
## Other-Native Hawaiian -39465.833 -90538.3486 11606.682
## p adj
## Native Hawaiian-Multi Race 1.538550e-02
## Native Hawaiian-Hispanic 6.054017e-02
## Native Hawaiian-Asian 3.128885e-01
## Native Hawaiian-Black 4.764124e-01
## White not Hispanic-Other 7.273480e-01
## White not Hispanic-Multi Race 1.967605e-06
## White not Hispanic-Hispanic 3.179679e-13
## Native Hawaiian-American Indian 9.998302e-01
## White not Hispanic-Asian 1.704754e-02
## White not Hispanic-Black 8.157783e-01
## Black-Asian 9.892957e-01
## Other-Multi Race 1.000000e+00
## Multi Race-Hispanic 6.411119e-01
## Hispanic-Asian 2.610206e-03
## Other-Hispanic 9.989583e-01
## Hispanic-Black 3.719715e-03
## White not Hispanic-American Indian 9.102784e-01
## Multi Race-Asian 1.065510e-02
## Other-Asian 9.457380e-01
## Black-American Indian 7.293359e-01
## Multi Race-Black 3.984018e-03
## Other-Black 8.887596e-01
## Asian-American Indian 5.306078e-01
## White not Hispanic-Native Hawaiian 6.910968e-01
## Hispanic-American Indian 1.118734e-01
## Multi Race-American Indian 2.764856e-02
## Other-American Indian 4.310424e-01
## Other-Native Hawaiian 2.691726e-01
#Comparison of means across all ethnicities in descending order. Significant differences were found between several groups, specifically Native Hawaiian, White not Hispanic, Asian, Multi Race, and Hispanic ethnicities.
#Boxplot visualization
ggplot(dds_clean, aes(x = ethnicity, y = expenditures)) +
geom_boxplot() +
labs(
title = "Annual Expenditures by Ethnicity",
x = "Ethnicity",
y = "Annual Expenditures ($)"
)
#The boxplot shows visible differences in annual expenditures across ethnic groups. White not Hispanic generally has higher expenditures, while Hispanic and Multi Race tend to have lower expenditures. The Hispanic group also contains many higher value outliers. Notably, American Indian and Native Hawaiian groups have a higher annual expenditure than the others, although the lower observation count must be considered when conducting further interpretation.