library(tidyverse)
library(pastecs)

texas_data <- read.csv("health_data.csv")

texas_data <- texas_data %>%
  rename(poor_fair_health = v002_rawvalue) %>%
  filter(!is.na(poor_fair_health))
nrow(texas_data)
## [1] 254
summary(texas_data$poor_fair_health)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1240  0.2050  0.2280  0.2355  0.2605  0.4650

Descriptive Statistics

pastecs::stat.desc(
  texas_data$poor_fair_health,
  basic = TRUE,
  norm = TRUE
)
##      nbr.val     nbr.null       nbr.na          min          max        range 
## 2.540000e+02 0.000000e+00 0.000000e+00 1.240000e-01 4.650000e-01 3.410000e-01 
##          sum       median         mean      SE.mean CI.mean.0.95          var 
## 5.982400e+01 2.280000e-01 2.355276e-01 3.323644e-03 6.545534e-03 2.805839e-03 
##      std.dev     coef.var     skewness     skew.2SE     kurtosis     kurt.2SE 
## 5.297017e-02 2.249001e-01 1.046050e+00 3.422999e+00 1.900678e+00 3.121685e+00 
##   normtest.W   normtest.p 
## 9.418762e-01 1.726970e-08

The descriptive statistics show that the average percentage of adults reporting poor or fair health across the 254 Texas counties is approximately 23.55%, with a median of 22.80%. The percentages range from 12.40% to 46.50%. The standard deviation is approximately 5.30 percentage points. The skewness value of 1.046 indicates that the distribution is positively skewed, meaning some counties have much higher percentages than others. These findings suggest that poor or fair health is not distributed evenly across Texas counties.

ggplot(texas_data, aes(x = poor_fair_health)) +
  geom_histogram(
    bins = 20,
    fill = "steelblue",
    color = "black"
  ) +
  labs(
    title = "Distribution of Poor or Fair Health Across Texas Counties",
    x = "Proportion Reporting Poor or Fair Health",
    y = "Number of Counties"
  ) +
  theme_minimal()

texas_data <- texas_data %>%
  mutate(sqrt_poor_fair_health = sqrt(poor_fair_health))

pastecs::stat.desc(
  texas_data$sqrt_poor_fair_health,
  basic = TRUE,
  norm = TRUE
)
##      nbr.val     nbr.null       nbr.na          min          max        range 
## 2.540000e+02 0.000000e+00 0.000000e+00 3.521363e-01 6.819091e-01 3.297727e-01 
##          sum       median         mean      SE.mean CI.mean.0.95          var 
## 1.225385e+02 4.774935e-01 4.824349e-01 3.317271e-03 6.532983e-03 2.795088e-03 
##      std.dev     coef.var     skewness     skew.2SE     kurtosis     kurt.2SE 
## 5.286860e-02 1.095870e-01 6.297117e-01 2.060611e+00 9.761837e-01 1.603290e+00 
##   normtest.W   normtest.p 
## 9.728749e-01 9.121332e-05
ggplot(texas_data, aes(x = sqrt_poor_fair_health)) +
  geom_histogram(
    bins = 20,
    fill = "mediumpurple",
    color = "black"
  ) +
  labs(
    title = "Square Root Transformation of Poor or Fair Health",
    x = "Square Root of Poor or Fair Health Proportion",
    y = "Number of Counties"
  ) +
  theme_minimal()