Categorical Data Analysis
Sakif Shadman
Introduction
In this assignment by using the NHIS data, I hypothesize there is a relationship between Sex and BMI(Body Mass Index). The relation is how BMI condition is differ between male and female. I will do following steps to test this hypothesis.
1. Load Packages
Loading the necessary packages.
library(readr)
library(ggplot2)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union2. Import Data
Importing data into R and named it Health_Data.
Health_Data = read_csv("/Users/sakif/Downloads/NHIS Data.csv")##
## ── Column specification ────────────────────────────────────────────────────────────────────────────────────
## cols(
## .default = col_double(),
## Demo_Race = col_logical(),
## Demo_Hispanic = col_character(),
## Demo_RaceEthnicity = col_character(),
## Demo_Region = col_character(),
## Demo_sex_C = col_character(),
## Demo_sexorien_C = col_logical(),
## Demo_agerange_C = col_character(),
## Demo_marital_C = col_character(),
## Demo_hourswrk_C = col_character(),
## MentalHealth_MentalIllnessK6_C = col_character(),
## MentalHealth_depressionmeds_B = col_logical(),
## Health_SelfRatedHealth_C = col_character(),
## Health_diagnosed_STD5yr_B = col_logical(),
## Health_BirthControlNow_B = col_logical(),
## Health_EverHavePrediabetes_B = col_logical(),
## Health_HIVAidsRisk_C = col_character(),
## Health_BMI_C = col_character(),
## Health_UsualPlaceHealthcare_C = col_character(),
## Health_AbnormalPapPast3yr_B = col_logical(),
## Behav_CigsPerDay_C = col_character()
## # ... with 1 more columns
## )
## ℹ Use `spec()` for the full column specifications.## Warning: 683386 parsing failures.
## row col expected actual file
## 68557 Demo_Race 1/0/T/F/TRUE/FALSE Black or African American '/Users/sakif/Downloads/NHIS Data.csv'
## 68558 Demo_Race 1/0/T/F/TRUE/FALSE Asian '/Users/sakif/Downloads/NHIS Data.csv'
## 68559 Demo_Race 1/0/T/F/TRUE/FALSE American Indian or Alaskan Native '/Users/sakif/Downloads/NHIS Data.csv'
## 68560 Demo_Race 1/0/T/F/TRUE/FALSE White '/Users/sakif/Downloads/NHIS Data.csv'
## 68561 Demo_Race 1/0/T/F/TRUE/FALSE White '/Users/sakif/Downloads/NHIS Data.csv'
## ..... ......... .................. ................................. ......................................
## See problems(...) for more details.head(Health_Data)## # A tibble: 6 x 50
## psu sampweight year year_strata Demo_Race Demo_Hispanic Demo_RaceEthnic…
## <dbl> <dbl> <dbl> <dbl> <lgl> <chr> <chr>
## 1 2 4316 1997 1998. NA Hispanic Hispanic (Race …
## 2 2 2845 1997 1998. NA Hispanic Hispanic (Race …
## 3 2 3783 1997 1998. NA Hispanic Hispanic (Race …
## 4 2 2466 1997 1998. NA Hispanic Hispanic (Race …
## 5 2 3794 1997 1998. NA Hispanic Hispanic (Race …
## 6 1 1793 1997 1998. NA Hispanic Hispanic (Race …
## # … with 43 more variables: Demo_Region <chr>, Demo_sex_C <chr>,
## # Demo_sexorien_C <lgl>, Demo_belowpovertyline_B <dbl>, Demo_age_N <dbl>,
## # Demo_agerange_C <chr>, Demo_marital_C <chr>, Demo_hourswrk_C <chr>,
## # MentalHealth_MentalIllnessK6_N <dbl>, MentalHealth_MentalIllnessK6_C <chr>,
## # MentalHealth_SeriousMentalIllnessK6_B <dbl>,
## # MentalHealth_depressionmeds_B <lgl>, Health_SelfRatedHealth_C <chr>,
## # Health_diagnosed_STD5yr_B <lgl>, Health_BirthControlNow_B <lgl>,
## # Health_EverHaveHeartAttack_B <dbl>, Health_EverHaveHeartCondition_B <dbl>,
## # Health_EverHaveCancer_B <dbl>, Health_EverHaveDiabetes_B <dbl>,
## # Health_EverHavePrediabetes_B <lgl>, Health_EverHaveAsthma_B <dbl>,
## # Health_StillHaveAsthma_B <dbl>, Health_HIVAidsRisk_C <chr>,
## # Health_HIVAidsHighRisk_B <dbl>, Health_EverTakeHIVTest_B <dbl>,
## # Health_EverHaveHypertension_B <dbl>, Health_BMI_N <dbl>,
## # Health_BMI_C <chr>, Health_BMIOverweight_B <dbl>, Health_BMIObese_B <dbl>,
## # Health_Weight_N <dbl>, Health_Height_N <dbl>,
## # Health_UsualPlaceHealthcare_C <chr>, Health_UsualPlaceHealthcare_B <dbl>,
## # Health_AbnormalPapPast3yr_B <lgl>, Behav_EverSmokeCigs_B <dbl>,
## # Behav_CigsPerDay_N <dbl>, Behav_CigsPerDay_C <chr>,
## # Behav_AgeStartSmoking <dbl>, Behav_AlcDaysPerYear_N <dbl>,
## # Behav_AlcDaysPerWeek_N <dbl>, Behav_BingeDrinkDaysYear_N <dbl>,
## # Behav_BingeDrinkDaysYear_C <chr>3. Prepare Data
Identifing two categorical variable named Demo_sex_C and Health_BMI_C. After renaming both to Sex and BMI; we can find the relationship between the both variables and named it as BMI_Per_Sex. It shows how BMI condiion differs to male and female.
BMI_Per_Sex = Health_Data %>%
select(Demo_sex_C, Health_BMI_C) %>%
rename(Sex = Demo_sex_C, BMI = Health_BMI_C) %>%
filter(BMI %in% c("Underweight", "Normal", "Overweight", "Obese", "Exremely Obese"))
BMI_Per_Sex ## # A tibble: 595,109 x 2
## Sex BMI
## <chr> <chr>
## 1 female Normal
## 2 female Overweight
## 3 male Obese
## 4 male Normal
## 5 male Normal
## 6 female Overweight
## 7 male Normal
## 8 female Normal
## 9 female Normal
## 10 male Normal
## # … with 595,099 more rows4. Table Distribution
Distributing data to Null hypothesis and Actual distribution. So we can compare between them.
(a) Null Hypothesis
Distributing both data separately to see their impects.
I. Distribution of Sex
It shows the actual (%) of responses given for each catagory of Sex.
table(BMI_Per_Sex$Sex) %>%
prop.table() %>%
round(2)##
## female male
## 0.55 0.45II. Distribution of BMI
It shows the actual (%) of responses given for each catagory of BMI.
table(BMI_Per_Sex$BMI) %>%
prop.table() %>%
round(2)##
## Exremely Obese Normal Obese Overweight Underweight
## 0.04 0.36 0.22 0.35 0.03(b) Actual Distribution
It shows the actual (%) of responses given for both catagory together.
table(BMI_Per_Sex$BMI, BMI_Per_Sex$Sex) %>%
prop.table() %>%
round(2)##
## female male
## Exremely Obese 0.03 0.01
## Normal 0.22 0.14
## Obese 0.12 0.10
## Overweight 0.16 0.19
## Underweight 0.02 0.015. Comparing the null hypothesis table to the actual table distribution
There is no difference between null hypothesis table and actual distribution table. Both got exact value.
6. Data Analysis
Calculating column% to highlight the relationship of interest between the variables.
table(BMI_Per_Sex$BMI, BMI_Per_Sex$Sex) %>%
prop.table(2)##
## female male
## Exremely Obese 0.04695415 0.02604850
## Normal 0.40646484 0.30851167
## Obese 0.21795071 0.22604100
## Overweight 0.28605022 0.42572992
## Underweight 0.04258009 0.013668907. Data Interpretation
It’s clearly showing that among the responded, 40% female have the normal weight where 42.5% male got overweight.
8. Data Visualization
Visualizing the results of the column% table.
BMI_Per_Sex %>%
group_by(Sex, BMI)%>%
summarize(n = n()) %>%
mutate(Percent = n/sum(n)) %>%
ggplot() +
geom_col(aes(x = Sex, y = Percent, fill = BMI))## `summarise()` regrouping output by 'Sex' (override with `.groups` argument)
9. Chi-Square Statistical Test
Calculating a chi-square test to determine if there is a statistically significant relationship between the variables.
chisq.test(BMI_Per_Sex$BMI, BMI_Per_Sex$Sex)##
## Pearson's Chi-squared test
##
## data: BMI_Per_Sex$BMI and BMI_Per_Sex$Sex
## X-squared = 18040, df = 4, p-value < 2.2e-1610. Interpret the Chi-Square Test
There is a statistically significant relationship between Sex and BMI. It’s showing most of the female have normal weight where most of the male have overweight.