SD2:Chi-Squared Test for Independence
Rebecca Gibble
Research Question / Hypothesis
I hypothesize that there is a relationship between Marital Status (marital_status) and Mental Health (mental_health). I will be analyzing responses to the Subset of National Health Interview Survey Responses data set in order to test this hypothesis.
Package Loading, Data Import, Data Prep
library(readr)
library(dplyr)## Warning: package 'dplyr' was built under R version 3.6.2##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)## Warning: package 'ggplot2' was built under R version 3.6.2data<-read_csv("/Users/rebeccagibble/Downloads/SD2 Data.csv")## Parsed with column specification:
## cols(
## sex = col_character(),
## race = col_character(),
## marital_status = col_character(),
## poverty_status = col_character(),
## age_range = col_character(),
## health = col_character(),
## bmi_category = col_character(),
## mental_health = col_character(),
## heart_attack_history = col_character(),
## heart_condition_history = col_character(),
## cancer_history = col_character(),
## prediabetes_history = col_character(),
## asthma_history = col_character(),
## hypertension_history = col_character(),
## smoking_history = col_character(),
## birthcontrol_status = col_logical()
## )data<-data%>%
select(marital_status, mental_health)%>%
filter(marital_status %in% c("Never Married","Married","Widowed","DivorcedOrSeparated"),
mental_health %in% c("Low Risk","Moderate Mental Distress","Serious Mental Illness"))Data Summary
Marital Status Response Summary
The table below shows the actual % of responses given for each category of marital_status.
table(data$marital_status)%>%
prop.table()%>%
round(2)##
## DivorcedOrSeparated Married Never Married Widowed
## 0.18 0.45 0.29 0.08Mental Health Response Summary
The table below shows the actual % of responses given for each category of mental_health. These are the values that we would expect to observe in a crosstab if the two variables were completely independent of eachother. This is what we might consider the “null hypothesis”.
table(data$mental_health)%>%
prop.table()%>%
round(2)##
## Low Risk Moderate Mental Distress Serious Mental Illness
## 0.80 0.16 0.03Expected Crosstab Distribution Across Marital Status and Mental Health
- DivorcedOrSeparated/Low Risk = 0.18*0.80 = 0.144
- DivorcedOrSeparated/Moderate Mental Distress = 0.18*0.16 = 0.0288
- DivorcedOrSeparated/Serious Mental Illness = 0.18*0.03 = 0.0054
- Married/Low Risk = 0.45*0.80 = 0.36
- Married/Moderate Mental Distress = 0.45*0.16 = 0.072
- Married/Serious Mental Illness = 0.45*0.03 = 0.0135
- Never Married/Low Risk = 0.29* 0.80 = 0.232
- Never Married/Moderate Mental Distress = 0.29*0.16 = 0.046
- Never Married/Serious Mental Illness =0.29*0.03 = 0.0087
- Widowed/Low Risk = 0.08*0.80 = 0.064
- Widowed/Moderate Mental Distress = 0.08*0.16 = 0.0128
- Widowed/Serious Mental Illness = 0.08*0.03 = 0.0024
The table below shows the actual % of responses for each category combination. A crosstab showing table %. These values are very different from the expected observations from the null hypothesis.
data%>%
group_by(marital_status,mental_health)%>%
summarize(n=n())%>%
mutate(percent=n/sum(n))## `summarise()` regrouping output by 'marital_status' (override with `.groups` argument)## # A tibble: 12 x 4
## # Groups: marital_status [4]
## marital_status mental_health n percent
## <chr> <chr> <int> <dbl>
## 1 DivorcedOrSeparated Low Risk 34619 0.739
## 2 DivorcedOrSeparated Moderate Mental Distress 9469 0.202
## 3 DivorcedOrSeparated Serious Mental Illness 2770 0.0591
## 4 Married Low Risk 98237 0.852
## 5 Married Moderate Mental Distress 14542 0.126
## 6 Married Serious Mental Illness 2462 0.0214
## 7 Never Married Low Risk 57073 0.774
## 8 Never Married Moderate Mental Distress 14046 0.190
## 9 Never Married Serious Mental Illness 2634 0.0357
## 10 Widowed Low Risk 15983 0.797
## 11 Widowed Moderate Mental Distress 3374 0.168
## 12 Widowed Serious Mental Illness 706 0.0352Because the numbers are different, we want to keep analyzing to see the relationship between each to see if we can reject the null hypothesis.
Data Analysis
Relationship of Interest: Crosstab showing row%.
table(data$marital_status, data$mental_health)%>%
prop.table(1)##
## Low Risk Moderate Mental Distress
## DivorcedOrSeparated 0.73880661 0.20207862
## Married 0.85244835 0.12618773
## Never Married 0.77383971 0.19044649
## Widowed 0.79664058 0.16817026
##
## Serious Mental Illness
## DivorcedOrSeparated 0.05911477
## Married 0.02136392
## Never Married 0.03571380
## Widowed 0.03518915Relationship of Interest: Marital Status vs. Mental Health Visualization
data%>%
group_by(marital_status, mental_health)%>%
summarize(n=n())%>%
mutate(percent=n/sum(n))%>%
filter(marital_status == "DivorcedOrSeparated")%>%
ggplot()+
geom_col(aes(x=mental_health, y=percent, fill=marital_status))## `summarise()` regrouping output by 'marital_status' (override with `.groups` argument)
data%>%
group_by(marital_status, mental_health)%>%
summarize(n=n())%>%
mutate(percent=n/sum(n))%>%
filter(marital_status == "Married")%>%
ggplot()+
geom_col(aes(x=mental_health, y=percent, fill=marital_status))## `summarise()` regrouping output by 'marital_status' (override with `.groups` argument)
data%>%
group_by(marital_status, mental_health)%>%
summarize(n=n())%>%
mutate(percent=n/sum(n))%>%
filter(marital_status == "Never Married")%>%
ggplot()+
geom_col(aes(x=mental_health, y=percent, fill=marital_status))## `summarise()` regrouping output by 'marital_status' (override with `.groups` argument)
data%>%
group_by(marital_status, mental_health)%>%
summarize(n=n())%>%
mutate(percent=n/sum(n))%>%
filter(marital_status == "Widowed")%>%
ggplot()+
geom_col(aes(x=mental_health, y=percent, fill=marital_status))## `summarise()` regrouping output by 'marital_status' (override with `.groups` argument)
We can see here that the majority of people have low risk for mental health (meaning they do not consider themselves to suffer from mental health), however, divorced/separated people suffer from the most moderate mental distress and more serious mental illness than other groups.
Chi-Squared Test
chisq.test(data$marital_status, data$mental_health)##
## Pearson's Chi-squared test
##
## data: data$marital_status and data$mental_health
## X-squared = 3856.6, df = 6, p-value < 2.2e-16