Statistical Inference with the GSS Data

Load packages

library(tidyverse)
library(statsr)

Load data

load("gss.Rdata")

Part 1: Data

Random saple were used in this survey. Resutls can be generalized to US population. No random assignment was used so causality cannot be inferred.

Part 2: Research Question

There is a general idea that women are more compassionate than men. So there is a chance that attitude to some social problem would be different between men and women.
Now, I want to see is there any difference in attitude of men and women toward the spending of the money for improving conditions of the blacks.

variable to be explored-

• sex - respondent’s sex
  
• natrace - attitude toward spending money for improving the conditions of blacks.

I will use data from 2012 for my ressearch question.

Part 3: Exploratory data analysis

I will build the contingency table for my two categorical variable sex and natrace.
Before that I will build a dataframe with the variable of interest.

# using select command from dplyr to build a dataframe with selected columns.
gss <- select(gss,sex, natrace, year)

Since I am only interested in 2012 data so I will filter the data using filter command from dplyr and I will also drop all missing values(NA).

gss <- gss %>% 
    filter(year ==  2012) %>% 
    drop_na()

Lets check the structure of the data

# structure of the data
str(gss)

## 'data.frame':    877 obs. of  3 variables:
##  $ sex    : Factor w/ 2 levels "Male","Female": 1 2 2 2 2 2 2 2 2 2 ...
##  $ natrace: Factor w/ 3 levels "Too Little","About Right",..: 2 3 2 1 1 1 1 1 2 1 ...
##  $ year   : int  2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 ...

# dimension of data

dim(gss)

## [1] 877   3

# head of data

head(gss)

# quick summary
summary(gss)

##      sex             natrace         year     
##  Male  :353   Too Little :329   Min.   :2012  
##  Female:524   About Right:420   1st Qu.:2012  
##               Too Much   :128   Median :2012  
##                                 Mean   :2012  
##                                 3rd Qu.:2012  
##                                 Max.   :2012

Now build the contingency table to summarise my data.

# I can use table function like this 
gss_tab <- table(gss$sex, gss$natrace)
gss_tab

##         
##          Too Little About Right Too Much
##   Male          113         184       56
##   Female        216         236       72

OR

# I can use xtabs function like this
gss_xtab <- xtabs(~sex + natrace, gss)
gss_xtab

##         natrace
## sex      Too Little About Right Too Much
##   Male          113         184       56
##   Female        216         236       72

# I will use gss_xtab table for further analysis

I can add column sum and row sum to my table if I want,
using addmargins command.

addmargins(gss_xtab)

##         natrace
## sex      Too Little About Right Too Much Sum
##   Male          113         184       56 353
##   Female        216         236       72 524
##   Sum           329         420      128 877

Now lets convert to proportion table.

#proportion to row sum and will round the value to 3 digits
round(prop.table(gss_xtab, margin = 1), 3)

##         natrace
## sex      Too Little About Right Too Much
##   Male        0.320       0.521    0.159
##   Female      0.412       0.450    0.137

I want to see as percentage so I have to multiply by 100 here.

# as percentage
100 * (round(prop.table(gss_xtab, margin = 1), 3))

##         natrace
## sex      Too Little About Right Too Much
##   Male         32.0        52.1     15.9
##   Female       41.2        45.0     13.7

From the above table, 32% male think that too little money is spending for improving conditions of blacks where 42% female think as same. Also there are diffence in male and female percentage who think spending is about right or too much.

Now plot the data to visualize.

ggplot(data = gss, aes(x= natrace, fill=sex))+
    geom_bar()+
    xlab('Money Spending')+
    ylab('Count')+
    labs(fill = 'Sex')+
    ggtitle('Attitudinal Differences of Men and Women')+
    theme(plot.title = element_text(hjust = 0.5))

From the above bar plot,
there are difference in male and female proportion in each sub categoty of spending money.

Part 4: Inference

# I have used gss_xtab table that I have built earlier

chisq.test(gss_xtab)

## 
##  Pearson's Chi-squared test
## 
## data:  gss_xtab
## X-squared = 7.6324, df = 2, p-value = 0.02201