LR5: Making and Comparing Confidence Intervals

#Lab Report 5: Making and Comparing Confidence Intervals
library(ggplot2)
library(dplyr)
library(lsr)
library(descr)
library(Hmisc)
library('lehmansociology')
data(gss123)
options(scipen = 999)

#For this LR we will be looking at the
#relationship between a dichotomous nominal independent variable
#and an interval ratio dependent variable
#First, we have to look at our dichotomous variable and see
#what the two categories are. 

#WHICH DICHOTOMOUS VARIABLE ARE YOU USING?

#REPLACE SEX WITH THE NAME OF YOUR DICHOTOMOUS VARIABLE
frequency(gss123$sex)
frequency(as.numeric(gss123$sex))
#The code below shows you how to formally dichotomize a variable so that
#the two groups are coded as 0 and 1. 
#This is important for doing statistical
#analyses. Note that we name the new dichotomous variable whatever the 
#category is that we have coded as 1

gss123$male<-(as.numeric(gss123$sex)) ==1
frequency(gss123$male)
mean(gss123$male)

#Look at the two cateogories in your frequency table
#and decide what you will call each of your mini
#datasets. Choose names that make sense. 

#Below, REPLACE men and women WITH THE NAMES OF YOUR TWO
#MINI DATASETS. REPLACE sex WITH THE NAME OF YOUR 
#DICHOTOMOUS VARIABLE. REPLACE "Male" and "Female"
#WITH THE TWO CATEGORIES OF YOUR FREQUENCY TABLE.
#REMEMBER TO INCLUDE THEM IN QUOTATION MARKS AND
#TO WRITE THEM EXACTLY AS THEY APPEAR (FOR
#EXAMPLE, IF THEY ARE CAPITALIZED IN THE FREQUENCY
#TABLE THEY NEED TO BE CAPITALIZED IN THE CODE).

men<-dplyr::filter(gss123, male=="TRUE")
women<-dplyr::filter(gss123, male=="FALSE")

#Follow the code below for the rest of your
#LR but replace men and
#women with the names of your two mini datasets
#and replace conrinc with the name of your 
#interval ratio variable.
#Make sure to change titles and labels, too!
#Fill in your answers below

#WHICH INTERVAL-RATIO VARIABLE ARE YOU USING?

#WHAT IS YOUR RESEARCH QUESTION?

#Summary statistics and a histogram for your dependent variable 
#for your first mini dataset

#CHANGE THIS CODE BY REPLACING men WITH THE NAME
#OF ONE OF YOUR TWO MINI DATASETS AND REPLACING
#conrinc WITH YOUR DEPENDENT VARIABLE
#AND BY EDITING THE TITLES AND LABELS FOR GRAPHS
#REMEMBER TO THINK ABOUT BINWIDTH AND WHETHER YOU WANT
#TO CHANGE IT TO SOMETHING BIGGER

summary(men$conrinc, na.rm=TRUE)
sd(men$conrinc, na.rm=TRUE)

ggplot(data = men, aes(x = conrinc)) + 
  geom_histogram(color="blue", fill="pink", binwidth =1, 
                 aes(y=(..count../sum(..count..))*100)) + 
  ggtitle("Distribution of Males' Income, GSS") + 
  labs(y="Percent", x="Income") 

#INTERPRET THE SUMMARY STATISTICS AND HISTOGRAM

#Now we are getting summary statistics and a
#histogram for your second mini dataset. 

#CHANGE THIS CODE BY REPLACING women WITH THE NAME
#OF YOUR OTHER MINI DATASET AND REPLACING
#conrinc WITH YOUR DEPENDENT VARIABLE
#AND BY EDITING THE TITLES AND LABELS FOR GRAPHS
#REMEMBER TO THINK ABOUT BINWIDTH AND WHETHER YOU WANT
#TO CHANGE IT TO SOMETHING BIGGER

summary(women$conrinc, na.rm=TRUE)
sd(women$conrinc, na.rm=TRUE)

ggplot(data = women, aes(x = conrinc)) + 
  geom_histogram(color="blue", fill="pink", binwidth =1, 
                 aes(y=(..count../sum(..count..))*100)) + 
  ggtitle("Distribution of Females' Income, GSS") + 
  labs(y="Percent", x="Income") 

#INTERPRET THE SUMMARY STATISTICS AND HISTOGRAM

#Comparing means in a bar graph
#CHANGE THE INDEPENDENT VARIABLE (replace sex)
#CHANGE THE DEPENDENT VARIABLE (replace conrinc) 
#CHANGE THE LABELS
ggplot(data=gss123) +   
  stat_summary(aes(x=sex, y=conrinc), fun=mean, geom="bar") +   
  xlab("Sex") +   
  ylab("Mean Income by Spouse") +   
  theme(axis.text.x=element_text(angle=-45))

#ANSWER THIS: Compare the results you got for your two groups. 
#Which has a bigger mean? Which has more variability? 
#Based on the bar graph of means, 
#does it seem like the two categories of your 
#dichotomous variable
#differ in the dependent variable?

#USING INFERENTAL STATISTICS TO COMPARE GROUPS
#Let's compare the confidence intervals for the mean of our
#dependent variable for the two categories of our independent variable.
#REPLACE men AND women WITH THE NAMES OF YOUR MINI DATASETS
#REPLACE conrinc WITH THE NAME OF YOUR DEPENDENT VARIABLE

#Comparing the CIs- 95%
ciMean(men$conrinc, na.rm=TRUE, conf =0.95)
ciMean(women$conrinc, na.rm=TRUE, conf =0.95)

#Comparing the CIs - 99%
ciMean(men$conrinc, na.rm=TRUE, conf =0.99)
ciMean(women$conrinc, na.rm=TRUE, conf =0.99)

#INTERPRET the confidence intervals and come to a conclusion about whether
#your independent and dependent variables are related.