Statistical Inference of Possible Relationships Between Financial Satisfaction and Marital Status in American Society

Introduction:

Research question:

Does the satisfaction of financial situation have a positive influence on individual marital status?

Background:

Financial situation matters a lot when someone makes decisions. Among all the decisons during one’s lifetime, to be married or not, when to marry and whether to divorce, are crucial for his/her happiness. Usually, people decide to get married when they have a stable and optimistic financial situation, though factors like age and affection may also play an important role. In this research, we will choose satisfaction of financial situation as our primary research object and explore its influence on individual marital status. Data set used in our research is from General Social Survey (GSS).

Since 1972, the General Social Survey (GSS) has been monitoring societal change and studying the growing complexity of American society. The GSS aims to gather data on contemporary American society in order to monitor and explain trends and constants in attitudes, behaviors, and attributes; to examine the structure and functioning of society in general as well as the role played by relevant subgroups; to compare the United States to other societies in order to place American society in comparative perspective and develop cross-national models of human society; and to make high-quality data easily accessible to scholars, students, policy makers, and others, with minimal cost and waiting.

Data:

A sociological survey used to collect data on demographic characteristics and attitudes of residents of the United States. The codebook (URL: https://d396qusza40orc.cloudfront.net/statistics%2Fproject%2FGSS1.html) lists all variables, the values they take, and the survey questions associated with them. There are a total of 57,061 cases and 114 variables in this dataset. Note that this is a cumulative data file for surveys conducted between 1972 - 2012 and that not all respondents answered all questions in all years.

GSS questions cover a diverse range of issues including national spending priorities, marijuana use, crime and punishment, race relations, quality of life, confidence in institutions, and sexual behavior.

The cases are 57,061 individuals who live in contemporary American society from 1972 to 2012.

Below are the two variables we will be studying, together with their types and levels.

satfin: Satisfaction with financial situation. (Ordinal categorical variable)

Satisfied
More or less
Not at all sat

marital: Marital status. (Regular categorical variable)

Married
Widowed
Divorced
Separated
Never married

It’s an observational study. There is no interference from GSS. All GSS doing is collecting data via questionnaires, monitoring and explaining trends and constants in attitudes, behaviors, and attributes. Besides, there are no principles like control, randomize, replicate and block in this study, while there are in experimental design.

The population of interest is the American society. The findings from this analysis can be generalized to that population, because the sample is randomly collected without bias. Also, the sample size (57,061 observations) is large enough to represent all the possible features in the population.

Potential sources of bias may lie in the accuracy of the responses from respondents, the non-response / voluntary response situation, the missing values as indicated by “NA” in the data, or convenience sample.

Since it is an observational survey, only correlations, rather than causal links can be made with the variables of interest. Chances are that there are confounding variables, such as education level and good growth environment, affect the satisfaction of financial situation and marital status at the same time.

Citation:

Smith, Tom W., Michael Hout, and Peter V. Marsden. General Social Survey, 1972-2012 [Cumulative File]. ICPSR34802-v1. Storrs, CT: Roper Center for Public Opinion Research, University of Connecticut /Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributors], 2013-09-11. doi:10.3886/ICPSR34802.v1

（Persistent URL: http://doi.org/10.3886/ICPSR34802.v1）

Exploratory data analysis:

library(inference)

## Loading required package: sandwich

# Make a subset of myData, including only the 2 variables of interest
myData <- gss[, c(72 , 17)]
names(myData)

## [1] "satfin"  "marital"

dim(myData)

## [1] 57061     2

# see the head of myData
head(myData)

##           satfin       marital
## 1 Not At All Sat Never Married
## 2   More Or Less       Married
## 3      Satisfied       Married
## 4 Not At All Sat       Married
## 5      Satisfied       Married
## 6   More Or Less Never Married

# assign variables to objects
satfin <- myData$satfin
marital <- myData$marital

# Summary of data set
summary(myData)

##             satfin               marital     
##  Satisfied     :15344   Married      :30761  
##  More Or Less  :23176   Widowed      : 5540  
##  Not At All Sat:13934   Divorced     : 7070  
##  NA's          : 4607   Separated    : 1984  
##                         Never Married:11686  
##                         NA's         :   20

# data table
table(x = satfin, y = marital)

##                 y
## x                Married Widowed Divorced Separated Never Married
##   Satisfied         9281    1925     1256       253          2626
##   More Or Less     13002    2150     2660       736          4624
##   Not At All Sat    6134    1096     2446       844          3408

# Chi-squared test for independence
summary(table(x = satfin, y = marital))

## Number of cases in table: 52441 
## Number of factors: 2 
## Test for independence of all factors:
##  Chisq = 1728.2, df = 8, p-value = 0

# Create the relative frequency tables
table(satfin) / 57061

## satfin
##      Satisfied   More Or Less Not At All Sat 
##      0.2689052      0.4061618      0.2441948

table(marital) / 57061

## marital
##       Married       Widowed      Divorced     Separated Never Married 
##    0.53908975    0.09708908    0.12390249    0.03476981    0.20479837

table(x = satfin, y = marital) / 57061

##                 y
## x                    Married     Widowed    Divorced   Separated
##   Satisfied      0.162650497 0.033735827 0.022011532 0.004433851
##   More Or Less   0.227861411 0.037678975 0.046616779 0.012898477
##   Not At All Sat 0.107498992 0.019207515 0.042866406 0.014791188
##                 y
## x                Never Married
##   Satisfied        0.046020925
##   More Or Less     0.081036084
##   Not At All Sat   0.059725557

# Create contingency table
table(satfin, marital)

##                 marital
## satfin           Married Widowed Divorced Separated Never Married
##   Satisfied         9281    1925     1256       253          2626
##   More Or Less     13002    2150     2660       736          4624
##   Not At All Sat    6134    1096     2446       844          3408

# Draw the barplot
barplot(table(satfin))

barplot(table(marital))

# plot the 2 variables of interest
plot(x = satfin, y = marital)
title(xlab = "Satisfaction of financial situation", ylab = "Marital")

par(ps = 12, cex.main = 1)

Inference:

Not including the NAs, there are 52441 observations in table for Chi-squared test for independence.

hypotheses:

H0 (nothing going on): Financial satisfaction and marital status are independent. Marital status does not vary by financial satisfaction.
HA (something going on): Financial satisfaction and marital status are dependent. Marital status does vary by financial satisfaction.

A improbably large test statistic of 1728.2 and a p-value of 0 indicate that we can safely reject the null hypothesis that the variables are independent. In other words, financial satisfaction and marital status are definitely dependent on one another.

Relative frequency tables show that 40% of the observations feel more or less satfied with their financial situation, followed by those satisfied and not at all satisfied, both of which occupie about 25%. As for marital status, more than half of observations are married while 20% are never married.

Most of the married are financially satisfied and more-or-less satisfied, and so are the widowed. Most of the divorced are more-or-less satisfied and not-at-all satisfied, and so are the separated and never married.

Conclusion:

In American society, financial satisfaction and marital status are dependent on one another. Further, most of the married are either financially satisfied or at least more-or-less satisfied, and so are the widowed. Most of the divorced are either not-at-all satisfied or at most more-or-less satisfied, and so are the separated and never married. In general, our research found that the more satisfied people are with their financial situation, the less likely they are tend to maintain a relationship like divorced, separated or never married. Note that since it is an observational survey, only correlations, rather than causal links can be made with the variables of interest.