Tag: Line Graph

Quant: In-depth Analysis in SPSS

Abstract

This short analysis attempts to understand the marital happiness level on combined income.  It was found that marital happiness levels are depended on a couples’ combined income, but for the happiest couples, they were happy regardless how much money they had.  This, quantitative analysis on the sample data, has shown that when the happiness levels are low, there is a higher chance of lower levels of combined income.

Introduction

Mulligan (1973), was one of the first that stated arguments about money was one of the top reasons for divorce between couples.  Factors for financial arguments could stem from: Goals and savings; record keeping; delaying tactics; apparel cost-cutting strategies; controlling expenditures; financial statements; do-it-yourself techniques; and cost cutting techniques (Lawrence, Thomasson, Wozniak, & Prawitz, 1993). Lawrence et al. (1993) exerts that financial arguments are common between families.  However, when does money no longer become an issue?  Does the increase in combined family income affect the marital happiness levels?  This analysis attempts to answer these questions.

Methods

Crosstabulation was conducted to get a descriptive exploration of the data.  Graphical images of box-plots helped show the spread and distribution of combined income per marital happiness.  In this analysis of the data the two alternative hypothesis will be tested:

  • There is a difference between the mean values of combined income per marital happiness levels.
  • There is a dependence between the combined income and marital happiness level

This would lead to finally analyzing the hypothesis introduced in the previous section, one-way analysis of variance and two-way chi-square test was conducted respectively.

Results

Table 1: Case processing summary for analyzing happiness level versus family income.

u6db1f7Table 2: Crosstabulation for analyzing happiness level versus family income (<$21,250).

u6db1f3Table 3: Crosstabulation for analyzing happiness level versus family income for (>$21,250).
u6db1f4

Table 4: Chi-square test for analyzing happiness level versus family income.

u6db1f5

Table 5: Analysis of Variance for analyzing happiness level versus family income.

u6db1f6

u6db1f1.png

Figure 1: Boxplot diagram per happiness level of a marriage versus the family incomes.

u6db1f2.png

Figure 2: Line diagram per happiness level of a marriage versus the mean of the family incomes.

Discussions and Conclusions

There are 1419 participants, and only 38.5% had responded to both their happiness of marriage and family income (Table 1).  What may have contributed to this huge unresponsive rate is that there could have been people who were not married, and thus making the happiness of marriage question not applicable to the participants.  Thus, it is suggested that in the future, there should be an N/A classification in this survey instrument, to see if we can have a higher response rate.  Given that there are still 547 responses, there is other information to be gained from analyzing this data.

As a family unit gains more income, their happiness level increases (Table 2-3).  This can be seen as the dollar value increases, the % within the family income and ranges recorded to midpoint for the very happy category increases as well from the 50% to the 75% level.    The unhappiest couples seem to be earning a combined medium amount of $7500-9000 and at $27500-45000.  Though for marriages that are pretty happy, it’s about stable at 30-40% of respondents at $13750 or more.

The mean values of family income to happiness (Figure 2), shows that on average, happier couples make more money together, but at a closer examination using boxplots (Figure 1), the happiest couples, seem to be happy regardless of how much money they make as the tails of the box plot extend really far from the median.  One interesting feature is that the spread of family combined income is shrinks as happiness decreases (Figure 1).  This could possibly suggest that though money is not a major factor for those couples that are happy, if the couple is unhappy it could be driven by lower combined incomes.

The two-tailed chi-squared test, shows statistical significance between family combined income and marital happiness allowing us to reject the null hypothesis #2, which stated that these two variables were independent of each other (Table 4).  Whereas the analysis of variance doesn’t allow for a rejection of the null hypothesis #1, which states the means are different between the groups of marital happiness level (Table 5).

There could be many reasons for this analysis, thus future work could include analyzing other variables that could help define other factors for marital happiness.  A possible multi-variate analysis may be necessary to see the impact on marital happiness as the dependent variable and combined income as one of many independent variables.

SPSS Code

GET

  FILE=’C:\Users\mkher\Desktop\SAV files\gss.sav’.

DATASET NAME DataSet1 WINDOW=FRONT.

CROSSTABS

  /TABLES=hapmar BY incomdol

  /FORMAT=AVALUE TABLES

  /STATISTICS=CHISQ CORR

  /CELLS=COUNT ROW COLUMN

  /COUNT ROUND CELL.

ONEWAY rincome BY hapmar

  /MISSING ANALYSIS

* Chart Builder.

GGRAPH

  /GRAPHDATASET NAME=”graphdataset” VARIABLES=hapmar incomdol MISSING=LISTWISE REPORTMISSING=NO

  /GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

  SOURCE: s=userSource(id(“graphdataset”))

  DATA: hapmar=col(source(s), name(“hapmar”), unit.category())

  DATA: incomdol=col(source(s), name(“incomdol”))

  DATA: id=col(source(s), name(“$CASENUM”), unit.category())

  GUIDE: axis(dim(1), label(“HAPPINESS OF MARRIAGE”))

  GUIDE: axis(dim(2), label(“Family income; ranges recoded to midpoints”))

  SCALE: cat(dim(1), include(“1”, “2”, “3”))

  SCALE: linear(dim(2), include(0))

  ELEMENT: schema(position(bin.quantile.letter(hapmar*incomdol)), label(id))

END GPL.

* Chart Builder.

GGRAPH

  /GRAPHDATASET NAME=”graphdataset” VARIABLES=hapmar MEAN(incomdol)[name=”MEAN_incomdol”]

    MISSING=LISTWISE REPORTMISSING=NO

  /GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

  SOURCE: s=userSource(id(“graphdataset”))

  DATA: hapmar=col(source(s), name(“hapmar”), unit.category())

  DATA: MEAN_incomdol=col(source(s), name(“MEAN_incomdol”))

  GUIDE: axis(dim(1), label(“HAPPINESS OF MARRIAGE”))

  GUIDE: axis(dim(2), label(“Mean Family income; ranges recoded to midpoints”))

  SCALE: cat(dim(1), include(“1”, “2”, “3”))

  SCALE: linear(dim(2), include(0))

  ELEMENT: line(position(hapmar*MEAN_incomdol), missing.wings())

END GPL.

References

Quant: ANOVA and Multiple Comparisons in SPSS

Introduction

The aim of this analysis is to look at the relationship between the dependent variable of the income level of respondents (rincdol) and the independent variable of their reported level of happiness (happy).   This independent variable has at least 3 or more levels within it.

From the SPSS outputs the goal is to:

  • How to use the ANOVA program to determine the overall conclusion. Use of the Bonferroni correction as a post-hoc analysis to determine the relationship of specific levels of happiness to income.

Hypothesis

  • Null: There is no basis of difference between the overall rincdol and happy
  • Alternative: There is are real differences between the overall rincdol and happy
  • Null2: There is no basis of difference between the certain pairs of rincdol and happy
  • Alternative2: There is are real differences between the certain pairs of rincdol and happy

Methodology

For this project, the gss.sav file is loaded into SPSS (GSS, n.d.).  The goal is to look at the relationships between the following variables: rincdol (Respondent’s income; ranges recoded to midpoints) and happy (General Happiness). To conduct a parametric analysis, navigate to Analyze > Compare Means > One-Way ANOVA.  The variable rincdol was placed in the “Dependent List” box, and happy was placed under “Factor” box.  Select “Post Hoc” and under the “Equal Variances Assumed” select “Bonferroni”.  The procedures for this analysis are provided in video tutorial form by Miller (n.d.). The following output was observed in the next two tables.

The relationship between rincdol and happy are plotted by using the chart builder.  Code to run the chart builder code is shown in the code section, and the resulting image is shown in the results section.

Results

Table 1: ANOVA

Respondent’s income; ranges recoded to midpoints
Sum of Squares df Mean Square F Sig.
Between Groups 11009722680.000 2 5504861341.000 9.889 .000
Within Groups 499905585000.000 898 556687733.900
Total 510915307700.000 900

Through the ANOVA analysis, Table 1, it shows that the overall ANOVA shows statistical significance, such that the first Null hypothesis is rejected at the 0.05 level. Thus, there is a statistically significant difference in the relationship between the overall rincdol and happy variables.  However, the difference between the means at various levels.

Table 2: Multiple Comparisons

Dependent Variable:   Respondent’s income; ranges recoded to midpoints
Bonferroni
(I) GENERAL HAPPINESS (J) GENERAL HAPPINESS Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
VERY HAPPY PRETTY HAPPY 4093.678 1744.832 .058 -91.26 8278.61
NOT TOO HAPPY 12808.643* 2912.527 .000 5823.02 19794.26
PRETTY HAPPY VERY HAPPY -4093.678 1744.832 .058 -8278.61 91.26
NOT TOO HAPPY 8714.965* 2740.045 .005 2143.04 15286.89
NOT TOO HAPPY VERY HAPPY -12808.643* 2912.527 .000 -19794.26 -5823.02
PRETTY HAPPY -8714.965* 2740.045 .005 -15286.89 -2143.04
*. The mean difference is significant at the 0.05 level.

According to Table 2, for the pairings of “Very Happy” and “Pretty Happy” did not disprove the Null2 for that case at the 0.05 level. But, all other pairings “Very Happy” and “Not Too Happy” with “Pretty Happy” and “Not Too Happy” can reject the Null2 hypothesis at the 0.05 level.  Thus, there is a difference when comparing across the three different pairs.

u3db3f1

Figure 1: Graphed means of General Happiness versus incomes.

The relationship between general happiness and income are positively correlated (Figure 1).  That means that a low level of general happiness in a person usually have lower recorded mean incomes and vice versa.  There is no direction or causality that can be made from this analysis.  It is not that high amounts of income cause general happiness, or happy people make more money due to their positivism attitude towards life.

SPSS Code

DATASET NAME DataSet1 WINDOW=FRONT.

ONEWAY rincdol BY happy

  /MISSING ANALYSIS

  /POSTHOC=BONFERRONI ALPHA(0.05).

* Chart Builder.

GGRAPH

  /GRAPHDATASET NAME=”graphdataset” VARIABLES=happy MEAN(rincdol)[name=”MEAN_rincdol”]

    MISSING=LISTWISE REPORTMISSING=NO

  /GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

  SOURCE: s=userSource(id(“graphdataset”))

  DATA: happy=col(source(s), name(“happy”), unit.category())

  DATA: MEAN_rincdol=col(source(s), name(“MEAN_rincdol”))

  GUIDE: axis(dim(1), label(“GENERAL HAPPINESS”))

  GUIDE: axis(dim(2), label(“Mean Respondent’s income; ranges recoded to midpoints”))

  SCALE: cat(dim(1), include(“1”, “2”, “3”))

  SCALE: linear(dim(2), include(0))

  ELEMENT: line(position(happy*MEAN_rincdol), missing.wings())

END GPL.

References: