Tag: analysis of variance

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

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

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

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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: Variances

Variance is considered as measures of average dispersion (Field, 2013; Schumacker, 2014).  Variance is a numerical value that describes how the observed data values are spread across the data distribution and how they differ from the mean on average (Huck, 2011; Field, 2013; Schumacker, 2014).  The smaller the variance indicates that the observed data values are close to the mean and vice versa (Field, 2013). What happens when researchers want to study if the difference between two means from two groups of data is statistically significant from each other? Researchers could use ANOVA, which is an analysis of variances that test whether or not to reject the null hypothesis of the mean of one group is equal to the mean of another group (Huck, 2011; Schumacker, 2014).  ANOVAs usually test categorical independent variables (groups) and continuous dependent variables (Creswell, 2014).  One of the results of a one-way analysis of variance presents in a table the variance between groups and within groups (Huck, 2011).  Schumacker (2014), explained that the variance between groups indicates the variation between the overall grand mean of the groups, while variance within the groups indicates the variance within the means of the groups.  The variances between groups have a degree of freedom equal to the number of groups analyzed – 1, whereas the variance within the groups has a degree of freedom equal to the number of data points within each group – 1 – the number of groups (Huck, 2011).  Information from within and between the groups are used to calculate the F-statistic to establish statistical significance which can allow the researcher to reject or fail to reject their null hypothesis (Field, 2013; Huck, 2011; Schumacker, 2014).

References

  • Creswell, J. W. (2014) Research design: Qualitative, quantitative and mixed method approaches (4th ed.). California, SAGE Publications, Inc. VitalBook file.
  • Field, A. (2013) Discovering Statistics Using IBM SPSS Statistics (4th ed.). UK: Sage Publications Ltd. VitalBook file.
  • Huck, S. W. (2011) Reading Statistics and Research (6th ed.). Pearson Learning Solutions. VitalBook file.
  • Schumacker, R. E. (2014) Learning statistics using R. California, SAGE Publications, Inc, VitalBook file.