Quant: ANOVA and Multiple Comparisons in SPSS

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.

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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.

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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:

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