Test of Homogeneity of Variances

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Test of Homogeneity of Variances
Q1. Age 
Levene Statistic df1 df2 Sig.
50.699 4 48573 .000
ANOVA
Q1. Age 
  Sum of Squares df Mean Square F Sig.
Between Groups 47762.220 4 11940.555 57.203 .000
Within Groups 10139121.233 48573 208.740    
Total 10186883.453 48577      
Multiple Comparisons
Dependent Variable:   Q1. Age 
  (I) Q43. Satisfaction with democracy (J) Q43. Satisfaction with democracy Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
  Lower Bound Upper Bound
Bonferroni The country is not a democracy Not at all satisfied .483 .493 1.000 -.90 1.87
Not very satisfied 1.528* .483 .016 .17 2.88
Fairly satisfied .198 .481 1.000 -1.15 1.55
Very satisfied -1.470* .494 .029 -2.86 -.09
Not at all satisfied The country is not a democracy -.483 .493 1.000 -1.87 .90
Not very satisfied 1.045* .199 .000 .49 1.60
Fairly satisfied -.284 .193 1.000 -.83 .26
Very satisfied -1.953* .223 .000 -2.58 -1.33
Not very satisfied The country is not a democracy -1.528* .483 .016 -2.88 -.17
Not at all satisfied -1.045* .199 .000 -1.60 -.49
Fairly satisfied -1.330* .165 .000 -1.79 -.87
Very satisfied -2.998* .200 .000 -3.56 -2.44
Fairly satisfied The country is not a democracy -.198 .481 1.000 -1.55 1.15
Not at all satisfied .284 .193 1.000 -.26 .83
Not very satisfied 1.330* .165 .000 .87 1.79
Very satisfied -1.669* .193 .000 -2.21 -1.13
Very satisfied The country is not a democracy 1.470* .494 .029 .09 2.86
Not at all satisfied 1.953* .223 .000 1.33 2.58
Not very satisfied 2.998* .200 .000 2.44 3.56
Fairly satisfied 1.669* .193 .000 1.13 2.21
Games-Howell The country is not a democracy Not at all satisfied .483 .497 .868 -.87 1.84
Not very satisfied 1.528* .486 .015 .20 2.86
Fairly satisfied .198 .485 .994 -1.13 1.52
Very satisfied -1.470* .502 .028 -2.84 -.10
Not at all satisfied The country is not a democracy -.483 .497 .868 -1.84 .87
Not very satisfied 1.045* .195 .000 .51 1.58
Fairly satisfied -.284 .191 .571 -.81 .24
Very satisfied -1.953* .231 .000 -2.58 -1.32
Not very satisfied The country is not a democracy -1.528* .486 .015 -2.86 -.20
Not at all satisfied -1.045* .195 .000 -1.58 -.51
Fairly satisfied -1.330* .161 .000 -1.77 -.89
Very satisfied -2.998* .207 .000 -3.56 -2.43
Fairly satisfied The country is not a democracy -.198 .485 .994 -1.52 1.13
Not at all satisfied .284 .191 .571 -.24 .81
Not very satisfied 1.330* .161 .000 .89 1.77
Very satisfied -1.669* .204 .000 -2.22 -1.11
Very satisfied The country is not a democracy 1.470* .502 .028 .10 2.84
Not at all satisfied 1.953* .231 .000 1.32 2.58
Not very satisfied 2.998* .207 .000 2.43 3.56
Fairly satisfied 1.669* .204 .000 1.11 2.22
*. The mean difference is significant at the 0.05 level.

To determine whether the difference in mean scores is significant, ANOVA examines the differences between multiple samples and within one sample (Frankfort-Nachmias, & Leon-Guerrero, 2015). This becomes my starting point of analyzing the data and using a single dependent variable and an independent variable.  My research question is whether the age of respondents determine their satisfaction with democracy. The null hypothesis goes on to say that the age of respondents cannot determine their satisfaction of democracy in Africa.

             In order to find the difference between a samples’s mean score and the total mean, we will need to understand the variation of individual scores within one sample. This is also to say that ANOVA allows us to find whether the variance between sample is bigger than the variance within the samples (Wagner, 2016).  In this study sample, our dependent variable is the age of respondents (i.e interval/ratio variable) while independent variable is the satisfaction with democracy (i.e. nominal variable).

             Looking at the test of homogeneity of variances, we can conclude that the statistical significant is at 0.000 level, thereby rejecting the null hypothesis that there is no difference in the variable samples being measured. As we view the overall test, we can see the omnibus test as significant. Since the omnibus test is significant, we can tell how at minimum, one of the means differs from another (Laureate Education, 2016b). Therefore, we want to study our post-hoc tests to limit which means differ. However, Post Hoc Tests of allows for the calculation of individual differences in means.

           Using Post Hoc Tests and the options for levene statistics, we can conclude the strength of statistical significance to be P<0.05= assigned P-value (Laureate Education, 2016b). I have decided to look at Bonferroni equal variances assumed and Games-Howell equal variances not assumed. Looking at the benferroni post hoc test for equal variances assumed, we can see pairwise differences in some independent variable test. There are differences in statistical significant and confidence intervals. Some of the pairwise correlations show statistical insignificant. Therefore, according the Bonferroni test of equal variances, we can conclude the notion of no statistical significant in specific samples (or specific independent variables) and accept the null hypothesis that there is no statistical difference between respondents’ satisfaction of democracy and their age. Or Using the Games-Howell Post Hoc Test for equal variances not assumed, we can specify which independent variable samples are statistically significant and which ones are statistically insignificant, thereby rejecting or accepting the null hypothesis.

Reference

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2015). Social statistics for a diverse society (7th ed.). Thousand Oaks, CA: Sage Publications.

Laureate Education (Producer). (2016h). One-way ANOVA demonstration [Video file]. Baltimore, MD: Author.

Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications.