Is there a difference in the participants’X1SES based on their level of education?
This research aims at examining whether the different levels of education contribute to the difference in the X1SES of the populations. The independent variable (factor variable) in this case is the level of education of a participant which is categorized into six groups (factor levels): ‘Master’s degree’, ‘Associate degree’, ‘P.H.D/M.D/Law/other high prof degree’, ‘Bachelor’s degree’, ‘High school diploma or GED’ and ‘Less than high school’. On the other hand, the dependent variable (response variable) is X1SES which is a continuous variable. Researchers use ONE WAY ANOVA test whenever their interest is to determine whether the means of two or more groups are different (Assaad, Zhou, Carroll & Wu, 2014)). Therefore, having one factor (education) with six different factor levels (the different education levels) as listed above and one dependent variable ‘X1SES’, makes this social research ideally suited for a ONE-WAY ANOVA test. Moreover, the assumption of homogeneity of variance will be considered.
Research Question & Objective
‘Is there any difference in the participants’X1SES based on their level of education?’ is the research question in this study. The latter research question aims at determining whether there are mean differences among the six different education levels. If the means are the same, then it implies that populations from the different education levels have the same X1SES. If the means differ, then there is a difference in X1SES in between the population groups. To answer our research question, we need to test a hypothesis as follows;
There is no significant difference in the participants’ X1SES based on their level of education.
There is a significant difference in the participants’ X1SES based on their level of education.
Conceptual framework concerning Data
For this particular study, the High school longitudinal study dataset was chosen as the dataset of interest and particularly the baseline phase. The raw data was imported into SPSS and coding done to change the type of the two variables from ‘string’ to ‘numeric’ to allow for analysis. Moreover, the raw data had missing observations, and editing was viable where the observations without response were also omitted. The edited and clean data was therefore used for the test.
Test of Homogeneity
The test of homogeneity of variances is another assumption that ought to be considered when running One Way ANOVA test in order give the researcher an approval to continue with the test (Shingala & Rajyaguru, 2015). The null hypothesis for this test is that the variances are equal. The (Table 1) below shows results for the homogeneity test.
Table 1; Test for homogeneity table
|Test of Homogeneity of Variances|
(Table 1) Shows that the p-value (sig) is .000 which is less than .05 meaning that the null hypothesis has been rejected and thus the variances are not equal. If the variances are not equal, then a parametric test like ANOVA is not suited. However, according to Shingala & Rajyaguru, we can proceed with our analysis because it is a robust statistic and allows a relatively small violation of the normality test (2014).
ONE WAY ANOVA Test
Table 2; one way ANOVA test table
|Sum of Squares||df||Mean Square||F||Sig.|
The one-way ANOVA test was conducted to study the mean difference between the six groups of education levels. From (table 2) the p-value (sig) of 0.00 < 0.05, we, therefore, have a significant approval to reject the null hypothesis and conclude that there is a significant difference in the participants’ X1SES based on their level of education. Assaad et al., recommends that there is a need to know how the means differ by conducting a post hoc analysis as a follow-up analysis (2014).
Post hoc analysis test
Table 3; post hoc comparisons table
|Dependent Variable: X1SES
|(I) X1PAR1EDU||(J) X1PAR1EDU||Mean Difference (I-J)||Std. Error||Sig.||95% Confidence Interval|
|Lower Bound||Upper Bound|
|master’s degree||Associates degree||.91307*||.01815||.000||.8613||.9648|
|P.H.D/M.D/Law/other high prof degree||-.69607*||.03316||.000||-.7908||-.6013|
|High school diploma or GED||1.41794*||.01561||.000||1.3734||1.4625|
|Less than high school||2.12994*||.01940||.000||2.0746||2.1853|
|Associates degree||master’s degree||-.91307*||.01815||.000||-.9648||-.8613|
|P.H.D/M.D/Law/other high prof degree||-1.60914*||.03232||.000||-1.7015||-1.5168|
|High school diploma or GED||.50487*||.01373||.000||.4657||.5440|
|Less than high school||1.21686*||.01792||.000||1.1658||1.2680|
|P.H.D/M.D/Law/other high prof degree||master’s degree||.69607*||.03316||.000||.6013||.7908|
|High school diploma or GED||2.11401*||.03096||.000||2.0255||2.2025|
|Less than high school||2.82601*||.03304||.000||2.7316||2.9204|
|Bachelor’s degree||master’s degree||-.39264*||.01699||.000||-.4411||-.3442|
|P.H.D/M.D/Law/other high prof degree||-1.08870*||.03168||.000||-1.1792||-.9982|
|High school diploma or GED||1.02531*||.01216||.000||.9906||1.0600|
|Less than high school||1.73730*||.01675||.000||1.6895||1.7851|
|High school diploma or GED||master’s degree||-1.41794*||.01561||.000||-1.4625||-1.3734|
|P.H.D/M.D/Law/other high prof degree||-2.11401*||.03096||.000||-2.2025||-2.0255|
|Less than high school||.71199*||.01535||.000||.6682||.7558|
|Less than high school||master’s degree||-2.12994*||.01940||.000||-2.1853||-2.0746|
|P.H.D/M.D/Law/other high prof degree||-2.82601*||.03304||.000||-2.9204||-2.7316|
|High school diploma or GED||-.71199*||.01535||.000||-.7558||-.6682|
|*. The mean difference is significant at the 0.05 level.|
Since the variances aren’t equal and the sample sizes are not equal, Games Howell post hoc analysis was conducted. According to (table 3), the p-value (sig) of 0.00< 0.05 meaning that the difference in means between all the groups is significant. The latter implies that participants from every level of education have a significant difference in mean from every other group.
Determining the effect size helps in knowing how big the effect in means difference is, to disseminate the magnitude of the findings from our data (lakens, 2013). According to Cohen’s (1992), the effect size is the sum of squares between the groups divided by the total sum of squares. In our case, the effect size is 0.57 which is a medium effect based on a study by Sullivan & Feinn (2012).
Assaad, H. I., Zhou, L., Carroll, R. J., & Wu, G. (2014). Rapid publication-ready MS-Word tables for one-way ANOVA. SpringerPlus, 3(1), 474.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Frontiers in psychology, 4, 863.
Shingala, M. C., & Rajyaguru, A. (2015). Comparison of post hoc tests for unequal variance. International Journal of New Technologies in Science and Engineering, 2(5), 22-33.
Sullivan, G. M., & Feinn, R. (2012). Using effect size—or why the P value is not enough. Journal of graduate medical education, 4(3), 279-282.