# Factorial ANOVA

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INSTRUCTIONS: Please refer to the Main post ((A)below), and answer the instructor’s feedback (B) which follows.Give a firm example as answer.
A. Main Post:
Research Question: “How does educational achievement impact happiness?”
Determining Appropriate ANOVA Design
Different cross-sectional studies have shown a positive correlation between educational achievement and subjective happiness. Generally, there is ambiguous evidence regarding this correlation (Helliwell, 2003; Veenhoven, 2010). The relationship between educational achievement or success and happiness or satisfaction in life can be studied through secondary and primary data. Primary data can be obtained through surveys on an identified population sample over time. The independent variable in this research problem will be educational achievement or success and lack of educational achievement or success, while happiness will be the dependent variable. The research will attempt to provide proof of the positive impacts of educational success on happiness by utilizing the common life satisfaction statistic regressions. In addition to this, the research on this problem will also offer evidence of heterogeneity in the sample population during data gathering, factoring in various levels of education, with regards to the determinants of personal happiness.
Since this experiment deals with more than one independent variable, factorial design ANOVA would be more appropriate in this case (Page, Braver, & MacKinnon, 2003; Wilson & Maclean, 2011, pp. 379-414). The main significance of using factorial design in this research is that it offers unique and applicable information on the interaction between variables and/or integrates the effects the variables have on the dependent variable. A ‘within group’ ANOVA will be significant in this research. This means that a repeated measure design will be used in comparing the quantitative and qualitative variables in determining the mean difference when the participants in the survey are subject to similar conditions. In addition, this can help in determining the research hypotheses: either group is greater than the other or the groups are equal, null hypothesis.
The independent variable in this research problem, also known as the ‘factor’, will be educational achievement or success and lack of educational achievement or success while happiness will be the dependent variables. The independent variables will be within the factors. The rating of happiness with educational achievement will be stored as a single variable in the data set while the rating of happiness without educational achievement will be stored as another variable (Moore & McCabe, 2003; Page, Braver & MacKinnon, 2003; Sheskin, 2004; Wilson & Maclean, 2011, pp. 379-414). The difference will be determined through:
Difference = (happiness with educational achievement) – (happiness without educational achievement).
After designing this variable, it is possible to use a single sample t-test to determine whether the mean difference has a significant difference from a consonant. This logic can be applied in testing if the mean happiness with educational achievement is significantly different from the mean happiness without educational achievement. In instances where the two means have an equal value, it is expected that the difference between them will be zero (Sheskin, 2004, p. 1138). In that case, it should be tested whether the means are significantly different through testing whether the mean of the determined difference variable has a significant difference from zero.
The main advantage of using factorial design in this research is that it offers unique and applicable information on the interaction between variables and/or integrates the effects the variables have on the dependent variable. Additionally, when there is a correlation along with the major variables, this design allows for re-examination of the identified variables to see whether they have statistical significance. The design of the ANOVA will also be significant in conducting t-tests in determining the mean differences between the variables (Wilson & Maclean).
References
Helliwell, J. F. (2003). How’s life? Combining individual and national variables to explain subjective well-being. Economic Modelling, 20 (2): 331–360.
Moore, D. S., & McCabe, G. P. (2003). Introduction to the Practice of Statistics (4th edition). New York, NY: Freeman.
Page, M. C., Braver, S. L., & MacKinnon, D. P. (2003). Levine’s Guide to SPSS for Analysis of Variance (2nd edition). Mahwah, NJ: Lawrence Erlbaum Associates.
Sheskin, D. J. (2004). Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition). Boca Raton, FL: Chapman & Hall.
Veenhoven, R. (2010). Capability and happiness: Conceptual difference and reality links, Journal of Socio-Economics, 39 (3): 344–350.
Wilson, S., & Maclean, R. (2011). Research methods and data analysis for psychology. New York: McGraw-Hill higher Education.

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