In the methods section of the dissertation or thesis, there is a statistical data analysis section. The statistical data analysis is the data analysis plan to examine the research questions or hypotheses in your dissertation.
Suppose the research question was: to what extent does meaning in life predict happiness? The statistical data analysis will include the specific statistic to be used and the assumptions of that statistic. The appropriate statistical data analysis to use in this case would be the linear regression analysis. The statistical data analysis section will discuss the assumptions of regression, which include the removing of outliers from the data set, the examining of the linearity, and constant variance. The statistical data analysis plan could look like this:
To examine the extent to which meaning in life predicts happiness, a linear regression will be conducted. Meaning in life will be the predictor variable and happiness will be the criterion variable. Outliers will be removed by standardizing the scores in SPSS.
Standardizing the scores in SPSS can be performed by going to “analyze,” requesting descriptive statistics, clicking over the variables, and checking the box for “save standardized values as variables.” Any value larger than the absolute value of 3.0 can be considered an outlier. The assumptions of linearity and constant variance can be assessed by clicking on “analyze,” going to regression, and then clicking on “Plots.” When you open the dialog box, you can put the “Zresid” on the Y-axis and “Zpred” on the X-axis. As long as the scatter looks random — that is, the scatter does not look curvilinear or cone-shaped, the linear regression assumptions are met.
Once the assumptions of regression are met, the statistical data analysis section should address how the linear regression will be interpreted. The statistical data analysis plan should state that the linear regression will be evaluated for the model fit, that is, to examine if the F-value is statistically significant. The next part of the statistical data analysis is to discuss the R-square value of the linear regression. The R-square value, in this case, is what percent of all of the reasons why happiness can vary can be explained by the meaning in life scores.
The next part of the statistical data analysis plan would be to examine the beta coefficient, the t-value, and the significance level associated with the beta coefficient. If the significance level of the t-value is .05 or less, we can state that the beta coefficient is a statistically significant and that the predictor (meaning of life scores) is a significant predictor of happiness.
The final part of the statistical data analysis would discuss the significant beta in terms of the criterion variable happiness. If the beta coefficient is significant at the .05-level and is .70, for example, we could state that for each 1-unit increase in the meaning in life score, the happiness scores will increase by .70 units.
The statistical data analysis also approximates the sample size needed for the analysis. For example, the rule of thumb for a linear regression is 23 participants. This sample size is based on a statistical power of .80, with a large effect size, evaluated at the alpha of .05-level. Be careful about the effect size. As the effect size gets smaller, more participants are needed. For example, a medium effect size requires 53 participants, and a small effect size requires 400 participants. The effect size can be based on previous studies. The truth is that, graduate students only have so much time, money and energy to secure participants for dissertation research. We generally select a large effect size, and dissertation committees generally agree.
In sum, statistical data analysis involves discussing the specific statistic to be used (e.g., linear regression), the assumptions of the statistic (e.g., the assumptions of linearity and constant variance), and how the statistic would be interpreted. The sample size requirement is also part of the statistical data analysis, which states how many participants would be required for the study using a linear regression.
Statistical data analysis is an important part of the method section. The professionals at Statistics Solutions are experts in statistical data analysis plans, in sample size justification, and in explaining these aspects to graduate students. If you’d like help with the statistical data analysis, please contact us. We will make sure your statistical data analysis plan is accurate and that you understand the statistical data analysis.
