Research Design fo One-Way ANOVA

Answer

Research Design for One-Way ANOVA

1. What is your research question?

Does the mean income in constant dollars vary across a respondent’s marital status?

2. What is the null hypothesis for your question?

There is no difference in income in constant dollars across the marital status groups

3. What research design would align with this question?

The appropriate research design would be an analytic cross sectional design. Both the dependent variable and the independent variable can be measured by collecting data on both, at one point in time, on the same respondents (Frankfort-Nachmias & Leon-Guerrero, 2015; Wagner, 2016).

4. What dependent variable was used and how is it measured?

The dependent variable is respondent’s income in constant dollars. The variable is measured on a metric scale

5. What independent variable is used and how is it measured?

Marital status measured on a nominal scale. The categories are married, widowed, divorced, separated and never married.

Assumptions for one-way ANOVA:

 The dependent variable has to be measured on a numerical scale while the independent variable has to be categorical with at least three groups. The data has to assume homogeneity of variances (Klingenberg, 2016; Walden University Library. (n.d.)).

Analysis

Testing for Homogeneity of Variances

Levenes test was used to test for homogeneity of variances as shown in the table below. The level of significance P < 0.05, we thus reject the null hypotheses that variances are equal. Assuming inequality of variances the post-hoc test to use in this analysis is Games-Howell

6. If you found significance, what is the strength of the effect?

Description of results from ANOVA

From the results represented in the ANOVA table, it can be determined that on the overall, there is a statistically significant difference in the mean income in constant dollars across respondent’s marital status, F(4, 1518) = 25.399, (95%, p <0.05). The null hypothesis that income in constant dollars does not vary across the marital status groups is thus rejected. To be able to tell which specific marital status groups differed, the post-hoc test used was James-Howell because homogeneity of variances could not be assumed (IBM Corp. Released 2011). The results are shown in the table below.

Description of Post-Hoc Results

The multiple comparison table giving post hoc results indicate that there is a statistically significant difference respondents mean income in constant dollars in the following combinations: Married respondents had a 16705.764 score higher than the widowed (p<0.05) and a 18041.032 score higher than the separated (p<0.05). Widowed respondents had a 16705.764 lower score than married people (p<0.05) and a 11672.872 lower score that the divorces (p=0.028). Divorced people had a 13008.139 higher score than separated respondents (p=0.19) and a 13576.433 higher score than never married (p<0.00). All the remaining combinations did not show significantly different difference is the mean difference of income in constant dollars.

7. Explain your results for a lay audience and further explain what the answer is to your research question.

On the overall, respondents’ income in constant dollars differed across the different marital groups. Specifically though, the differences were only statistically different in some groups. To answer the research question; yes, generally the mean income in constant dollars varies across a respondent’s marital status.