Submit Your Answers To The Following Questions Using 905906

Submit Your Answers To The Following Questions Using the Anova Source

Submit your answers to the following questions using the ANOVA source table below. The table depicts a two-way ANOVA in which gender has two groups (male and female), marital status has three groups (married, single never married, divorced), and the means refer to happiness scores (n = 100): What is/are the independent variable(s)? What is/are the dependent variable(s)? What would be an appropriate null hypothesis? Alternate hypothesis?

What are the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance? Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance. Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status. Identify the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status. If alpha is set at .05, what conclusions can you make?

Paper For Above instruction

The purpose of this analysis is to examine the effects of gender and marital status on happiness scores using two-way ANOVA. The independent variables in this study are gender and marital status, while the dependent variable is the happiness score. The null hypotheses posit that there are no differences in happiness scores across genders, marital statuses, or their interaction. Conversely, the alternative hypotheses suggest that significant differences exist in happiness scores among these groups and their combinations.

The independent variables are clearly identified as gender and marital status. Gender has two levels: male and female, which constitutes one factor with 1 degree of freedom (df = level count minus one). Marital status has three levels: married, single (never married), and divorced, with 2 degrees of freedom. The interaction between gender and marital status measures whether the impact of one variable depends on the level of the other and has an df calculated as the product of their individual dfs, which is 2.

The degrees of freedom for the residual or error term can be calculated as total observations minus the number of groups and factors. Based on the total df of 99 (n - 1 for 100 observations), the df allocated to gender (1), marital status (2), and their interaction (2) sum to 5. The remaining degrees of freedom, 94 (99 - 5), are attributed to residual error.

The sum of squares (SS) for each source is provided in the table: gender SS = 68.15, marital status SS = 127.37, and interaction SS = 41.90. The error SS is 864.82, and total SS is 1102.24. To compute the mean square (MS) for each source, divide the SS by their respective df:

  • MS for gender = 68.15 / 1 = 68.15
  • MS for marital status = 127.37 / 2 = 63.685
  • MS for interaction = 41.90 / 2 = 20.95
  • MS for error = 864.82 / 94 ≈ 9.204

The F ratios are calculated by dividing each of the mean squares of the factors and interaction by the error mean square:

  • F for gender = 68.15 / 9.204 ≈ 7.41
  • F for marital status = 63.685 / 9.204 ≈ 6.92
  • F for interaction = 20.95 / 9.204 ≈ 2.28

Critical F values at alpha = 0.05, with corresponding degrees of freedom, can be obtained from F-distribution tables:

  • F critical for gender (df1=1, df2=94) ≈ 3.94
  • F critical for marital status (df1=2, df2=94) ≈ 3.08
  • F critical for interaction (df1=2, df2=94) ≈ 3.08

Comparing the calculated F values with the critical F:

  • Gender: 7.41 > 3.94 → significant effect
  • Marital Status: 6.92 > 3.08 → significant effect
  • Interaction: 2.28

Therefore, at the 0.05 significance level, gender and marital status significantly influence happiness scores independently, but their interaction does not have a significant effect. These results suggest that male and female may differ in happiness, and different marital statuses are associated with disparities in happiness scores, but the combination of gender and marital status does not produce an interaction effect.

References

  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied Statics for the Behavioral Sciences. Houghton Mifflin Company.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson.
  • Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the Behavioral Sciences. Cengage Learning.
  • Stevens, J. P. (2009). Applied Multivariate Statistics for the Social Sciences. Routledge.
  • McHugh, M. L. (2013). Multiple Comparison Procedures. ANOVA and the F-test. Biochemia Medica, 23(3), 302–307.
  • Montgomery, D. C. (2017). Design and Analysis of Experiments. Wiley.
  • Glass, G. V. (1976). Primary, Secondary, and Meta-Analysis of Research. Educational Researcher, 5(2), 3-8.
  • Keselman, H. J., et al. (1998). Testing Statistical Assumptions. American Psychologist, 53(4), 386–398.
  • Rao, C. R. (2001). Linear Statistical Inference and Its Applications. Wiley-Interscience.

Related Assignments