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Analyze whether there are significant differences in salary and compensation across different grades and genders, based on the provided data. Conduct statistical tests including one-way ANOVA, two-way ANOVA with and without replication, and interpret the results to assess if equal pay for equal work exists between males and females. Clearly state hypotheses, show test outcomes, and draw conclusions about population means and independence of variables.

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Ensure that in your analysis, you accurately formulate null and alternative hypotheses for each statistical test, including differences in means across grades and genders, as well as interaction effects. For the one-way ANOVA on salary by grade, compile all salary data corresponding to each grade and perform the test assuming equal variances. The null hypothesis posits that the population mean salaries are equal across grades, while the alternative suggests at least one grade differs.

With the ANOVA output, compare the calculated F-value against the critical F-value at a 0.05 significance level. If the p-value is less than 0.05, reject the null hypothesis, indicating that salaries differ significantly by grade. If not, conclude there is no significant difference in mean salaries across grades. This analysis confirms whether employees within different pay grades receive comparable pay, given the assumption of equal variances.

Moving to the two-way ANOVA with replication by grade and gender, interpret the main effects and interaction. The hypotheses here for the main effects are: (a) no difference in average salaries between genders; (b) no difference in average salaries across grades. The null hypothesis for the interaction claims that there is no interaction effect between grade and gender on salary.

Utilize the ANOVA table outputs, focusing on p-values and F-statistics. A significant p-value (less than 0.05) for the gender effect suggests pay disparities between males and females. Similar conclusions apply to grade effects. If the interaction term is significant, it indicates that the difference in salaries between genders varies across grades, complicating the interpretation of main effects. Conversely, a non-significant interaction implies that gender effects are consistent across grades.

For assessing the equivalence of compensation (compa) values across grades and genders, conduct similar two-way ANOVA tests. Null hypotheses include: (a) no difference in compa means across grades; (b) no difference across genders; and (c) no interaction effect. Use the compa values for each employee, checking if mean differences are statistically significant or if the variables operate independently.

In the context of variable selection for a simple two-way ANOVA without replication, choose a variable of interest that might influence salary or compensation, such as performance rating or years of service. This analysis evaluates whether the mean values differ significantly across categories of the selected variable and gender, indicating potential disparities or factors influencing pay. Justify the choice based on the variable's relevance to pay equity or compensation structure.

Summarize your overall conclusions regarding gender pay equity based on your analyses. Determine whether your findings support the existence of equal pay for equal work, considering potential confounding factors and interaction effects. Discuss implications for policy or further research.

References

  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Glass, G. V. (1982). Primary, secondary, and meta-analysis of research. American Educational Research Journal, 19(3), 426-442.
  • Hatcher, L. (1994). A Step-by-Step Approach to Using the SAS System for Factor Analysis and Structural Equation Modeling. SAS Institute Inc.
  • Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis. Pearson.
  • McHugh, M. L. (2013). The Chi-Square Test of Independence. Biochemia Medica, 23(2), 143–149.
  • Ramsey, F. L., & Schafer, D. W. (2010). The Statistical Sleuth: A Course in Methods of Data Analysis. Cengage Learning.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.
  • Willing, B. (2009). Fundamentals of Applied Statistics. Springer.
  • Yuan, K., & Bentler, P. M. (2000). Structural Equation Modeling with Data Marred by Outliers. Journal of Experimental Education, 68(1), 113-130.
  • Zhou, X. (2014). The Use of ANOVA in Social Science Research. Journal of Modern Education Review, 4(6), 437-445.

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