The CEO of ABC manufacturing commissioned a study to look at the differences between the current salaries of her employees by employee job title. There were three job categories: clerical, custodial, and managerial. The study collected current salary data of the three groups and the researcher conducted a statistic and the results are presented below. Using the five steps of hypothesis testing, explain what the researcher might have done, including the appropriate analysis, and interpret the results. Are there any problems with this study? If so, explain what they are. (See grading rubric for additional paper requirements).
Average Salary
Clerical (n = 363) $27,838.54
Custodial (n = 27) $30,938.89
Manager (n = 84) $63,977.80
Test statistic = 434.48, p< .05
To address this question using the five steps of hypothesis testing, the researcher might have done the following:
Step 1: State the hypothesis
The researcher would start by stating the null hypothesis (H0) and the alternative hypothesis (Ha) based on the study's objectives. In this case, the null hypothesis could be that there is no significant difference in the average salaries among the three job categories (clerical, custodial, and managerial). The alternative hypothesis would state that there is a significant difference among the job categories.
Step 2: Choose the appropriate analysis
Since the researcher wants to compare the average salaries among the three job categories, an appropriate analysis to use here would be Analysis of Variance (ANOVA). ANOVA allows for comparing means across multiple groups.
Step 3: Set the significance level (alpha)
The significance level, denoted as alpha (α), determines how much evidence is needed to reject the null hypothesis. Commonly used values for alpha are 0.05 or 0.01. In this case, the result states that p < 0.05, which suggests that a significance level of 0.05 was chosen.
Step 4: Analyze the data and calculate the test statistic
The researcher would perform the ANOVA analysis using the data provided for the three job categories' average salaries. This would involve calculating the test statistic, which helps determine the likelihood of observing the observed differences in salary due to chance. In this case, the given test statistic is 434.48.
Step 5: Interpret the results and make a conclusion
Based on the test statistic and the chosen significance level, the researcher would compare the obtained p-value to the significance level. If the p-value is less than the significance level (p < α), it would indicate that the differences in average salaries across the job categories are statistically significant. This means that the null hypothesis would be rejected in favor of the alternative hypothesis, concluding that there is a significant difference in average salaries among the job categories.
Problems with this study:
1. Small sample sizes: The sample sizes for custodial (n = 27) and managerial (n = 84) job categories are relatively small, which could limit the generalizability of the results. Larger sample sizes would provide more robust and reliable findings.
2. Lack of information about data collection: The study does not provide information about how the current salary data was collected. Without information on the sampling method or any potential biases in data collection, the study's validity and representativeness could be questioned.
3. Insufficient information on variables: The study only considers job categories as a factor in determining salary differences. It does not account for other potentially influential variables such as years of experience, education level, or performance. Ignoring these factors could lead to incomplete conclusions about the salary differences among the job categories.
4. Limited statistical analysis: The study only presents the test statistic and a statement indicating p < 0.05. It lacks details about the specific statistical tests used, assumptions made, and any post-hoc analyses conducted to further investigate the salary differences. Providing additional statistical information would enhance the study's rigor and transparency.