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 explain what the researcher might have done using the five steps of hypothesis testing, let's break it down:
Step 1: Formulate the null and alternative hypotheses
The null hypothesis (H0) would state that there is no significant difference in average salaries between the three job categories: clerical, custodial, and managerial. The alternative hypothesis (Ha) would state that there is a significant difference in average salaries among the job categories.
Step 2: Select the appropriate analysis
Based on the information provided, it seems the researcher conducted an analysis of variance (ANOVA) to compare the means of more than two groups. ANOVA is commonly used when dealing with multiple groups or categories.
Step 3: Set the significance level
The significance level, denoted as alpha (α), is generally set at 0.05 or 5%. It represents the threshold below which we reject the null hypothesis. In this case, the results indicate that p < .05, which means that the significance level was set appropriately at 0.05.
Step 4: Compute the test statistic and p-value
The test statistic mentioned in the question is 434.48, and the p-value is reported as less than 0.05. The test statistic value is typically obtained from the ANOVA analysis, and the p-value represents the probability of observing such an extreme result (or more extreme) under the null hypothesis.
Step 5: Analyze and interpret the results
Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in average salaries among the job categories. The test statistic being 434.48 further supports this conclusion, as large test statistic values generally suggest a significant difference between groups.
However, there are some potential problems with this study. Here are a few possibilities:
1. Small sample sizes: Particularly for the "Custodial" category, the sample size of only 27 may raise concerns about the representativeness of the data, potentially impacting the generalizability of the study's findings.
2. Potential confounding variables: The study did not mention control for other factors such as experience, education, or location. The presence of uncontrolled variables could influence the salaries across the job categories and affect the interpretation of the results.
3. Lack of randomization: The study did not specify how the participants were selected or assigned to their job categories. If the assignment was not truly random, it could introduce bias into the results.
4. External validity: The study focuses on one specific manufacturing company (ABC Manufacturing) and may not necessarily generalize to other industries or organizations.
Considering these potential problems, it is important to interpret the study findings with caution and consider the limitations that may affect the validity and generalizability of the conclusions.