# What is the standard error of estimate for supervisory ratings and dollar revenue? Show your calculations.

COLLAPSE

XYZ is a new start up company that has about 150 employees. The company provides plumbing services to residential customers. The company has had a high turnover of plumbers, mostly due to the plumber’s lack of knowledge and customer service skills. In order to address this, the company wanted to strengthen their selection process. So, they followed the procedure outlined below:

1. They selected 40 of their most successful plumbers (those who received outstanding customer feedback and had near zero calls from the customers about the work performed by these plumbers).

2. The company developed a 50-items multiple choice exam with four possible answers with only one answer being the correct one. Also, the company had another 50 questions consisting of True or False choices. Thus, the test had 100 questions.

3. The company asked the 40 plumbers to take the Plumbing Knowledge Test (PKT) during their work hours (they were paid for the time). These plumbers had an average of 2.5 years of plumbing experience and their experience ranged from 1 to 6 years. After the scoring of the test, the company correlated their test scores with the supervisory rating of their job performance which was measured using 5= Excellent, 4 = Above Average, 3 = Average, 2 = Needs Improvement, and 1 = Well Below Average. This process yielded a correlation of 0.68. The company also correlated the test scores of these 40 individuals with the revenue generated by each of them (\$). This process yielded a correlation of 0.43.

4. As the company decided that it is useful to use the test for future hires, they starting using it in the next round of hiring. They filled another twenty vacancies and the prospective applicants were asked to take the PKT and used a minimum cutoff score of 70% to hire the 20 plumbers. After six months, the company used the same process of correlating their test scores with supervisory rating (r = 0.52) and revenue generated in \$ (r = 0.37).

Discussion Questions:

1. What are the validation strategies used by this company? Explain.

2. What are the reasons for the validity coefficients to be different for the supervisory ratings and revenue generated for both the 40 employees sample and the 20 employees sample?

XYZ is a new start up company that has about 150 employees. The company provides plumbing services to residential customers. The company has had a high turnover of plumbers, mostly due to the plumber’s lack of knowledge and customer service skills. In order to address this, the company wanted to strengthen their selection process. So, they followed the procedure outlined below:

1. They selected 40 of their most successful plumbers (those who received outstanding customer feedback and had near zero calls from the customers about the work performed by these plumbers).

2. The company developed a 50-items multiple choice exam with four possible answers with only one answer being the correct one. Also, the company had another 50 questions consisting of True or False choices. Thus, the test had 100 questions.

3. The company asked the 40 plumbers to take the Plumbing Knowledge Test (PKT) during their work hours (they were paid for the time). These plumbers had an average of 2.5 years of plumbing experience and their experience ranged from 1 to 6 years. After the scoring of the test, the company correlated their test scores with the supervisory rating of their job performance which was measured using 5= Excellent, 4 = Above Average, 3 = Average, 2 = Needs Improvement, and 1 = Well Below Average. This process yielded a correlation of 0.68. The company also correlated the test scores of these 40 individuals with the revenue generated by each of them (\$). This process yielded a correlation of 0.43.

4. As the company decided that it is useful to use the test for future hires, they starting using it in the next round of hiring. They filled another twenty vacancies and the prospective applicants were asked to take the PKT and used a minimum cutoff score of 70% to hire the 20 plumbers. After six months, the performed two simple linear regression models.

a. In model 1, they used the supervisory rating as the criterion and the test scores as the predictor. They got the following equation:

Y = 1.28 + 0.38(X). The standard deviation of Y was 0.90 and the validity coefficient of the test with supervisory rating is 0.53.

b. In model 2, they used the dollar revenue as the criterion and the test scores as the predictor. They got the following equation:

Y = 358.08 + 1.70(X). The standard deviation of Y was 258.04 and the validity coefficient of the test with dollar revenue is 0.58.

Discussion Questions:

1. What is the standard error of estimate for supervisory ratings and dollar revenue? Show your calculations.

2. Assume that an applicant scored 85 on the test. What are his predicted supervisory ratings? Dollar revenue generated for the company?

3. Using the standard error of estimate you calculated above, provide the range of expected performance as indicated by the supervisory rating and dollar revenue for a person who scored 85 on the test.

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