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Propter, lnc, It all started out peaceably enough. Tom Johnson, one of the new service reps, asked AI Washington and Michael Post about their salaries. It was an innocent enough question and the answers suggested that all three were making about the same money. Nobody seemed concerned. Then, Michael Post said that he had seen a memo on his boss' desk on which salaries for the entire department were listed and noticed something "funny." All three of them were near the bottom of the list. In fact, he said, "Just about every other black in the department was in the bottom half of the list." Well, this started the three of them wondering out loud about whether their company, Propter, Inc., was discriminating against minorities. They kicked it around all through lunch and then talked about it again each day for the next week. And each day, somebody would come in with information from one of the other offices from throughout the country that continued to suggest that all minorities, not just black employees, were not being paid on par with their white counterparts. They had "rough" information from four additional offices that, when they calculated averages, suggested that minorities were making about $250 a month less than white employees. This incensed Tom Johnson. He told the others, "When Al Miller recruited me here last year, he told me that Propter's management believed in affirmative action. He promised me that I would go as far in this company as my effort and good work would take me. I'm not saying that this past year has been bad, but this salary stuff makes me wonder about whether I should stay or start looking for a place where minorities are treated the same as whites!" Al and Michael agreed. The more they talked, the more they felt betrayed by a company that at first looked like a place that would ignore skin color. Indeed, they were all impressed with the company's strong affirmative action stance. They were told that advancement, and salary, would depend on how well they did their jobs - that they could expect to move from an Assistant Service Rep (Grade 1) to Service Rep (Grade 2) in two to three years and then move to Senior Service Rep (Grade 3) somewhere from three to four years later. They were led to expect annual performance reviews, with pay raises determined by their performance during the previous year. They liked the developmental program Propter had to offer and looked forward to the responsibility that their jobs would offer as they moved up the career progression ladder. It was disappointing to think that Propter might turn out to be the kind of place where skin color would limit their opportunities. Tom Johnson didn't say anything for several weeks about the salary incident. On his own, however, he started reading about fair employment law and his options if he believed that his civil liberties were being violated. He even called the local office of the Equal Employment Opportunity Commission (EEOC) and spoke with a field agent about his situation. The agent, Mr. Mark Malone, suggested that he bring the matter up with his supervisor. Malone told him that, in his experience, appearances were not always what they seemed, and that usually matters such as this are easily explained by the company. He did, however, clarify that a $250 per month salary difference between minorities and non-minorities was not trivial and would, indeed, command the attention of EEOC if Mr. Johnson were still concerned with this issue after going through official company channels. Tom Johnson, escorted by his two friends, went to see Howard Kirk, his department manager. Kirk seemed somewhat agitated when Johnson confronted him with the "facts." He simply dismissed their protest as complete nonsense. He told the three of them to leave the management work to managers and to get back to work so they could learn their jobs well enough to earn a good evaluation and, thus, a good pay raise next year. When Tom Johnson "wondered out loud" about whether their performance evaluations were chosen to justify lowered pay raises to minorities, Kirk flew off the handle. He abruptly told them to quit trying to cause trouble. He informed them, rather curtly and very loudly, that "... salary is based on performance and loyalty to the company. The single best way you can improve your salaries is to pay as much attention to your jobs as apparently you're paying to information that is none of your business." He then "dismissed" them. Predictably, Mr. Johnson found the content and tone of Mr. Kirk's remarks offensive. Together with Al Washington and Michael Post, they have now organized a small group of minority peers who have threatened to visit the EEOC claims office in order to pursue their conviction that Propter practices discriminatory pay practices. Larry Greer, President of Propter, got word of the problem almost immediately through the grapevine. Greer called a meeting with Johnson, Washington and Post that afternoon. It was a more relaxed conversation. Greer began by asking them to explain their concerns. Tom Johnson went through the "facts," this time adding information about how they were treated by Howard Kirk. Greer responded by assuring the three of them that Propter did not discriminate against anybody. He repeated Mr. Kirk's message about how pay is determined, but without the offensive tone. Indeed, Mr. Greer outlined the voluntary affirmative action program initiated by Propter over two years ago as being just an example of the philosophy that Propter values what people do on the job over their race or gender. Mr. Johnson was willing to listen to the pay policy and talk about the affîrmative hiring program, but continued to focus on the apparent salary differences that occurred despite such policies. He insisted that salary equity be achieved and, thus, would not relinquish his claim of discrimination. However, because he was impressed by Mr. Greer's statements regarding the company's affirmative stance in hiring, Mr. Johnson expressed a willingness to meet with Greer again, once additional information became available. Greer promised that he would report back to his three employees personally at the second meeting, based on having looked into this matter and into the data relevant to it. Mr.Johnson, and the others, seemed willing for Mr. Greer to gather and organize that information. Assignment You have been appointed to a task force to investigate this discrimination claim. Mr. Greer has a series of issues that your committee must resolve. He has given you access to the employment and pay histories for service reps. These data are contained in the PROPTER.XLS file and are described in the Data Description section. You will need to examine the employment and pay history data contained in this file and attempt to resolve the issues brought forth by Mr. Johnson. Based on your understanding of the issues and your interpretation of the employment and salary data, write a brief report to Mr. Greer summarizing your beliefs about Propter's liability. The attached Case Questions will guide your thinking. Use important details from your analysis to support your recommendation. Data Description The PROPTER.XLS file contains the employment and salary data for Propter's 140 employees. A partial listing of the data is shown below. ID Pay Grade Gender Race Married Age Tenure Rating Salary 1 1 2 2 0 18 0.5 2 890 2 1 2 1 0 25 2.4 3 1360 3 2 2 1 0 23 3.6 7 2070 4 1 1 2 0 26 1.9 3 1190 5 2 2 1 1 22 3.4 6 1290 These data are coded as follows: ID Number: Sequential ID number assigned to all employees. Pay Grade: Pay grade (= 1,2, or 3). Gender: 1, if female, 2, if male. Race: 1, if white, 2, if minority. Married: 1, if married, 0, if non-married. Age: Age in years at last birthday. Tenure: Number of years employed as a service representative at Propter. Rating: Employee performance rating, on a l0-point scale, where 1 = poor performance and 10 = excellent performance. Salary: Currently monthly salary, expressed in dollars. Case Questions:Propter, Inc. 1. What is the difference between the average salary of minorities and non- minorities? Does this evidence support Mr. Johnson's claim of discrimination? 2. What proportion of minority and non-minority employees are found in each pay grade? How do these proportions influence Mr. Johnson's claim of salary discrimination? Do these proportional differences suggest discrimination in promotions across racial groups? 3. What is the average tenure of minority and non-minority employees in each pay grade? Do these results suggest discrimination in promotions across racial groups? 4. When was the company's Affirmative Action program started? Does this information help explain why more minorities are in the lower pay grades? Explain. 5. What data should be examined to see whether Propter rewards performance and loyalty, as claimed by Mr. Greer? 6. What type of analyses would indicate if pay was dependent upon performance and loyalty? Do these results suggest that Propter rewards performance and loyalty? Explain. 7. Do your analyses support Mr. Johnson’s allegation of discrimination? Briefly explain why the salary data suggest apparent discrimination and what will "remedy" this salary discrepancy? CASE ANALYSIS PROCESS These cases are designed to create a problem-solving environment that closely matches the environment experienced in an actual business. Case solutions require significant statistical analysis and interpretation of results. The focus is on creating a concise professional report that responds to the original business or public policy question. In contrast, textbook problems often require only a set of statistical analyses and computations. To simulate an actual business setting, you should use software to perform the statistical computations and a text editor to prepare a professional-looking report. These cases are perfect for team work. Please try to keep everyone involved in discussions. Working in teams permits a broader examination of the case questions and fosters useful discussion. In addition, most real-life business problems are solved by teams. Thus students gain practical experience by working with others on a common problem. At the beginning of the semester, I will give a series of questions designed to help guide your analysis. The ultimate goal of your analysis, though, is a formal written report that helps solve the original problem. After you get comfortable with the cases, I will stop giving specific questions and let you work on the business problem. Statistical studies follow a general structure, with a number of side diversions resulting from discoveries made along the way. The process usually consists of the following steps: 1. Identifying the business analysis questions 2. Converting business questions into statistical questions 3. Performing a descriptive analysis of the data 4. Applying formal analysis procedures 5. Developing conclusions and recommendations 6. Identifying unusual outcomes and future analysis Each of these steps should be accompanied by written descriptions in the final report. After all of the analysis and blocks of writing are completed, you may wish to move blocks of text and statistical output around to produce a more coherent report. The final step is then to prepare the Executive Summary, which is the very first section of your report. Each step entails a wide range of options. 1. IDENTIFYING THE ANALYSIS QUESTIONS Your first task is to read the entire case carefully and make notes concerning key details. From this reading, you can begin to identify the important business questions in the case. In a real business application, this process consists of talking with key managers and other knowledgeable persons. That process usually leads to an analysis proposal, which is then "signed off' by the executive responsible for underwriting the study. 2. CONVERTING ANALYSIS QUESTIONS INTO STATISTICAL QUESTIONS Statistical analysis can answer specific well-structured questions. You have seen many examples of these questions in textbook problems and examples. An important task in any applied study is to convert the case analysis questions into statistical questions. This process requires thorough understanding of the problem requirements and of the available data. In many cases the available data, including the data form and source, limit the kinds of analysis that are possible. 3. PERFORMING A DESCRIPTIVE ANALYSIS OF THE DATA Performing a descriptive analysis provides the analyst with a general picture of the data. Means, variances, ranges, and simple correlations are computed for appropriate variables. The analyst may also prepare histograms, box-and-whisker plots, and other graphical displays. If the data have been collected over time, creating time plots will help identify patterns that change over time. From this analysis, you can define the range of applicability for your analysis conclusions. 4. APPLYING FORMAL ANALYSIS PROCEDURES By this point in the study, you will have developed a good understanding of the problem issues and the basic structure of the data. In addition, if you have been writing intermediate results, you will probably have additional questions. These can be compared against the assumptions required for the various standard statistical procedures. Do you have everything needed for a formal hypothesis test? Do the data satisfy the assumptions required for regression analysis? Which of the available analyses will answer the questions you have formulated? The analysis should be driven by the questions and not by a desire to demonstrate how clever you can be with various statistical tools. You should be willing to try a variety of procedures to test the stability of the conclusions. For example, means, standard deviations, and other descriptive statistics should show the same results as bar charts and graphs; and regression models of different forms should provide similar conclusions. Analysis of residuals and analysis of outliers in general evince a careful analyst. Study of the distribution patterns for important variables indicates the validity of your analysis. Many strange patterns can occur in data, and you should try the analysis in enough different ways to ensure reliability of the results. Incidentally, the ability to support different analyses is a major advantage of the computer analysis environment. This is also the time to perform some basic reality checks on your conclusions. Do the results make sense, given what you know about the area being studied? You can also ask other persons with experience in problems of this type to react to your initial conclusions. Computer-based problem solving can create undeserved support for certain answers, if there were initial errors in the analysis. Older, more tedious non-computer-based analysis procedures were closer to the data and the detailed steps. Thus, errors in computation or analysis approach were more likely to be detected. In our modem computer-based statistical analysis environment, results must be examined for reasonableness and reality. 5. DEVELOPING CONCLUSIONS AND RECOMMENDATIONS At this point you should review the initial objectives and questions to confirm that all of the required analyses have been completed. If you have been writing after completing each analysis step, you already have the basis for discussion of your major conclusions. Key ideas should be extracted and combined for a smooth-flowing discussion. Some of the more basic details can be moved to an appendix. This is also the time to write the Executive Summary. Ideally this step involves bringing together your results and then writing a clear discussion that links them. However, real studies do not always proceed linearly (such that the previous step is completed before the next step is begun). Thus you may identify additional questions when you are preparing your conclusions. In that case you must cycle back to perform additional analysis. 6. IDENTIFYING UNUSUAL OUTCOMES AND FUTURE ANALYSIS Research, analysis, and problem solving are an ongoing process. Answers at one point identify additional questions. Analysis often indicates additional paths that should be followed. However, studies in a business or public policy environment must reach a close. Decision makers require timely answers, and limited resources are allocated to each study. Personnel and financial resources are allocated to a study, and results must be produced within resource limits. As a student, you have only so many hours to devote to each course and/or to special projects. Thus completion of a study is important. Closure typically includes a final written report and/or an oral presentation. Given the need for closure, you will often be left with unexplored questions in your study. These should be documented and noted as questions for future work. In some cases, the questions might be important enough to justify another study. Your task is to document the additional questions objectively and to suggest how they might be answered. Information users must then decide whether additional work should be undertaken. PREPARING THE WRITTEN REPORT Since producing a written report is your ultimate objective, you would be wise to begin writing your report after you have identified the analysis questions but simultaneously with performing the statistical calculations. For example, start the case report by preparing the introduction and the project scope. Initial statistical analysis can then be transferred to your emerging report. Next, prepare comments on the initial statistical work, and move back to perform more statistical computations. This strategy has the advantage of encouraging you to keep your results well organized as you proceed. More importantly, the process of writing forces you to define specific questions that you can then answer by using statistical analysis. And good writing almost always requires several revisions. For these cases, your report will typically be limited to two (or three pages only if necessary) with appendices that present specific analyses and data displays, again, if necessary. Integrating the charts and tables to your report always makes it an easier read for the audience. The report should begin with an Executive Summary of one to three paragraphs. This summary-which is the last item written-should identify the problem, indicate your approach to solving it, and concisely state your conclusion. The body of your report should indicate how you developed your conclusions and recommendations. Begin with a concise presentation of the question from the business perspective and explain how you conducted the analysis. Define the data set and specify the statistical procedures you used. Include specific statements of statistical models and hypothesis tests, and outline the results. Discuss the statistical results, indicating how they provide a solution to the case problem. Include additional observations and extensions of your results, as appropriate, given the case objective. Business writing tends to be short and concise. Managers and executives seek results and conclusions. They need to understand your analysis and conclusions. In addition, any limitations and alternatives need to be clearly expressed. Managers do not have time for extensive reading of analysis details. In many instances, the Executive Summary is the only part of a report that is read. Thus you should prepare the Executive Summary with great care. The results of all of your hard work may be revealed or hidden depending on the quality of the Executive Summary. Persons who seek more detailed information will read the entire report. The report should describe your analysis and present conclusions together with supporting evidence. Well-designed graphs and figures greatly enhance communication. Mathematical equations and data tables provide strong reinforcement for readers who desire rigorous and complete understanding. However, you need to avoid both intimidation and boredom. Analysis details, including detailed statistical computer outputs and supporting graphs, should be in an appendix. These reports are a series of layers that supply further depth as more accessible layers are peeled away. The first layers, however, must provide the most important results and key conclusions. Think about this design for your report as you prepare case solutions. CONCLUSION Work on the cases that you will be assigned can provide a valuable capstone to your study of applied statistics. By developing solutions to applied problems you will think carefully about the assumptions behind various statistical procedures. Executive Summary: 1-3 paragraphs, ** Last part written *** identify the problem, indicate your approach to solving it and concisely state conclusion Introduction: ~1 Paragraph,  intro to the case, project scope.  BODY: indicate how you developed your conclusions and recommendations Part 1: Begin with concise presentation of the question from the business perspective and explain how you conducted the analysis Part 2: Define the data set and specify the statistical procedures used Include specific statements of statistical models and hypothesis tests · Results: Discuss the statistical results, indicating how they provide a solution to the case problem Include additional observations and extensions of your result Identify unusual outcomes, go into detail on the unexplored questions in the study (Questions for future work), might be important enough to justify another study.  Document the additional questions and suggest how they might be answered and decide whether or not additional work should be taken Conclusion Questions 1. What is the difference between the average salary of minorities and non- minorities? Does this evidence support Mr. Johnson's claim of discrimination? $530 difference between the average salary of minorities vs whites. This data alone would suggest that Mr. Johnson’s claim of discrimination is accurate. Initial argument was centered around 230$ difference but it ended up being a larger one 2. What proportion of minority and non-minority employees are found in each pay grade? How do these proportions influence Mr. Johnson's claim of salary discrimination? Do these proportional differences suggest discrimination in promotions across racial groups? the average salary across pay grades by race does not have much of a difference. If they are equal across pay grade, why are they not equal overall? Number of people across each pay grade: There are a lot more whites in the promoted positions, and a lot more minorities in the lower positions. This may suggest discrimination when it comes to promoting employees. However, the company’s stance is that advancement and salary would be dependent on how well they did their jobs, and they could expect to move from Grade 1 to Grade 2 in two to three years, and to Grade 3 three to four years later. So how long have most minorities been at the company vs whites? And how have the average performance reviews differed? Are they kept at lower levels because of discrimination, or because of lower performance reviews? Are they getting lower performance reviews because of discrimation? 3. What is the average tenure of minority and non-minority employees in each pay grade? Do these results suggest discrimination in promotions across racial groups? On average, whites have been working at the company longer than minorities. This could argue that there is not discrimination. Minorites seem to be getting promoted faster than whites. 4. When was the company's Affirmative Action program started? Does this information help explain why more minorities are in the lower pay grades? Explain. The affirmative action program started over two years ago. This would explain why more minorities were hired in recent years, so would currently be in lower pay grades. 5. What data should be examined to see whether Propter rewards performance and loyalty, as claimed by Mr. Greer? Correlation between rating and net salary is .845. that is a high position correlation. Showing that salary is based on performance rating, as the company claims. This is shown in the graph: 6. What type of analyses would indicate if pay was dependent upon performance and loyalty? Do these results suggest that Propter rewards performance and loyalty? Explain. 7. Include in Results: Do your analyses support Mr. Johnson’s allegation of discrimination? Briefly explain why the salary data suggest apparent discrimination and what will "remedy" this salary discrepancy? STEPS: 1. Identifying the business analysis questions 2. Converting business questions into statistical questions 3. Performing a descriptive analysis of the data 4. Applying formal analysis procedures 5. Developing conclusions and recommendations 6. Identifying unusual outcomes and future analysis Sections: · Executive Summary: 1-3 paragraphs, ** Last part written *** identify the problem, indicate your approach to solving it and concisely state conclusion · Introduction: ~1 Paragraph, intro to the case, project scope. · BODY: indicate how you developed your conclusions and recommendations · Part 1: Begin with concise presentation of the question from the business perspective and explain how you conducted the analysis · Part 2: Define the data set and specify the statistical procedures used · Include specific statements of statistical models and hypothesis tests · Results: Discuss the statistical results, indicating how they provide a solution to the case problem · Include additional observations and extensions of your results · Identify unusual outcomes, go into detail on the unexplored questions in the study (Questions for future work), might be important enough to justify another study. · Document the additional questions and suggest how they might be answered and decide whether or not additional work should be taken · Conclusion · Introduction: Identifying the business analysis questions, Converting business questions into statistical questions · Within Propter Inc, there have been several complaints by minority employees about notable salary differences compared to their white colleagues after viewing a salary memo. After learning about these concerns, Larry Greer, President of Propter, set up a meeting with the minority employees; where he explained that salary is formulated upon loyalty and performance to the company. However, Mr. Greer decided to investigate the discrimination claim further by hiring a task force. When examining Mr. Johnson’s claim, it is understandable that Mr. Johnson has approached the head of the company over discrimiation concerns. Mr. Johnson brought forward this claim based on the average salary of whites vs minorities alone, and he is correct in that whites on average make a notable amount more than than minority workers. However, average salary alone is not enough to draw a conclusion in this case. Factors such as average pay grade, tenure, and performance scores must be looked at in order to determine what factors are truly contributing to a discrepancy between average salaries across race. These factors were examined and statistically analyzed to give further insight as to what could be causing this pay gap. Propter, Inc states that pay raises and position advancements are based on annual performance reviews and the amount of time an employee has been at the company. It is essential to investigate whether or not the company’s claimed stance on advancement is accurate. · Body: The difference between the average salary between whites and minorities at Propter, Inc is $530 monthly, with whites making an average of the higher salary. However, once the data is split up across pay grades, there no longer seems to be an inconsistency between salary across race. Table 1 shows the average salary of whites and minorites across each pay grade. The averages for each pay grade do not have notable differences. Table 1: The finding of average salary across pay grade is helpful, but it leads to the another question: if the salaries are equal across pay grade, why are they not equal overall? It was then looked at how many people in each race group belonged to each pay grade. The number of employees per pay grade is shown in Table 2: Table 2: The data in Table 2 shows that there are many more white employees in the higher pay grade, and many more minority employees in lower pay grades. This explains why the average salary across pay grade is more consistent between races than the overall average salaries. However, new concerns emerge. Why are there fewer minorities in higher positions? Could this be a result of discrimination? Propter, Inc states that pay raises and position advancements are based on annual performance reviews and the amount of time an employee has been at the company. For this case, it is essential to determine if the company adheres to this policy. The average tenure of whites at the company is 3.37 years, whereas the average tenure for minorities is 2.43 years. This information shows that whites have been at the company for an average longer amount of time than minorities. In addition, Propter Inc has implemented the affirmative action hiring program just over two years ago. This could explain why more minorities were hired in recent years, so would currently be in lower pay grades, as opposed to being due to discrimination. In addition, Table 3 shows the average tenure across race per pay grade: Table 3: Based on this data, minorities have spent an average of less time in each pay grade, indicating that minorities are being promoted in less amount of time than their white counterparts. When it comes to rewarding employee performance, the correlation between rating and net salary is .845. This is a high positive correlation, suggesting that the higher an employee’s rating, the higher the net salary is, this is shown in Graph 1. Graph 1 Results: · There is no discrimation based on race for salary · Although there is a big difference between overall average salaries, when broken down by pay grade there was no noteworthy difference · There are more whites in higher positions and minorities in lower positions, but when looking at tenure minorities have been at the company for less time than whites, which would explain why whites are in higher positions- the company says it takes a couple of years to be promoted · In addition, Propter Inc has implemented the affirmative action hiring program just over two years ago. This could explain why more minorities were hired in recent years, so would currently be in lower pay grades, as opposed to being due to discrimination. · This information shows that whites have been at the company for an average longer amount of time than minorities. Although this might look like discrimation, the company started affirmative action over two years ago, so it would make sense that minorities were hired in more recent years · The high positive correlation between rating and salary-> this shows that Propter Inc goes by performance when it comes to salary raises · This should be reassessed in a couple of years and see where minority salaries are · We need info on at what point on average did minorites leave/get fired from the company. Because if they were fired before being able to be promoted it would skew the data to look like the minorities were being favored for promotion (Table 3) Propter, Inc. Case Study Introduction Within Propter Inc, there have been several complaints by minority employees, such as Mr.Johnson, about notable salary differences compared to their white colleagues after viewing a salary memo. After learning about these concerns, Larry Greer, President of Propter, set up a meeting with the minority employees; where he explained that salary is formulated upon loyalty and performance to the company. However, Mr. Greer decided to investigate the discrimination claim further by hiring a task force. When examining Mr. Johnson’s claim, it is understandable that Mr. Johnson has approached the head of the company over discrimiation concerns. Mr. Johnson brought forward this claim based on the average salary of whites vs minorities alone, and he is correct in that whites on average make a notable amount more than than minority workers. However, average salary alone is not enough to draw a conclusion in this case since many of the minority employees were hired within the last two years due to the affirmative action policy. Factors such as average pay grade, tenure, and performance scores must be looked at in order to determine what factors are truly contributing to a discrepancy between average salaries across race. These factors were examined and statistically analyzed to give further insight as to what could be causing this pay gap. Propter, Inc states that pay raises and position advancements are based on annual performance reviews and the amount of time an employee has been at the company. It is essential to investigate whether or not the company’s claimed stance on advancement is accurate. Investigating Pay Histories In order to understand Mr.Johnson's claims regarding the salary differences between minorities versus non-minorities, it is important to first calculate the average salary between each group. Through creating a Pivot table to understand the averages of the categorical data, we found that minority individuals make an average of 2820$ whereas non-minorities make an average of 3351$. The difference between the average salary between whites and minorities at Propter, Inc is $530, with whites making an average of the higher salary. However, once the data is split up across pay grades, there no longer seems to be an inconsistency between salary across race. Table 1 shows the average salary of whites and minorities across each pay grade. The averages for each pay grade do not have notable differences. Result - Executive Summary