Data Analytics Assignment #2 Using the Chi-Square Test to Assess Disparate Impact Background Given the downsides of the 4/5ths rule, including its high rate of false positives and its sensitivity to sampling errors, companies may rely on more sophisticated analyses. The 4/5ths rule is simply a rule of thumb adopted by the courts and is not based on a formal statistical test. An alternative method is the chi-square test. Consider the following example. Assume that the use of a knowledge test resulted in the following distribution: Pass Fail Total Men 70 90 160 Women 42 72 114 Total 112 162 274 These results indicate that if you disregard gender, 112 of 274 (40.9%) of all applicants passed the test, and 162 of 274 (59.1%) failed the test. Now you need to calculate the distribution you would expect to see if gender plays no role. Without any systematic effects of gender, you would expect men and women to have the same pass and fail ratios. This is the expected distribution. Pass Fail Total Men 65.4 (of 160 men, 40.9% should pass) 94.6 (of 160 men, 59.1% should fail) 160 Women 46.6 (of 114 women, 40.9% should pass) 67.4 (of 114 women, 59.1% should fail) 114 Total 112 162 274 Now you need to enter these data into Excel, as shown in the screenshot below. Then insert the formula you see at the top into cell B12. The result is the p value, which indicates whether the difference you observe between actual distribution and expected distribution is purely by chance. A p value lower than .05 is considered statistically significant. The result presented below has a p value of .25, which is not statistically significant (which indicates that there is no evidence of a gender effect on selection). Now you try! Use the Excel worksheet and consider the following observed distribution of selection method performance for White and African American job candidates. 1. Is there evidence of disparate impact according to your chi-square analysis? 2. If so, for which job candidates: African American candidates or White candidates? Pass Fail Total African American 66 140 206 White 50 64 114 In the PowerPoint for Chapter 4 and the first sheet of the data, you learned how to apply the 2 test of independence to assess whether there is evidence of disparate (adverse) impact for a selection knowledge test. At the bottom of the Excel workbook, you will see a sheet titled PhysicalAbility, which contains the observed data for a physical ability test used for selection. You will be comparing the pass and fail rates for Black and White candidates. 1. For the physical ability test, is there evidence of disparate impact according to your 2 test analysis? 2. If so, for which job candidates: Black candidates or White candidates? This analytics assignment will have you use a statistical test, the chi-square test of independence, to determine whether there is prima facie evidence of adverse (disparate) impact. Remember, adverse impact is when a seemingly neutral policy, selection criteria, etc. is leading to differences in selection, promotion, firing, etc. based on a protected class. We talked in class about using the 4/5ths rule as primary evidence for adverse impact. However, its just a rule of thumb and there are more precise ways to do it. Enter: the chi-square test. The chi-square test allows you to statistically compare the selection, promotion, and termination rates of a group compared to the rates we would typically expect. If they are statistically significantly different from each other (e.g., p value is less that .05), we can argue that we have prima facie evidence of adverse impact. That is, there is less than a 5% chance that those differences are occurring due to chance theres something more systematic happening. Instructions The PowerPoint walks you through an example on how to run the chi-square test on the KnowledgeTest tab. For this assignment, you should run those same analyses on the PhysicalAbility tab you can find the tab at the bottom of the Excel workbook. The PhysicalAbility tab contains the observed data for a physical ability test used for selection. You will be comparing the pass and fail rates for Black and White candidates. 1. What is the p-value associated with the chi-square test of independence? 2. For the physical ability test, is there evidence of disparate impact according to your 2 test analysis? 3. If so, for which job candidates: Black candidates or White candidates? 4. Consider your results. How would you describe your results to a hiring manager? That is, what would you tell the hiring manager about the physical ability test? Then, give the hiring manager some advice about 1) if they should use the test and 2) if they do use it, some recommendations about HOW to use it appropriately. Submission Instructions You should submit 2 documents: 1. The Microsoft Excel spreadsheet with the correlations using the Excel functions a. This is the equivalent of showing your work - do not just put a number in a cell. I want to see what you included in the formula/function you used to run the analyses 2. A word document with the answers to the questions above. Please use appropriate headings and labels in your document