Compensation 101 for Federal Contractors: Part 2 of 2 Statistical Concepts and Methods BCG Institute for Workforce Development (BCGi) The following presentation is not to be construed as legal advice. For specific legal advice, please consult your corporate counsel or a labor attorney.
Contact Information Daniel Kuang, Ph.D. Vice President of Legal and Audit Support Services 916-294-4250 ext. 145 dkuang@biddle.com Fe Ramos EEO/Sr. Consultant mramos@biddle.com 1-800-999-0438 ext. 129 The following presentation is Copyrighted by Biddle Consulting Group, Inc. 2
Overview of Biddle Consulting Group, Inc. Leader in the EEO/AA Consulting Niche Affirmative Action Plan (AAP) Consulting & Fulfillment Assessments EEO Litigation Consulting /Expert Witness Services Compensation Analysis Publications/Books BCG Institute for Workforce Development Nation-wide Speaking and Training Largest EEO/AAP Consulting Firm (since 1974) 40-50 EEs Develops thousands of AAPs for hundreds of contractors Audit and compliance assistance Enterprise AAP software used by hundreds of contractors AutoGOJA job analysis software (geared for validation) Test Validation & Analysis Program (TVAP) CritiCall callcenter testing for 911 operators (900+ clients) OPAC Administrative skills testing (1,000+ clients) Situational Assessments (General and Nursing) C4 callcenter testing for in/outbound call takers Over 200+ cases in EEO/AA (both plaintiff and defense) Focus on disparate impact/validation cases Proactive and litigation/enforcement pay equity studies COMPare compensation analysis software EEO Insight : Leading EEO Compliance Journal Adverse Impact Analysis (2 nd ed.) / Compensation Analysis (1 st ed.) 3,000+ members who receive free webinars and publications BCGi Platinum paid subscription membership w/eeo tools Several consultants on national speaking circuit Topics include 3 EEO compliance, statistics, and validation
Disclaimer Disclaimer OFCCP audits are a complex topic But they are an important topic And one that has significant ramifications We are not giving legal advice This presentation has been designed to benefit all stakeholders in the EEO compliance community 4
Agenda Compensation 101 Part 1: Quick Recap Laws and Regulations Compensation Analysis: Logic (t-test) Statistical Model: t-test Compensation Analysis: Logic (Regression) Statistical Model: Regression
Laws and Regulations
Laws and Regulations Executive Order 11246 According to 41 CFR 60-2.17(b)(3), contractors must evaluate their compensation system(s) to determine whether there are gender-, race-, or ethnicitybased disparities. According to 41 CFR 60-20.5, the employer s wage schedules must not be related to or based on the sex of the employee. 7
Laws and Regulations Title VII of the 1964 Civil Rights Act It shall be an unlawful employment practice for an employer to fail or refuse to hire or to discharge any individual, or otherwise to discriminate against any individual with respect to his compensation... because of such individual's race, color, religion, sex, or national origin. Lilly Ledbetter Fair Pay Act of 2009 Amends Title VII, the ADEA, ADA, and the Rehabilitation Act of 1973 to clarify discriminatory compensation decisions/practices are unlawful and the discrimination occurs each time the compensation is paid. 8
Analysis Logic 9
Analysis Logic We understand why it is important to analyze compensation data Ensure fair-pay and equity Stay in compliance with federal laws and regulations What are you looking for? How do you investigate pay disparity?
Analysis Logic: What? Q: What are we looking for in a comp analysis? A: We are looking for difference in pay. Examples: Is there difference in pay between men v. women? Is there difference in pay between whites v. minorities? 11
Analysis Logic: Simple Simplest Case: 1 to 1 comparison Employee Gender Salary ($) Mary Female 40,000 Bob Male 45,000 How confident are you that this difference is not due to chance alone? Very confident! Probability=100% that there is a $5,000 difference Male is paid more than Female 12
Analysis Logic: Less Simple Less Simple Case: 2 to 1 comparison Employee Gender Salary ($) Mary Female 40,000 Bob Male 45,000 Jane Female 46,000 How do you determine if there is difference in pay between Male and Females now? Mary < Bob < Jane Answer: Compare Average Group Salary 13
Analysis Logic: Less Simple Employee Gender Salary ($) Mary Female 40,000 Bob Male 45,000 Jane Female 46,000 Average Average Female Female Female = = 40,000 + 2 $43,000 46,000 Average Average Male Male Male = = 45,000 1 $45,000 Average Female $43,000 < Average Male $45,000 How confident are you that this difference is not due to chance alone? 14
Analysis Logic: Significance Testing When is differences in group averages meaningful and statistically significant? Statistical significance testing: Evaluates group difference and determines: Probably of observing the difference given the data Whether the difference is due to chance alone Events that would occur with p 0.05 are statistically significant. Probability of less than 1 in 20 random trials 15
Finding statistical significance is a function of Statistical Power. Statistical Power is a function of 3-factors 1. Effect Size: The size of the difference between groups o Larger Effect Size is more powerful 2. Standard Deviation: The average difference in pay within each group. o Analysis Logic: Significance Testing Smaller Standard Deviation is more powerful 3. Sample Size: The number of individuals in the data o Larger Sample Size is more powerful 16
Analysis Logic: Significance Testing Effect Size Small Difference Less confident the difference is real. Large Difference More confident the difference is real. 17
Analysis Logic: Significance Testing Standard Deviation Std. Dev. is average difference in pay within each group Std. Dev. is computed separately for Male and Female groups Low Std Dev: It is easy to be sure what the average is More certainty, so higher statistical power High Std Dev: It is less clear what the average is Less certainty, so lower Statistical power 18
Analysis Logic: Significance Testing Standard Deviation When salary is closely clustered (low standard deviation), it is easier to determine if difference is meaningful and significant. The distribution of pay for Male and Female are clearly separated Salary Distribution by Group Salary Distribution by Group Female Male Female Male Counts Counts 30 35 40 45 50 55 60 65 70 75 Salary (x1000) SD=0% 30 35 40 45 50 55 60 65 70 75 Salary (x1000) SD=5% 19
Analysis Logic: Significance Testing Standard Deviation When salary is more dispersed (high standard deviation), it is more difficult to conclude with confidence that observe difference is meaningful and significant. The distribution of pay is more overlapped, and is more difficult to conclude there is a difference Salary Distribution by Group Salary Distribution by Group Female Male Female Male Counts Counts 30 35 40 45 50 55 60 65 70 75 Salary (x1000) SD=15% 30 35 40 45 50 55 60 65 70 75 Salary (x1000) SD=30% 20
Analysis Logic: Significance Testing Combing Concepts When salary is more dispersed (high standard deviation), the difference must be greater to confidently conclude that difference is meaningful and significant. In a high SD situation (SD=15%), increasing salary difference increases confidence that there is a difference Salary Distribution by Group Female Male Salary Distribution by Group Female Male Counts Counts 30 35 40 45 50 55 60 65 70 75 Salary (x1000) 30 35 40 45 50 55 60 65 70 75 Salary (x1000) 21
Analysis Logic: Significance Testing Sample Size Large sample sizes are more statistically powerful Logic: if an event is observed in many-many instances, you are more confident that it is not due to chance. Large sample size allows you to conclude with greater confidence that observed difference is true Small sample sizes are less statistically powerful Logic: if an event is observed in a few instances, you are less confident that it is not due to chance. To conclude with confidence that observed difference is true when sample size is small, you will need o Larger effect size/difference o Smaller Standard Deviation 22
Statistical Model: t-test 23
t = Analysis: t-test AverageGroup 1 AverageGroup 2 Standard Deviation Sample Size t-test evaluates whether difference in salary is due to chance t > 2 is statistically significant (typically) Statistical Power: t-test formula clearly shows effect of Effect Size (Average difference) Standard Deviation Sample Size 24
Analysis: t-test The t-test is a powerful and simple method to test for differences in pay between any two (2) groups The t-test on tests for simple differences. It does not take into account explanatory factors that may impact compensation (e.g., tenure, performance, education). Multiple Regression is a more advanced and generalized model of t-test. Multiple Regression tests for between group differences after controlling for explanatory factors 25
Multiple Regression: Logic 26
Multiple Regression Logic The t-test perspective. Is there significant difference in pay? Example 1a Group Avg Salary Sample Size Std. Dev. ($) Female $45,000 100 0 Male $50,000 100 0 Example 2a Group Avg Salary Sample Size Std. Dev. ($) Female $50,000 100 0 Male $50,000 100 0 27
Multiple Regression Logic The Multiple Regression perspective. Is there significant difference in pay? Example 1b Group Avg Salary Sample Size Std. Dev. ($) Example 2b Tenure Female $45,000 100 0 5-years Male $50,000 100 0 9-years Group Avg Salary Sample Size Std. Dev. ($) Education Female $50,000 100 0 Masters Male $50,000 100 0 High School 28
Multiple Regression Logic Example 3a: t-test perspective Group Salary($) Male 35,000 Male 35,000 Male 35,000 Male 40,000 Male 40,000 Male 40,000 Female 40,000 Female 40,000 Female 40,000 Female 55,000 Female 55,000 Female 55,000 Average Salary Male=$37,500 Female=$47,500 Simple Mean Group Difference=$10,000 t=2.83, p=0.009 29
Multiple Regression Logic Example 3b: Regression perspective Group Salary($) Tenure Male 35,000 1 Male 35,000 1 Male 35,000 1 Male 40,000 2 Male 40,000 2 Male 40,000 2 Female 40,000 2 Female 40,000 2 Female 40,000 2 Female 55,000 3 Female 55,000 3 Female 55,000 3 Adjust Mean Group Difference=$0.00 p=1.00 30
Statistical Model: Regression 31
Multiple Regression Method Typically, Multiple Regression requires 2-semesters of graduate-level instruction. Therefore, the actual underlying math and proper methodology is well beyond the scope of our webinar. Setting up and running a regression is EASY. Proper set-up and interpretation is DIFFICULT. Multiple Regression is iterative You must specify a valid model for analysis. It is very easy to mis-specify a model and draw incorrect conclusions: false positives or false negatives Please ask for help if you are unsure. 32
Questions 33
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