Revised City of South Bend Disparity Study Report

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APPENDIX C: SIGNIFICANCE LEVELS Many tables in this Report contain asterisks indicating that a number has sta- tistical significance at 0.001, 0.01, or 0.05 levels (sometimes, this is presented as 99.9 percent; 99 percent and 95 percent, respectively) and the body of the report repeats these descriptions. While the use of the term seems important, it is not self-evident what the term means. This Appendix provides a general explanation of significance levels. This Report seeks to address the question whether non -Whites and White women received disparate treatment in the economy relative to White males. From a statistical viewpoint, this primary question has two sub -questions: What is the relationship between the independent variable and the dependent variable? • What is the probability that the relationship between the independent variable and the dependent variable is equal to zero? For example, an important question facing the City of South Bend as it explores whether each racial and ethnic group and White women continue to experi- ence discrimination in its markets is do non -Whites and White women receive lower wages than White men?. As discussed in Appendix A, one way to uncover the relationship between the dependent variable (e.g., wages) and the independent variable (e.g. non -Whites) is through multiple regression analysis. An example helps to explain this concept. Let us say, for example, this analysis determines that non -Whites receive wages that are 35 percent less than White men after controlling for other fac- tors, such as education and industry, which might account for the differences in wages. However, this finding is only an estimate of the relationship between the independent variable (e.g., non -Whites) and the dependent variable (e.g., wages) —the first sub -question. It is still important to determine how accurate is that estimation, that is, what is the probability the estimated relationship is equal to zero — the second sub -question. To resolve the second sub -question, statistical hypothesis tests are utilized. Hypothesis testing assumes that there is no relationship between belonging to a particular demographic group and the level of economic utilization relative to White men (e.g., non -Whites earn identical wages compared to White men or non -Whites earn 0 percent less than White men). This sometimes is called 0 2020 Colette Holt & Associates, All Rights Reserved. 107