the EEOC presented the theory that this practice is discriminatory because minorities in the U.S. are more likely to be convicted criminals with bad credit histories than white Americans. Ergo, employers should have to include criminals and debtors in their hiring. In this instance U.S. District Judge Roger Titus ruled firmly against the disparate impact theory, stating that EEOC's action had been "a theory in search of facts to support it." "By bringing actions of this nature, the EEOC has placed many employers in the "Hobson's choice" of ignoring criminal history and credit background, thus exposing themselves to potential liability for criminal and fraudulent acts committed by employees, on the one hand, or incurring the wrath of the EEOC for having utilized information deemed fundamental by most employers. Something more... must be utilized to justify a disparate impact claim based upon criminal history and credit checks. To require less, would be to condemn the use of common sense, and this is simply not what the laws of this country require." Thomas Sowell has argued that assuming that disparities in outcomes are caused by discrimination is a logical fallacy. Statistical criticism of disparate impact Another avenue of criticism of disparate impact rests on a mathematical analysis of: The threshold effect size of disparities to assume discrimination has occurred with the commonly used 80% threshold arguably leading to a large number of false positives If correction for confounding variables in a regression model took place and was applied appropriately Effect size threshold We are able to convert between measures of effect size using the relationships:where is Cohen's d, is the odds ratio, is the Pearson correlation, and is the standard normal cumulative distribution function. The coefficient of determination is the square of the correlation. The term is the probability that a member of group obtains a score greater than a member of group . For a set of odds ratios, which is often used to determine if there is a disparate impact, we may convert between effect sizes as such: Using these different measures of effect size, we are able to quantitatively determine the size of a gap based on several common interpretations. Notably, we may interpret the effect size as: The amount of explained variation (coefficient of determination) The difference in terms of standard deviations (Cohen's d) The probability of a greater score If we take the 80% rule to apply