# Adverse Impact Ratio for Females (0/ 1) = 0 (5/ 17) = Adverse impact as defined by the 4/5ths rule was not found in the above data.

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2 2 of 9 12/8/ :57 PM (0/ 1) = 0 (5/ 17) = Adverse impact as defined by the 4/5ths rule was not found in the above data. Observed Not Row Totals Expected 5 12 Males Females Column Total Chi-Square = The value of the statistic is less than This indicates that there is a 95 percent chance that these results have been obtained absent any form of bias. Therefore, you may conclude that these results fall within normal random variations and are not the result of bias. Observed Not Row Totals Expected 5 12 Non-Minorities Minorities Column Total Chi-Square = The value of the statistic is less than This indicates that there is a 95 percent chance that these results have been obtained absent any form of bias. Therefore, you may conclude that these results fall within normal random variations and are not the result of bias. The difference between the proportion of the protected class and the proportion of all has a normal distribution with a mean and standard deviation. The statistic is shown below: (r / n) - p sqrt(p * (1-p) / n) * sqrt(1-q)

3 3 of 9 12/8/ :57 PM Analysis of proportion of Females where: r = number of Females. n = number of (Females and Males). p = proportion of that are Females. q = proportion of. Not Row Totals Males Females Column Total r = 0 n = 5 p = 1 / 18 = q = (0 + 5) / (1 + 17) = Standard Deviation Statistic = These results show that the proportion of Females is standard deviations below the proportion of. A result of less than 2 standard deviations is generally considered non-significant. Analysis of proportion of Minorities where: r = number of Minorities. n = number of (Minorities and Non-Minorities). p = proportion of that are Minorities. q = proportion of. Not Row Totals Non-Minorities Minorities Column Total r = 0 n = 5 p = 1 / 18 = q = (0 + 5) / (1 + 17) = Standard Deviation Statistic = These results show that the proportion of Minorities is standard deviations below the proportion of. A result of less than 2 standard deviations is generally considered non-significant.

4 4 of 9 12/8/ :57 PM The proportion of the protected class has an expected value that would fall within a specified confidence interval. The statistic is shown below: Observed value = (r / n) Expected value = p Standard Deviation = sqrt(p * (1-p) / n) * sqrt(1-q) Confidence Interval: Lower Bound = p * Std Dev Upper Bound = p * Std Dev Analysis of proportion of Females where: r = number of Females. n = number of. p = proportion of Females among those. q = proportion of. r = 0 n = 5 p = (1/(1+17))=0.056 q = ((0 + 5)/(1 + 17))=0.278 (r/n)=0/5=0 The lower bound of the confidence interval is: (1.96* )= The upper bound of the confidence interval is: (1.96* )= Confidence Interval = to These results show that the proportion of Females Females (r/n=0) is contained in the confidence interval. Therefore a finding of disparate impact is not supported by this data. Analysis of proportion of Minorities where: r = number of Minorities. n = number of. p = proportion of Minorities among those. q = proportion of. r = 0 n = 5 p = (1/(1+17))=0.056 q = ((0 + 5)/(1 + 17))=0.278 (r/n)=0/5=0 The lower bound of the confidence interval is: (1.96* )= The upper bound of the confidence interval is: (1.96* )=

5 5 of 9 12/8/ :57 PM Confidence Interval = to These results show that the proportion of Minorities Minorities (r/n=0) is contained in the confidence interval. Therefore a finding of disparate impact is not supported by this data. Females Males Rate of Females Rate of Males Adverse Impact Ratio of Females Adverse Impact against Females? Cumulative Probability Probability -> 0 5 (0/1) (5/17) 0 YES (1/1) (4/17) 4.25 NO Given that 5 were from a pool of 17 Males and 1 Females it was possible to have from 0 to 1 Females. Adverse Impact would be found if you 0 or fewer Females. The probability of Adverse Impact occurring even if the employment decisions were random (i.e. unbiased) is (the sum of the probabilities of having 0 or fewer Females). Since the probability of Adverse Impact occurring even if the employment decisions were random (i.e. unbiased) is greater than 10%, an observed Adverse Impact may be not significant since the probability is greater than 1 in 10 that Adverse Impact would have occurred due to chance. 0 1 of female

6 6 of 9 12/8/ :57 PM The probability distribution of having from 0 to 1 Females is displayed above. As can be seen, the most likely event (highest probability) to have occurred by chance (or decisions not affected by any form of bias) is to have 0 female. This represents the mean of the probability distribution. Approximately half of the probability distribution is above this point and approximately half is below this point. The total area contained in the probability distribution is equal to 1. Thus, probabilities for each number of female are a fraction of the total probability distribution. The larger areas of the distribution represent higher probabilities of occurance. Adding the individual probabilities up to a certain point enable you to compute the probability of having that many or fewer female. Adding the individual probabilities from a certain point and higher enable you to compute the probability of having that many or more female. The characteristics of the probability distribution--its mean and standard deviation--are a function of the number of female and male and the number of to be. Though it is possible to have from 0 to 1 female, the individual probabilities of having each number of female can be computed and accumulated. As noted before, these individual probabilities are a function of the number of female and male and the number of to be. Using the distribution above, a 90 percent confidence interval on the variable ' of Females ' would have a lower bound of 0 and an upper bound of 1. The significance of having 0 or fewer Females is graphically displayed below. 0 1 of female As noted earlier, Adverse Impact, according to the 4/5ths rule, would be found if you 0 or fewer female. You have 0 female. The probability of having 0 or fewer Females is equal to the cumulative probability for having 0 Females. The cumulative probability of having 0 female is and is graphically displayed, in red, above. Since the probability is greater than 10%, we are unable to reject the hypothesis that the decisions occurred due to chance. Therefore, we must conclude that it is entirely possible that having 0 or fewer female is an event that occurred due to chance and not from discriminatory actions by

7 7 of 9 12/8/ :57 PM the employer. Minorities Non-Minorities -> 0 Rate of Rate of Minorities Non-Minorities Adverse Impact Ratio of Minorities Adverse Impact against Minorities? Probability Cumulative Probability 5 (0/1) (5/17) 0 YES (1/1) (4/17) 4.25 NO Given that 5 were from a pool of 17 Non-Minorities and 1 Minorities it was possible to have from 0 to 1 Minorities. Adverse Impact would be found if you 0 or fewer Minorities. The probability of Adverse Impact occurring even if the employment decisions were random (i.e. unbiased) is (the sum of the probabilities of having 0 or fewer Minorities). Since the probability of Adverse Impact occurring even if the employment decisions were random (i.e. unbiased) is greater than 10%, an observed Adverse Impact may be not significant since the probability is greater than 1 in 10 that Adverse Impact would have occurred due to chance. 0 1 of minority The probability distribution of having from 0 to 1 Minorities is displayed above. As can be seen, the most likely event (highest probability) to have occurred by chance (or decisions not affected by any form of bias) is to have 0 minority. This represents the mean of the probability distribution. Approximately half of the probability distribution is above this point and approximately half is below this point. The total area contained in the probability distribution is equal to 1. Thus, probabilities for each number of minority are a fraction of the total probability distribution. The

8 8 of 9 12/8/ :57 PM larger areas of the distribution represent higher probabilities of occurance. Adding the individual probabilities up to a certain point enable you to compute the probability of having that many or fewer minority. Adding the individual probabilities from a certain point and higher enable you to compute the probability of having that many or more minority. The characteristics of the probability distribution--its mean and standard deviation--are a function of the number of minority and non-minority and the number of to be. Though it is possible to have from 0 to 1 minority, the individual probabilities of having each number of minority can be computed and accumulated. As noted before, these individual probabilities are a function of the number of minority and non-minority and the number of to be. Using the distribution above, a 90 percent confidence interval on the variable ' of Minorities ' would have a lower bound of 0 and an upper bound of 1. The significance of having 0 or fewer Minorities is graphically displayed below. 0 1 of minority As noted earlier, Adverse Impact, according to the 4/5ths rule, would be found if you 0 or fewer minority. You have 0 minority. The probability of having 0 or fewer Minorities is equal to the cumulative probability for having 0 Minorities. The cumulative probability of having 0 minority is and is graphically displayed, in red, above. Since the probability is greater than 10%, we are unable to reject the hypothesis that the decisions occurred due to chance. Therefore, we must conclude that it is entirely possible that having 0 or fewer minority is an event that occurred due to chance and not from discriminatory actions by the employer.

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