When the number of positions is, 5 and the ratio of minority is, 0.1 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.590490 The corresponding power curve is 1+ HHH + HHHH + HHHH + HHHH + HHHH 0.9+ HHH + HHHH + HHHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHHH + HHHHH + HHHH 0.7+ HHHHH + HHHHH + HHHHH + HHHHH + HHHHH 0.6****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.590490 The corresponding power curve is 1+ HHH + HHHH + HHHH + HHHH + HHHH 0.9+ HHH + HHHH + HHHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHHH + HHHHH + HHHH 0.7+ HHHHH + HHHHH + HHHHH + HHHHH + HHHHH 0.6****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.590490 The corresponding power curve is 1+ HHH + HHHH + HHHH + HHHH + HHHH 0.9+ HHH + HHHH + HHHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHHH + HHHHH + HHHH 0.7+ HHHHH + HHHHH + HHHHH + HHHHH + HHHHH 0.6****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.590490 The corresponding power curve is 1+ HHH + HHHH + HHHH + HHHH + HHHH 0.9+ HHH + HHHH + HHHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHHH + HHHHH + HHHH 0.7+ HHHHH + HHHHH + HHHHH + HHHHH + HHHHH 0.6****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.590490 The corresponding power curve is 1+ HHH + HHHH + HHHH + HHHH + HHHH 0.9+ HHH + HHHH + HHHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHHH + HHHHH + HHHH 0.7+ HHHHH + HHHHH + HHHHH + HHHHH + HHHHH 0.6****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.590490 The corresponding power curve is 1+ HHH + HHHH + HHHH + HHHH + HHHH 0.9+ HHH + HHHH + HHHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHHH + HHHHH + HHHH 0.7+ HHHHH + HHHHH + HHHHH + HHHHH + HHHHH 0.6****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 5 and the ratio of minority is, 0.2 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.327680 The corresponding power curve is 1+ HHH + HHH + HHHH 0.9+ HHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHH 0.7+ HHHH + HHHH + HHHH 0.6+ HHHHH + HHHH + HHHH 0.5+ HHHH + HHHHH + HHHHHH 0.4+ HHHHHH + HHHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.327680 The corresponding power curve is 1+ HHH + HHH + HHHH 0.9+ HHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHH 0.7+ HHHH + HHHH + HHHH 0.6+ HHHHH + HHHH + HHHH 0.5+ HHHH + HHHHH + HHHHHH 0.4+ HHHHHH + HHHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.737280 The corresponding power curve is 1+ HHHHHHHHHHH + HHHHHHH + HHHHH + HHHHH 0.95 HHHH + HHHH + HHHH + HHH 0.9+ HHH + HHH + HHH 0.85 HHHH + HHH + HHH + HHH 0.8+ HHH + HHH + HHH + HHH 0.75 HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.327680 The corresponding power curve is 1+ HHH + HHH + HHHH 0.9+ HHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHH 0.7+ HHHH + HHHH + HHHH 0.6+ HHHHH + HHHH + HHHH 0.5+ HHHH + HHHHH + HHHHHH 0.4+ HHHHHH + HHHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.327680 The corresponding power curve is 1+ HHH + HHH + HHHH 0.9+ HHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHH 0.7+ HHHH + HHHH + HHHH 0.6+ HHHHH + HHHH + HHHH 0.5+ HHHH + HHHHH + HHHHHH 0.4+ HHHHHH + HHHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.327680 The corresponding power curve is 1+ HHH + HHH + HHHH 0.9+ HHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHH 0.7+ HHHH + HHHH + HHHH 0.6+ HHHHH + HHHH + HHHH 0.5+ HHHH + HHHHH + HHHHHH 0.4+ HHHHHH + HHHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 5 and the ratio of minority is, 0.3 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.168070 The corresponding power curve is 1+ HHH + HH + HH + HHH + HHH 0.8+ HH + HHH + HHHH + HHH + HHH 0.6+ HHH + HHHH + HHHH + HHHHH 0.4+ HHHHH + HHHHH + HHHHH + HHHHHH + HHHHHH 0.2+ HHHHHHHH -*****-+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.168070 The corresponding power curve is 1+ HHH + HH + HH + HHH + HHH 0.8+ HH + HHH + HHHH + HHH + HHH 0.6+ HHH + HHHH + HHHH + HHHHH 0.4+ HHHHH + HHHHH + HHHHH + HHHHHH + HHHHHH 0.2+ HHHHHHHH -*****-+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.528220 The corresponding power curve is 1+ HHHHHHHHHH + HHHHHHHH + HHHHHH + HHHHH 0.9+ HHHH + HHHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHH + HHH + HHH 0.7+ HHHH + HHH + HHH + HHHH 0.6+ HHH + HHH + HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.168070 The corresponding power curve is 1+ HHHHHHHHHH + HHHHHHHH + HHHHHH + HHHHH 0.9+ HHHH + HHHH + HHHH + HHHH 0.8+ HHHH + HHHH + HHHH + HHH + HHH 0.7+ HHHH + HHH + HHH + HHHH 0.6+ HHH + HHH + HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.168070 The corresponding power curve is 1+ HHH + HH + HH + HHH + HHH 0.8+ HH + HHH + HHHH + HHH + HHH 0.6+ HHH + HHHH + HHHH + HHHHH 0.4+ HHHHH + HHHHH + HHHHH + HHHHHH + HHHHHH 0.2+ HHHHHHHH -*****-+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.168070 The corresponding power curve is 1+ HHH + HH + HH + HHH + HHH 0.8+ HH + HHH + HHHH + HHH + HHH 0.6+ HHH + HHHH + HHHH + HHHHH 0.4+ HHHHH + HHHHH + HHHHH + HHHHHH + HHHHHH 0.2+ HHHHHHHH -*****-+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 5 and the ratio of minority is, 0.4 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.077760 The corresponding power curve is 1+ HH + HH + HHH + HHH 0.8+ HH + HHH + HHH + HHH + HHH 0.6+ HHH + HHH + HHHH + HHHH 0.4+ HHHH + HHHH + HHHHH + HHHHHH 0.2+ HHHHHHH + HHHHHHH + HHHHHHHHH -********-+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.077760 The corresponding power curve is 1+ HH + HH + HHH + HHH 0.8+ HH + HHH + HHH + HHH + HHH 0.6+ HHH + HHH + HHHH + HHHH 0.4+ HHHH + HHHH + HHHHH + HHHHHH 0.2+ HHHHHHH + HHHHHHH + HHHHHHHHH -********-+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.682560 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHH + HHHHHHHHH + HHHHHH 0.95 HHHHH + HHHH + HHHH 0.9+ HHH + HHH + HHH 0.85 HHH + HHH + HHH + HHH 0.8+ HHH + HHH + HHH 0.75 HH + HH + HH 0.7+HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.336960 The corresponding power curve is 1+ HHHHHHHHH + HHHHHH + HHHH 0.9+ HHHH + HHHH + HHHH 0.8+ HHHH + HHH + HHHH 0.7+ HHHH + HHHH + HHHH 0.6+ HHH + HHH + HHHH 0.5+ HHHH + HHH + HHHH 0.4+ HHHH + HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.077760 The corresponding power curve is 1+ HHHHHHHHH + HHHHHH + HHHH 0.9+ HHHH + HHHH + HHHH 0.8+ HHHH + HHH + HHHH 0.7+ HHHH + HHHH + HHHH 0.6+ HHH + HHH + HHHH 0.5+ HHHH + HHH + HHHH 0.4+ HHHH + HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.077760 The corresponding power curve is 1+ HHHHHHHHH + HHHHHH + HHHH 0.9+ HHHH + HHHH + HHHH 0.8+ HHHH + HHH + HHHH 0.7+ HHHH + HHHH + HHHH 0.6+ HHH + HHH + HHHH 0.5+ HHHH + HHH + HHHH 0.4+ HHHH + HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 5 and the ratio of minority is, 0.5 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.031250 The corresponding power curve is 1+ HH + HH + HH + HH 0.8+ HH + HH + HHH + HHH 0.6+ HHH + HHH + HHH + HHH 0.4+ HHHH + HHHH + HHHH + HHHHH + HHHHHH 0.2+ HHHHHH + HHHHHHH + HHHHHHHHHHH -***********-+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.031250 The corresponding power curve is 1+ HH + HH + HH + HH 0.8+ HH + HH + HHH + HHH 0.6+ HHH + HHH + HHH + HHH 0.4+ HHHH + HHHH + HHHH + HHHHH + HHHHHH 0.2+ HHHHHH + HHHHHHH + HHHHHHHHHHH -***********-+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.500000 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHH + HHHHHHHHH + HHHHHH + HHHHH 0.9+ HHHHH + HHHH + HHH + HHH 0.8+ HHH + HHH + HHH + HHH 0.7+ HH + HHH + HHH + HHH 0.6+ HHH + HHH + HH +HHH 0.5**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.187500 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHH + HHHHHHHHH + HHHHHH + HHHHH 0.9+ HHHHH + HHHH + HHH + HHH 0.8+ HHH + HHH + HHH + HHH 0.7+ HH + HHH + HHH + HHH 0.6+ HHH + HHH + HH +HHH 0.5**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.187500 The corresponding power curve is 1+ HHHHHHHH + HHHHHH + HHHHH + HHHH + HHHH 0.8+ HHH + HHH + HHH + HHH + HHHH 0.6+ HHH + HHH + HHH + HHHH + HHHH 0.4+ HHHH + HHHH + HHHH + HHHHH + HHHHH 0.2****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.031250 The corresponding power curve is 1+ HHHHHHHH + HHHHHH + HHHHH + HHHH + HHHH 0.8+ HHH + HHH + HHH + HHH + HHHH 0.6+ HHH + HHH + HHH + HHHH + HHHH 0.4+ HHHH + HHHH + HHHH + HHHHH + HHHHH 0.2****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 15 and the ratio of minority is, 0.1 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2058911321 The corresponding power curve is 1+ HH + HH + HH + HHH + HHH 0.8+ HHH + HHHH + HHH + HHHH + HHHH 0.6+ HHHH + HHHH + HHHHH + HHHH + HHHH 0.4+ HHHHHH + HHHHH + HHHHHH + HHHHHHH + HHHHHHHH 0.2******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2058911321 The corresponding power curve is 1+ HH + HH + HH + HHH + HHH 0.8+ HHH + HHHH + HHH + HHHH + HHHH 0.6+ HHHH + HHHH + HHHHH + HHHH + HHHH 0.4+ HHHHHH + HHHHH + HHHHHH + HHHHHHH + HHHHHHHH 0.2******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5490430190 The corresponding power curve is 1+ HHHHHHHHH + HHHHHHH + HHHHH + HHHH 0.9+ HHH + HHHH + HHHH + HHHH + HHH 0.8+ HHHH + HHHH + HHHH + HHHH 0.7+ HHH + HHH + HHH + HHH + HHHH 0.6+ HHHH + HHHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2058911321 The corresponding power curve is 1+ HHHHHHHHH + HHHHHHH + HHHHH + HHHH 0.9+ HHH + HHHH + HHHH + HHHH + HHH 0.8+ HHHH + HHHH + HHHH + HHHH 0.7+ HHH + HHH + HHH + HHH + HHHH 0.6+ HHHH + HHHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2058911321 The corresponding power curve is 1+ HH + HH + HH + HHH + HHH 0.8+ HHH + HHHH + HHH + HHHH + HHHH 0.6+ HHHH + HHHH + HHHHH + HHHH + HHHH 0.4+ HHHHHH + HHHHH + HHHHHH + HHHHHHH + HHHHHHHH 0.2******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2058911321 The corresponding power curve is 1+ HH + HH + HH + HHH + HHH 0.8+ HHH + HHHH + HHH + HHHH + HHHH 0.6+ HHHH + HHHH + HHHHH + HHHH + HHHH 0.4+ HHHHHH + HHHHH + HHHHHH + HHHHHHH + HHHHHHHH 0.2******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 15 and the ratio of minority is, 0.2 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.03518437209 The corresponding power curve is 1+ HH + HH + H + HH 0.8+ HH + HH + HH + HHH 0.6+ HHH + HHH + HHH + HHH 0.4+ HHH + HHHH + HHHH + HHHHH + HHHHHH 0.2+ HHHHHH + HHHHHHHHH + HHHHHHHHHHHH -************+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.03518437209 The corresponding power curve is 1+ HH + HH + H + HH 0.8+ HH + HH + HH + HHH 0.6+ HHH + HHH + HHH + HHH 0.4+ HHH + HHHH + HHHH + HHHHH + HHHHHH 0.2+ HHHHHH + HHHHHHHHH + HHHHHHHHHHHH -************+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.6481621045 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHH + HHHHHHHH + HHHHHH 0.95 HHHHH + HHHH + HHHH 0.9+ HHH + HHH + HHH 0.85 HHH + HHH 0.8+ HH + HHH + HH 0.75 HHH + HHH + HH 0.7+ HH + HHH +HHH 0.65*-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3980232092 The corresponding power curve is 1+ HHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHH + HHHH + HHHH 0.8+ HHH + HHHH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HHH + HHH + HHH 0.5+ HHH + HHH + HHHH 0.4***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1671257674 The corresponding power curve is 1+ HHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHH + HHHH + HHHH 0.8+ HHH + HHHH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HHH + HHH + HHH 0.5+ HHH + HHH + HHHH 0.4***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.03518437209 The corresponding power curve is 1+ HHHHHHH + HHHHH + HHHH + HHHH + HHHH 0.8+ HHH + HHHH + HHH + HHH + HHHH 0.6+ HHH + HHH + HHH + HHH 0.4+ HHHH + HHHH + HHHHH + HHHHH + HHHHHH 0.2+ HHHHHH -*****-+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 15 and the ratio of minority is, 0.3 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.004747561510 The corresponding power curve is 1+ HH + HH + H + H 0.8+ H + H + HH + HH 0.6+ HH + HH + HH + HH 0.4+ HH + HH + HHH + HHHH 0.2+ HHHH + HHHHHH + HHHHHHH + HHHHHHHHHHHH -************************+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.004747561510 The corresponding power curve is 1+ HH + HH + H + H 0.8+ H + H + HH + HH 0.6+ HH + HH + HH + HH 0.4+ HH + HH + HHH + HHHH 0.2+ HHHH + HHHHHH + HHHHHHH + HHHHHHHHHHHH -************************+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5154910592 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHHH + HHHHH + HHHH 0.9+ HHHH + HHHH + HHH + HHH 0.8+ HHH + HHH + HH + HHH 0.7+ HHH + HH + HH + HH + HH 0.6+ HH + HH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2968679279 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH 0.9+ HHHH + HHHH + HHHH 0.8+ HHH + HHHH + HHH 0.7+ HHH + HH 0.6+ HHH + HHH + HHH 0.5+ HHHH + HHH + HHH 0.4+ HHH + HHH + HHH 0.3***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1268277146 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH 0.9+ HHHH + HHHH + HHHH 0.8+ HHH + HHHH + HHH 0.7+ HHH + HH 0.6+ HHH + HHH + HHH 0.5+ HHHH + HHH + HHH 0.4+ HHH + HHH + HHH 0.3***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.03526759979 The corresponding power curve is 1+ HHHHHHHHHHHH + HHHHHH + HHHH + HHH + HHH 0.8+ HHHH + HHH + HHHH + HHH 0.6+ HHH + HHH + HHH + HHH + HHH 0.4+ HHH + HHH + HHHH + HHHH 0.2+ HHHH + HHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 15 and the ratio of minority is, 0.4 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.005172034831 The corresponding power curve is 1+ HHHH + HHH + HHH + HH 0.8+ HH + HHH + HH + HH 0.6+ HH + HH + HH + HHH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHH + HHHH + HHHHHH + HHHHHHHHHH -******************+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.005172034831 The corresponding power curve is 1+ HHHH + HHH + HHH + HH 0.8+ HH + HHH + HH + HH 0.6+ HH + HH + HH + HHH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHH + HHHH + HHHHHH + HHHHHHHHHH -******************+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.6098131557 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHHH + HHHHH + HHHH + HHH 0.9+ HHH + HHH + HHH + HH + HH 0.8+ HHH + HH + HH + HH + HH 0.7+ HH + H + H + HH |HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 5 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.4032155504 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHHH + HHHHH 0.9+ HHHH + HHH + HHHH + HHH 0.8+ HHH + HHH + HHH 0.7+ HH + HH + HH 0.6+ HH + HH + HH + HH 0.5+ HH + HH +HHH 0.4**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2172777056 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH + HHHH + HHH 0.8+ HHH + HHH + HHH + HHH + HH 0.6+ HHH + HH + HHH + HHH + HHH 0.4+ HHH + HHH + HH + HHH + HHHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.09050190240 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH + HHHH + HHH 0.8+ HHH + HHH + HHH + HHH + HH 0.6+ HHH + HH + HHH + HHH + HHH 0.4+ HHH + HHH + HH + HHH + HHHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 15 and the ratio of minority is, 0.5 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.01757812500 The corresponding power curve is 1+ HHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HHH + HHH + HHH + HHH 0.6+ HH + HHH + HH + HH 0.4+ HH + HHH + HHH + HHHH 0.2+ HHH + HHHH + HHHHHH + HHHHHHHH -*********+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.003692626953 The corresponding power curve is 1+ HHHHHHHH + HHHH + HH + HHH 0.8+ HH + HH + HHH + HH 0.6+ HH + HHH + HH + HHH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHHH + HHHH + HHHHH + HHHHHHHHHH -*****************-+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.4999999999 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHHH + HHHHH + HHH 0.9+ HHH + HHH + HHH + HH 0.8+ HH + HHH + HH + HH 0.7+ HHH + HH + HH + HH 0.6+ H + H + HH +HH 0.5**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3036193847 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH 0.8+ HHH + HHH + HH 0.7+ HH + HH 0.6+ HHH + HH + HHH 0.5+ HH + HH + HH 0.4+ HH + HHH +HHH 0.3**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 5 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1508789062 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH 0.8+ HHH + HHH + HH 0.7+ HH + HH 0.6+ HHH + HH + HHH 0.5+ HH + HH + HH 0.4+ HH + HHH +HHH 0.3**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.05923461914 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH + HHHH + HHH 0.8+ HHH + HH + HHH + HH 0.6+ HH + HH + HH + HHH + HHH 0.4+ HHH + HHH + HHH + HHH + HHH 0.2+ HHHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 25 and the ratio of minority is, 0.1 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.07178979877 The corresponding power curve is 1+ HH + H + HH + HH 0.8+ HH + HHH + HHH + HH + HHH 0.6+ HHH + HHH + HHH + HHHH 0.4+ HHHH + HHHH + HHHHH + HHHHHH 0.2+ HHHHHHH + HHHHHHHH + HHHHHHHHHHH -*********+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.07178979877 The corresponding power curve is 1+ HH + H + HH + HH 0.8+ HH + HHH + HHH + HH + HHH 0.6+ HHH + HHH + HHH + HHHH 0.4+ HHHH + HHHH + HHHHH + HHHHHH 0.2+ HHHHHHH + HHHHHHHH + HHHHHHHHHHH -*********+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5370940501 The corresponding power curve is 1+ HHHHHHHHHHHHHHHH + HHHHHHH + HHHHH + HHHHH 0.9+ HHHH + HHHH + HHH + HHH + HHHH 0.8+ HHH + HH + HHH + HHHH 0.7+ HHH + HHH + HH + HHH 0.6+ HHH + HHHH + HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2712059065 The corresponding power curve is 1+ HHHHHHHHHHHHHHHH + HHHHHHH + HHHHH + HHHHH 0.9+ HHHH + HHHH + HHH + HHH + HHHH 0.8+ HHH + HH + HHH + HHHH 0.7+ HHH + HHH + HH + HHH 0.6+ HHH + HHHH + HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2712059065 The corresponding power curve is 1+ HHHHHHHH + HHHHH + HHHH 0.9+ HHHH + HHHH 0.8+ HHH + HHH + HHHH 0.7+ HHHH + HHH + HHH 0.6+ HHH + HHH + HHHH 0.5+ HHHH + HHHH 0.4+ HHHH + HHHH + HHHH 0.3+ HHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.07178979877 The corresponding power curve is 1+ HHHHHHHH + HHHHH + HHHH 0.9+ HHHH + HHHH 0.8+ HHH + HHH + HHHH 0.7+ HHHH + HHH + HHH 0.6+ HHH + HHH + HHHH 0.5+ HHHH + HHHH 0.4+ HHHH + HHHH + HHHH 0.3+ HHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 25 and the ratio of minority is, 0.2 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.003777893186 The corresponding power curve is 1+ HH + HH + H + H 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HH + HH 0.4+ HH + HH + HHH + HHHH 0.2+ HHHH + HHHHH + HHHHHHH + HHHHHHHHHHHHH -***************************--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.003777893186 The corresponding power curve is 1+ HH + HH + H + H 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HH + HH 0.4+ HH + HH + HHH + HHHH 0.2+ HHHH + HHHHH + HHHHHHH + HHHHHHHHHHHHH -***************************--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 5 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.6166894119 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.95 HHHH + HHHH 0.9+ HHH + HHH + HHH 0.85 HHH + HH 0.8+ HH + HH + HH 0.75 HH + HH + HH 0.7+ HH + HH 0.65 HH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.4206743093 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHH + HHHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH + HHH 0.8+ HHH + HHH + HHH 0.7+ HH + HH + HH + HH 0.6+ HH + HH + HH 0.5+ HHH + HH + HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2339932593 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH 0.8+ HHH + HHH + HH 0.7+ HHH + HHH 0.6+ HHHH + HHH + HHH 0.5+ HH + HHH + HHHH 0.4+ HHH + HHH 0.3+ HHHH + HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.09822522286 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH 0.8+ HHH + HHH + HH 0.7+ HHH + HHH 0.6+ HHHH + HHH + HHH 0.5+ HH + HHH + HHHH 0.4+ HHH + HHH 0.3+ HHHH + HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 25 and the ratio of minority is, 0.3 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.008960527880 The corresponding power curve is 1+ HHHHHHHH + HHHH + HHH + HH 0.8+ HH + HHH + HHH + HH 0.6+ HHH + HHH + HH + HH 0.4+ HH + HHH + HHH + HHHH 0.2+ HHHH + HHHH + HHHHHH + HHHHHHHHHH -**************-+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.008960527880 The corresponding power curve is 1+ HHHHHHHH + HHHH + HHH + HH 0.8+ HH + HHH + HHH + HH 0.6+ HHH + HHH + HH + HH 0.4+ HH + HHH + HHH + HHHH 0.2+ HHHH + HHHH + HHHHHH + HHHHHHHHHH -**************-+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5118485441 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH + HHHH 0.9+ HHH + HHH + HHH + HHH 0.8+ HH + HHH + HH + HH 0.7+ HH + HHH + HH + HH 0.6+ HH + HH + HH +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3406549044 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH 0.8+ HHH + HHH + HHH 0.7+ HHH + HHH + HH 0.6+ HHH + HHH + HH 0.5+ HH + HHH + HHH 0.4+ HH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 5 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1934884421 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH 0.8+ HHH + HHH + HHH 0.7+ HHH + HHH + HH 0.6+ HHH + HHH + HH 0.5+ HH + HHH + HHH 0.4+ HH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.09047191856 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH + HHHH + HHHH 0.8+ HHH + HHH + HH + HH + HH 0.6+ HH + HH + HH + HH + HHH 0.4+ HHH + HHH + HHH + HHHH + HHHH 0.2***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 25 and the ratio of minority is, 0.4 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.009470830924 The corresponding power curve is 1+ HHHHHHHHHHHHHH + HHHHH + HHHH + HHH 0.8+ HHH + HHH + HH + HH 0.6+ HH + HHH + HH + HH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHH + HHHH + HHHHH + HHHHHHHH -***********-+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.009470830924 The corresponding power curve is 1+ HHHHHHHHHHHHHH + HHHHH + HHHH + HHH 0.8+ HHH + HHH + HH + HH 0.6+ HH + HHH + HH + HH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHH + HHHH + HHHHH + HHHHHHHH -***********-+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 10 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5857749564 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH + HHHH + HHH 0.9+ HHH + HH + HH + HH + H 0.8+ HH + HH + HH + HH + HH 0.7+ H + H + HH + HH 0.6+H -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 8 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2735314502 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHH + HHHH + HH + HH 0.8+ HH + HH + HH 0.7+ HH + HH + HH + HH 0.6+ H + HH + HH 0.5+ HH + H +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1535517348 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH 0.9+ HHH + HHH 0.8+ HH + HH + HH 0.7+ HHH + HH + HH 0.6+ HHH + HH + HH 0.5+ HH + HH + HH 0.4+ HHH + HHH 0.3+HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.07356525783 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH + HHH + HHH 0.8+ HH + HHH + HH + HH 0.6+ HHH + HHH + HH + HH + HHH 0.4+ HHH + HH + HHH + HHH + HHH 0.2+ HHHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 25 and the ratio of minority is, 0.5 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02164262533 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HH + HH 0.4+ HHH + HH + HH + HH 0.2+ HHH + HHHH + HHHH + HHHHHH -******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.007316648960 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HH + HH + HHH + HH 0.6+ HH + HH + HH + HH 0.4+ HH + HH + HHH + HHH 0.2+ HHH + HHH + HHHHH + HHHHHHH -**********--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 12 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.4999999999 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH 0.9+ HH + HH + HHH + HH 0.8+ HH + HH + HH + H 0.7+ H + H + HH + H 0.6+ H + H + HH +H 0.5**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 11 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3450189828 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HH + HHH 0.8+ HHH + HH + HHH 0.7+ HH + HH + HH 0.6+ HHH + HH + HH 0.5+ HH + HH + H 0.4+ H +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 10 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2121781110 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HH + HHH 0.8+ HHH + HH + HHH 0.7+ HH + HH + HH 0.6+ HHH + HH + HH 0.5+ HH + HH + H 0.4+ H +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 8 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.05387607217 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH + HH 0.8+ HH + HH + HH + HH + HH 0.6+ HH + HH + HH + HH + HHH 0.4+ HH + HH + HH + HHH +HHH 0.2**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 35 and the ratio of minority is, 0.1 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02503155505 The corresponding power curve is 1+ HH + HH + HH + HH 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HHH + HHH 0.4+ HHH + HHH + HHHH + HHHHH 0.2+ HHHHH + HHHHHH + HHHHHHHH + HHHHHHHHHHHHH -***************+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02503155505 The corresponding power curve is 1+ HH + HH + HH + HH 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HHH + HHH 0.4+ HHH + HHH + HHHH + HHHHH 0.2+ HHHHH + HHHHHH + HHHHHHHH + HHHHHHHHHHHHH -***************+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Government method would need at most 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5309848659 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHHH + HHHH 0.9+ HHHH + HHH + HHH + HHH + HHH 0.8+ HHH + HH + HHH + HHH 0.7+ HHH + HHH + HHH + HHH 0.6+ HHH + HH + HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3062502599 The corresponding power curve is 1+ HHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH 0.8+ HHH + HHHH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HHH 0.5+ HHH + HHHH + HHHH 0.4+ HHHH + HHHH + HHH 0.3***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1223764913 The corresponding power curve is 1+ HHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH 0.8+ HHH + HHHH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HHH 0.5+ HHH + HHHH + HHHH 0.4+ HHHH + HHHH + HHH 0.3***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02503155505 The corresponding power curve is 1+ HHHHHH + HHHHH + HHHH + HHHH + HHH 0.8+ HHHH + HHH + HHHH + HHH 0.6+ HHH + HHH + HHH + HHHH + HHHH 0.4+ HHHH + HHHHH + HHHHH + HHHHH 0.2+ HHHHH + HHHHHHH -******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 35 and the ratio of minority is, 0.2 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.01904011201 The corresponding power curve is 1+ HHHHHHHH + HHHHH + HHH + HHH 0.8+ HH + HHH + HHH + HH 0.6+ HH + HH + HHH + HH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHHH + HHHHH + HHHHHH + HHHHHHHHH -***********-+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.003955069873 The corresponding power curve is 1+ HHHH + HHH + HHH + HH 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HH + HHH 0.4+ HHH + HHH + HHH + HHHH 0.2+ HHH + HHHH + HHHHHH + HHHHHHHHHHH -**********************--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5993327252 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH + HHH + HHH 0.9+ HHH + HH + HHH + HHH + HH 0.8+ HH + HH + H + HH + HH 0.7+ HH + HH + HH + H +HH 0.6**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 5 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2720916939 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH + HHHH 0.9+ HHH + HHH + HHH 0.8+ HHH + HHH + HHH + HH 0.7+ HH + HH + HH 0.6+ HH + HH + HH + HH 0.5+ HHH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1434917097 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHH 0.8+ HHH + HH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HHH + HHH 0.5+ HHH + HHH + HHH 0.4+ HHH + HHHH 0.3+ HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.06052397790 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHHH + HHH 0.8+ HHH + HHH + HHH + HHH 0.6+ HH + HHH + HHH + HHH + HHH 0.4+ HHHH + HHH + HHHH + HHHH + HHHH 0.2+ HHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 35 and the ratio of minority is, 0.3 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.009117801459 The corresponding power curve is 1+ HHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HHH + HHH + HH + HHH 0.6+ HH + HH + HHH + HH 0.4+ HH + HH + HH + HHH 0.2+ HHHH + HHHH + HHHHH + HHHHHHHH -************+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.009117801459 The corresponding power curve is 1+ HHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HHH + HHH + HH + HHH 0.6+ HH + HH + HHH + HH 0.4+ HH + HH + HH + HHH 0.2+ HHHH + HHHH + HHHHH + HHHHHHHH -************+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 10 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5099571167 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH 0.9+ HHH + HHH + HH + HH 0.8+ HHH + HH + HH + HH 0.7+ HH + HH + HH + HH 0.6+ H + HH + HH +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 9 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3645828677 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHHH + HHH + HHH 0.8+ HH + HHH + HHH 0.7+ HH + HHH + HH + HH 0.6+ HH + HH + HH 0.5+ HH + HH + HH 0.4+HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1326467440 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHHH 0.9+ HHHH + HHH 0.8+ HHH + HH + HHH 0.7+ HHH + HH 0.6+ HH + HHH + HH 0.5+ HH + HHH + HH 0.4+ HH + HHH 0.3+ HH + HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.06499870790 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHHH 0.9+ HHHH + HHH 0.8+ HHH + HH + HHH 0.7+ HHH + HH 0.6+ HH + HHH + HH 0.5+ HH + HHH + HH 0.4+ HH + HHH 0.3+ HH + HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 35 and the ratio of minority is, 0.4 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.01016642540 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HH + HHH 0.4+ HH + HH + HHH + HHH 0.2+ HHH + HHH + HHHH + HHHHHHH -*********+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.003400670832 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HH + HHH 0.4+ HH + HHH + HHH + HHH 0.2+ HHH + HHHH + HHHHH + HHHHHHHH -**************-+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 14 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5727540626 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH + HH 0.9+ HH + HH + HH + HH 0.8+ HH + HH + HH + HH + HH 0.7+ HH + HH + H + H + H 0.6+H -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 12 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3057349821 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHH + HHH 0.9+ HHH + HHH + HH 0.8+ HHH + HH + HH + HH 0.7+ HH + HH + HH 0.6+ H + HH + HH + HH 0.5+ HH +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 11 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1951745034 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HHH + HHH 0.8+ HH + HH + HH 0.7+ HH + HH + HH 0.6+ H + HH 0.5+ HH + HH + HH 0.4+ HH + HH +HHH 0.3**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 9 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.05752670740 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH + HH 0.8+ HH + HHH + HHH + HH + HH 0.6+ HH + HHH + HH + HH + HH 0.4+ HH + HH + HHH + HH + HH 0.2**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 35 and the ratio of minority is, 0.5 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 11 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02047979576 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HH + HH + HH + HH 0.6+ HHH + HH + HH + HH 0.4+ HH + HH + HH + HH 0.2+ HHH + HH + HHH + HHHHH -******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 10 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.008336923900 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HHH + HH + HH + HH 0.6+ HHH + HH + HH + HH 0.4+ HH + HH + HH + HH 0.2+ HHH + HHH + HHHH + HHHHHH -********-+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 17 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5000000000 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HH 0.9+ HH + HH + HH + HH 0.8+ HH + HH + HH + HH 0.7+ H + H + H + H 0.6+ HH + H + H +H 0.5**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 16 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3679394004 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HHH + HH 0.8+ HHH + HH + HH 0.7+ HH + HH + H + HH 0.6+ HH + HH + H 0.5+ HH + HH + HH 0.4+HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 14 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1552523296 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HHH 0.8+ HHH + HH + HH 0.7+ HH + HH + HH 0.6+ HH + HH 0.5+ H + H + HH 0.4+ HH + HH + HH 0.3+HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 13 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.08773262451 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH + HHH 0.8+ HHH + HH + HHH + HH 0.6+ HH + HHH + HH + HH + HH 0.4+ HHH + HH + HH + HH + HH 0.2+ HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 45 and the ratio of minority is, 0.1 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.008727963568 The corresponding power curve is 1+ HH + HH + H + H 0.8+ H + H + HH + HH 0.6+ HH + HHH + HH + HHH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHHH + HHHHHH + HHHHHHHH + HHHHHHHHHHHHHH -**********************--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.008727963568 The corresponding power curve is 1+ HH + HH + H + H 0.8+ H + H + HH + HH 0.6+ HH + HHH + HH + HHH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHHH + HHHHHH + HHHHHHHH + HHHHHHHHHHHHHH -**********************--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5271378709 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHHH + HHHHH + HHHH 0.9+ HHHH + HHH + HHH + HHH 0.8+ HHHH + HH + HHH + HH + HHH 0.7+ HH + HH + HHH + HHH 0.6+ HHH + HH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3289328820 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH 0.8+ HHH + HHH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HHH + HHH 0.5+ HHH + HHH + HHH 0.4+ HHH + HHHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1590428916 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHH 0.8+ HHH + HHH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HHH + HHH 0.5+ HHH + HHH + HHH 0.4+ HHH + HHHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.05236778141 The corresponding power curve is 1+ HHHHHHHHHHH + HHHHHH + HHHH + HHHH + HHH 0.8+ HHH + HHH + HHH + HHH + HHH 0.6+ HHH + HHH + HHH + HHH 0.4+ HHHH + HHH + HHHHH + HHHH + HHHH 0.2+ HHHHH -****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 45 and the ratio of minority is, 0.2 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.01288581267 The corresponding power curve is 1+ HHHHHHHHHH + HHHH + HHHH + HHH 0.8+ HHH + HH + HH + HH 0.6+ HHH + HH + HH + HHH 0.4+ HHH + HHH + HH + HHH 0.2+ HHH + HHHHH + HHHHHH + HHHHHHHHH -************+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.003228599097 The corresponding power curve is 1+ HHHHHH + HHH + HH + HH 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HH + HH 0.4+ HHH + HH + HHH + HHH 0.2+ HHH + HHHHH + HHHHHH + HHHHHHHHHH -*********************+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 9 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5879555125 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH + HHHH + HHH 0.9+ HHH + HHH + HHH + HH + HH 0.8+ HH + HH + HH + HH + HH 0.7+ HH + H + HH + HH 0.6+HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2974567358 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH + HHHH 0.9+ HH + HH + HHH 0.8+ HH + HH + HH + HH 0.7+ HH + HH + HH 0.6+ HH + HH + HH + HH 0.5+ HH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1768170131 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHH + HHH + HHH 0.8+ HH + HH + HH 0.7+ HH + HHH 0.6+ HH + HH + HH 0.5+ HHH + HHH + HH 0.4+ HH + HH + HHH 0.3**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.03823599831 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHHH + HHH + HHH 0.8+ HHH + HHH + HH + HH + HH 0.6+ HH + HH + HHH + HHH + HHH 0.4+ HH + HH + HHH + HHHH 0.2+ HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 45 and the ratio of minority is, 0.3 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 7 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02086530028 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HH + HH + HH + HHH 0.6+ HH + HH + HHH + HH 0.4+ HHH + HHH + HHH + HHH 0.2+ HHH + HHH + HHHH + HHHHHH -********-+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.007969890183 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HHH + HHH + HH + HHH 0.6+ HH + HH + HH + HH 0.4+ HH + HH + HH + HHH 0.2+ HHH + HHHH + HHHHH + HHHHHHH -************+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 13 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5087530942 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHH + HHH 0.9+ HHH + HHH + HH + HH 0.8+ HH + HH + H + HH 0.7+ HH + HH + HH + HH 0.6+ HH + HH + HH +HH 0.5**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 11 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2620402297 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HHH + HH 0.8+ HHH + HH + HH + HH 0.7+ HH + HH + HH 0.6+ HH + H + HH 0.5+ HH + HH + HH 0.4+HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 10 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1647299543 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HHH 0.8+ HHH + HHH + HH 0.7+ HHH + HH + HH 0.6+ HH + HH + HH 0.5+ HHH + HH 0.4+ HH + HH + HHH 0.3+HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 8 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.04711667085 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHH + HHH + HH 0.8+ HH + HH + HHH + HH + HH 0.6+ HHH + HH + HHH + HH 0.4+ HH + HH + HH + HH + HHH 0.2+ HHH -***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 45 and the ratio of minority is, 0.4 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 11 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02158968390 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HH + HHH + HH + HH 0.6+ HH + HHH + HH + HH 0.4+ HH + HHH + HH + HHH 0.2+ HH + HHHH + HHHH + HHHHHH -******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 10 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.009391534265 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHHH + HHH 0.8+ HH + HH + HH + HH 0.6+ HH + HH + HH + HH 0.4+ HH + HH + HH + HH 0.2+ HH + HHH + HHHH + HHHHHH -*********+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 18 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5642914444 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HH + HH 0.9+ HH + HH + HH + HH 0.8+ HH + HH + HH + HH + HH 0.7+ H + H + HH + H 0.6+ H +H -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 16 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3272325185 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHHH + HHH 0.9+ HH + HH + HH 0.8+ HH + H + H + HH 0.7+ HH + H + H 0.6+ HH + H + H + H 0.5+ HH +H -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 14 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1430399625 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HHH + HH 0.8+ HH + HH + H 0.7+ HH + HH + HH 0.6+ HH + HH + HH 0.5+ HH + H + H 0.4+ H +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 13 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.08362300899 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH + HHH 0.8+ HH + HH + HH + HH + HHH 0.6+ HH + HH + HH + HH + HH | HH 0.4+ HH + HH + HH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 45 and the ratio of minority is, 0.5 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 15 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.01784890178 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HHH + HH + HHH + HH 0.6+ HH + HH + HHH + HH 0.4+ HH + HHH + HH + HH 0.2+ HH + HH + HHH + HHHHH -******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 14 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.008047180019 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HH 0.8+ HHH + HH + H + HH 0.6+ HH + HH + H + HH 0.4+ HH + HH + HH + HHH 0.2+ HH + HHH + HHH + HHHHH -********-+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 22 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5000000001 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HH 0.9+ HH + HH + HH + HH 0.8+ HH + HH + HH + H 0.7+ H + H + HH + H 0.6+ H + HH +HH +H 0.5**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 20 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2757421650 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH 0.9+ HH + HH + HH 0.8+ H + H + H + HH 0.7+ H + H + H 0.6+ HH + HH + HH 0.5+ H + H + H 0.4+H -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 19 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1856490173 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH 0.9+ HHH + HH + HH 0.8+ HHH + HH 0.7+ HH + HH + HH 0.6+ HH + HH + HH 0.5+ HH + HH + HH 0.4+ HH + HH 0.3+HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 17 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.06757822542 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHHH + HHH + HH 0.8+ HH + HH + H + HH + HH 0.6+ HH + HH + HH + H + H 0.4+ H + HH + HH + HH +HHH 0.2**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 55 and the ratio of minority is, 0.1 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 1 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02164090825 The corresponding power curve is 1+ HHHHH + HHH + HH + HH 0.8+ HH + HH + HH + HH 0.6+ HHH + HHH + HHH + HHH 0.4+ HHH + HHHH + HHH + HHH 0.2+ HHHH + HHHHH + HHHHHHHH + HHHHHHHHHHH -*************--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 0 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.003043252722 The corresponding power curve is 1+ HH + H + H + HH 0.8+ HH + H + H + H 0.6+ H + HH + HH + HH 0.4+ HH + HHH + HHH + HHH 0.2+ HHH + HHHH + HHHHHHH + HHHHHHHHHHHHH -*****************************+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 5 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5244357960 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHHH + HHHHH + HHHH 0.9+ HHH + HHHH + HHH + HHH 0.8+ HH + HHH + HH + HHH + HHH 0.7+ HH + HH + HHH + HH 0.6+ HH + HH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3451482741 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHHH 0.8+ HHH + HH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HH + HHH 0.5+ HHH + HHH + HHH 0.4+ HHHH + HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 3 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1869534018 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHHH 0.9+ HHHH + HHHH + HHHH 0.8+ HHH + HH + HHH 0.7+ HHH + HHH + HHH 0.6+ HHH + HH + HHH 0.5+ HHH + HHH + HHH 0.4+ HHHH + HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 2 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.07743387482 The corresponding power curve is 1+ HHHHHHHHHHHHHHH + HHHHHH + HHHHH + HHHH + HHHH 0.8+ HHH + HHH + HHH + HHH + HHHH 0.6+ HHH + HHH + HH + HHH + HHHH 0.4+ HHH + HHH + HHH + HHHH + HHHHH 0.2****--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 55 and the ratio of minority is, 0.2 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 5 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.02453900071 The corresponding power curve is 1+ HHHHHHHHHHHHHHHH + HHHHH + HHH + HHH 0.8+ HHH + HHH + HHH + HHH 0.6+ HH + HHH + HHH + HH 0.4+ HHH + HH + HHH + HHH 0.2+ HHHH + HHHH + HHHHH + HHHHHHHH -********-+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 4 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.008650829148 The corresponding power curve is 1+ HHHHHHHHHHHH + HHHH + HHH + HHH 0.8+ HHH + HH + HH + HH 0.6+ HH + HH + HH + HH 0.4+ HH + HHH + HHH + HHHH 0.2+ HHH + HHHHH + HHHHH + HHHHHHHHH -*************--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 11 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5797626249 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHHH + HHH 0.9+ HHH + HH + HH + HH + HH 0.8+ HH + HH + H + H 0.7+ H + HH + HH + HH + HH 0.6+HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 9 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3158911050 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHHH + HHHH + HHH 0.9+ HHH + HHH + HH 0.8+ HH + HH + HH + HH 0.7+ HH + HH + HH 0.6+ HH + HH + HH + HH 0.5+ HH +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 8 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2024534218 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHHH + HHH + HH 0.8+ HHH + HH + HH 0.7+ HH + HH + HHH 0.6+ HH + HH + HH 0.5+ HH + HH + HHH 0.4+ HHH +HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 6 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.05763935812 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHHH + HHH 0.8+ HHH + HHH + HH + HHH + HHH 0.6+ HH + HHH + HHH + HHH + HH 0.4+ HH + HHH + HHH + HHHH + HHH 0.2***+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 55 and the ratio of minority is, 0.3 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 9 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.01592896342 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HH 0.8+ HHH + HH + HHH + HH 0.6+ HH + HH + HH + HH 0.4+ HH + HHH + HH + HH 0.2+ HHH + HHH + HHHH + HHHHHHH -********-+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 8 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.006554441721 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHH + HHHH + HHH + HHH 0.8+ HHH + HH + HHH + HH 0.6+ HH + HH + HH + HH 0.4+ HHH + HH + HH + HH 0.2+ HHH + HHH + HHHHH + HHHHHHH -***********-+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 16 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5079010550 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHHH + HHH 0.9+ HHH + HH + HHH + HH 0.8+ HH + HH + HH + H 0.7+ H + H + H + H 0.6+ H + H + HH +H 0.5**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 14 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2827124475 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HH + HH + HH 0.8+ HH + HH + H 0.7+ HH + HH + HH 0.6+ HH + HH + HH 0.5+ H + H + HH +HH 0.4**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 13 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1899097413 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH 0.9+ HHH + HHH + HH 0.8+ HH + HH 0.7+ HH + HH + HH 0.6+ HH + HH + HHH 0.5+ HH + HH + HH 0.4+ HH + HH +HHH 0.3**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 11 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.06681226706 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHHH + HHH + HHH 0.8+ HH + HH + HH + HH + HH 0.6+ HH + HHH + HH + HH + HH 0.4+ HH + HH + HHH + HH + HH 0.2**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 55 and the ratio of minority is, 0.4 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 14 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.01751644718 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHHH + HHH 0.8+ HH + HHH + HH + HH 0.6+ HH + HH + H + HH 0.4+ HH + HH + HH + HH 0.2+ HHH + HHH + HHHH + HHHHHH -******+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 13 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.008143318518 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHHH + HH 0.8+ HH + HH + HH + HHH 0.6+ HH + HH + HH + HH 0.4+ HH + HH + HH + HHH 0.2+ HHH + HHH + HHHH + HHHHHH -********-+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 22 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.5582278741 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HHH + HH 0.9+ HH + HH + HH + HH 0.8+ HH + H + H + H + H 0.7+ HH + H + H + HH 0.6+HH +H -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 20 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.3428825782 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH 0.9+ HHH + HH + HH 0.8+ HHH + HH + HH 0.7+ HH + HH + HH 0.6+ HH + HH + HH 0.5+ HH + HH + HH 0.4+ HH +HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 18 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1678743489 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHHH 0.9+ HHH + HH 0.8+ HH + HH + HH 0.7+ HH + HH + H 0.6+ H + HH 0.5+ HH + HH + HH 0.4+ HH + HH + HH 0.3+HH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 16 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.06306290942 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHHH + HHH + HH + HH 0.8+ HH + HH + HH + HH + HH 0.6+ H + H + HH + HH 0.4+ HH + HH + HH + HH + HH 0.2+HHH -**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 When the number of positions is, 55 and the ratio of minority is, 0.5 The Princeton method would detect bias, with confidence level 1/40, for any\ number of minority hires less-than-or equal to 19 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.01501447270 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HH 0.8+ HH + HH + HH + H 0.6+ H + HH + HH + HH 0.4+ HH + HH + HH + HH 0.2+ HH + HHH + HHH + HHHH -*****-+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 and with confidence level 1/100, for any number of minority hires less-tha\ n-or equal to 18 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.007226916765 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HH 0.8+ HH + H + HH + HH 0.6+ HH + HH + H + HH 0.4+ HH + HH + HH + HH 0.2+ HH + HH + HHH + HHHHH -*******--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0.2 0.4 0.6 0.8 1 The Government method would need at most 27 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.4999999999 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH + HH 0.9+ HH + HH + HH + HH 0.8+ HH + H + H + HH 0.7+ HH + H + H + HH 0.6+ H + H +HH +H 0.5*--+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=0.5, would need 25 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.2950266659 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHH 0.9+ HHH + HH + HH + HH 0.8+ H + HH + H 0.7+ H + H + HH 0.6+ HH + H + H + HH 0.5+ H + H +H 0.4**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1, would need 23 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.1403048589 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HHHH 0.9+ HH + HH + HH 0.8+ HH + HH + HH 0.7+ HH + H 0.6+ HH + HH + H 0.5+ HH + H + H 0.4+ HH + HH +HH 0.3**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1 The Constant Standard Deviation method with a=1.5, would need 21 Hence the probability that an innocent, unbiased department, would be labell\ ed as biased is 0.05239474121 The corresponding power curve is 1+ HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH + HHHHH + HH + HH + HH 0.8+ HH + HHH + HH + HH + H 0.6+ H + HH + H + H + H 0.4+ H + H + H + H +HH 0.2**-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+-+--+--+--+--+--+--+--+--+- 0 0.2 0.4 0.6 0.8 1