Two Standard Deviations

The 2 Standard Deviation Analysis is a complex mathematical test which usually results in a lower showing of under representation than the Four-Fifths Rule, especially if the job group being tested is small. This analysis is available in the Utilization Summary, Availability Analysis, Adverse Impact Analysis, and Salary Regression.

CALCULATION EXAMPLE:

Main Group = 29 && Male Employees
Main Action= 3 && Male Layoffs
Compare Group = 203 && Female Employees
Compare Action = 55 && Female Layoffs

R = 58 && Main Action + Compare Action
J = 55 && Compare Action
P = 232 && Main Group + Compare Group
H = 203 && Compare Group

nSqrtval = (R/P) * ((P-R)/P) * (1/H)+(1/(P-H))
nSqrtval = .007389162561375

nSqrt = SQRT(nSqrtval)
nSqrt = 0.08596023825802

nValue = (((R-J)/(P-H))-(J/H))/nSqrt
nValue = -1.948432067234

nFinal = ROUND(nValue) && Round to 2 decimal places
nFinal = -1.95

Additional Notes For the Adverse Impact Analysis:

If the analysis being performed is positive, then the group passes the 2 Standard Deviations test if the number being reported is less or equal to 1.96 (or the report states the result is not statistically significant). If the analysis being performed is negative, then the group passes the 2 Standard Deviations if the number being reported is greater than or equal to –1.96 (or the report states the result is not statistically significant).

2 Standard Deviation Test for Goals Setting

The 2 Standard Deviation Test is used to establish placement goals when comparing the availability to the current utilization of women and minorities in the workforce.

Calculation Example:

P = Availability % of women or minorities = 20%
N = Total employees in job group = 200
O = Total women or minorities in job group = 31
SD = Standard Deviation
SQRT = Square Root

SD Formula:

SD = SQRT[P x N (1-P)]
SD = SQRT[(.20) x (200) (1-.20)]
SD = 5.66

Expected Number = P x N = (.20) x (200) = 40

Number of Standard Deviations = [Expected Number – (O)] / SD

= (40 – 31) / 5.66

= 1.59 Standard Deviations

In this example, 1.59 standard deviations falls below the 2 standard deviation threshold and the contractor does not need to establish a placement goal.

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