# About AAP Statistical Calculations

#### Standard Deviation

The primary statistical test for utilization and adverse impact is calculating the standard deviation. A standard deviation score of 2.00 or greater is considered statistically significant.

For utilization:
[(Availability x ~~total~~Total ~~employees~~Persons in ~~the~~Job ~~job group)~~Group) - ~~number~~Number of ~~protected~~Protected-class ~~class~~Employees] ~~employees] divided by~~/ the square root of [(1 - Availability ) x Availability x ~~total~~Total ~~employees~~Persons in ~~the~~Job ~~job group]~~Group]

For adverse impact of positive actions:
Non-protected ~~class~~Class ~~selection~~Selection ~~rate~~Rate - Protected ~~class~~Class ~~selection~~Selection ~~rate~~Rate / the square root of ~~(overall~~(Overall ~~selection~~Selection ~~rate~~Rate ~~*(1-overall~~*(1 ~~selection~~- ~~rate)~~Overall Selection Rate) * ~~((1/total~~((1 ~~protected)~~/ Total Protected) + ~~(1/total~~(1 ~~non-protected))~~/ Total Non-protected))

For adverse impact of negative actions: Protected class selection rate - non-protected class selection rate divided by the square root of (overall selection rate *(1-overall selection rate) * ((1/total protected) + (1/total non-protected))

#### Exact Binomial

Used to test statistical significance for difference between employment and availability; use if Job Group is fewer than 30 employees. An exact binomial result of .05 or less is considered statistically significant.

P^N + (((N/1) * P^(N -1)*Q)) + (((N * (N-1))/(1 * 2))) * (P^(N-2) * Q^2) + (((N * (N-1) * (N-2))/(1 * 2 * 3))) * (P^(N-3) * Q^3) + .... + Q^N

*Where:*
P = The probability of being non-protected (1 - availability of the protected group)

Q = The probability of being protected (the availability)

N = The number of people in the group (i.e. the number of trials)

The aggregation of the expanded members should only include up to the number of protected members + 1 (i.e., only add the first four expansion terms when there are three protected members in the group).

In the exact binomial formula, the "^" is the symbol for an exponential.

#### Fisher’s Exact Test

For Adverse Impact, if there are fewer than 30 incumbents or applicants in the the ~~job~~Job ~~group,~~Group, the Fisher’s Exact Test will be used to ~~test~~calculate significance. Fisher's Exact Test scores of .025 or lower are considered statistically significant. The threshold of 30 can be adjusted under: Plan Settings (with careful consideration and consultation with a statistician).

#### Rule of Nines

When selecting Significant Difference as the selected Utilization Rule, an alternate rule can also be selected. The alternate rule will be used instead of the significant difference rule if the group size is too small, as determined by the Rule of Nines test.

The formula is the total number in the group multiplied by the protected class availability multiplied by its complement. The result should be greater than nine to rely on standard deviation as a test of significance.

(Job Group Total) * (Protected Class Availability) * (1 – Protected Class Availability)

** Example:**
If a Job Group has 76 employees and the availability for minorities is 7.8%, the formula would

In this instance, the validity of standard deviation to measure the significance of any differences between minority availability and employment would be questionable.

~~The use of this~~This rule is ~~infrequent~~used infrequently because it may establish too high a “small group” threshold. For example, under the Rule of Nines any Job Group with less than 36 employees will score less than 9. Some statisticians would set a lower absolute threshold.