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Federal Register / Vol. 86, No. 142 / Wednesday, July 28, 2021 / Rules and Regulations
discussion of them in this Appendix is limited. To be as conservative as possible, the Commission chooses the confidence level for the critical value to be 99%. The Thompson Tau test identifies 98 total outliers: 94 jails with average daily populations of less than 1,000, 3 larger jails, and 1 prison. The Grubbs test identifies 25 total outliers: 22 Jails with average daily populations less than 1,000 and three larger jails.
6. Both the Grubbs and Thompson Tau tests assume that each observation is drawn from a normal distribution, and that outlier observations are those that would not typically occur from the same data generating process. However, if the true data-generating process leads to a right-skewed distribution, then observations identified as outliers under an assumption of normality may in fact be legitimate data points. In a right-skewed distribution, the mean is greater than the median. To ensure the outlier results are
robust to normality assumptions, the Commission also employs a well-known nonparametric approach to outlier detection: The box plot. This approach does not rely on the assumption of normality and instead uses only the mean, median, and quartiles of the data. A box plot defines outlier observations as those that are more than 1.5 times the interquartile range from the upper or lower quartiles of the per-minute cost data the upper and lower bounds. These bounds are referred to as Tukeys fences. The procedure identifies a total of 52 observations above the upper bound: 49 Jails with average daily populations less than 1,000 and 3 larger jails.
7. The Grubbs, Thompson Tau, and box plot approaches identify the same overlapping set of contracts as outliers, but with increasing restriction based on the technique. Specifically, there is no outlier identified by Grubbs that is not also an
outlier for Thompson Tau and the box plot.
Similarly, there is no outlier identified by the box plot that is not also an outlier for Thompson Tau. Though Thompson Tau appears to be least conservative and Grubbs most conservative, what is important is that all three approaches lead to the identification of the same nested set of outlier observations.
To retain as much data as possible, and to be as conservative with the analysis as possible, the Commission excludes from the contracts data only those 25 observations identified by Grubbs as being outliers.
8. The results of the outlier analysis are presented in Tables 1, 2, and 3 below. Table 1 lists the outlier observations for each firm and facility type, while Table 2 presents the full list of contracts identified as outliers.
Finally, Table 3 presents the summary statistics of per-minute costs for the group of outlier contracts.

TABLE 1OUTLIER OBSERVATIONS BY FIRM AND FACILITY TYPE
Number of contracts ATN
Smaller Jails
Larger Jails
Total

Correct 2
0

I

2

Crown 5
3

I

GTL
4 0

I

8

4

Pay Tel 2
0

I

Securus 6
0

I

2

6

Total 3
0

I

3

22
3

I

25

TABLE 2CONTRACTS CLASSIFIED AS OUTLIERS
Firm
Contract identifier
Facility type
Correct
Correct
Correct
ATN
ATN
Correct
Correct
Correct
Correct
Correct
Crown
Crown
Crown
Crown
GTL
GTL
Pay Tel
Pay Tel
Pay Tel
Pay Tel
Pay Tel
Pay Tel
Securus
Securus
Securus

Williamson
San Luis
West Texas
REDACTED
REDACTED
Morgan City
Little River
Rolling Plains
Wise
Livingston WR
Graham County Jail NCICCrown
Thayer County Jail NCICCrown
Pawnee County Jail NCICCrown
Phillips County Jail NCICCrown
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED

Larger Jail
Larger Jail
Larger Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail
Smaller Jail

ADP
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED

CPM
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED

RPM
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED
REDACTED

khammond on DSKJM1Z7X2PROD with RULES2

Notes: ADP is the average daily population covered by the contract; CPM is a contracts average cost per minute; and RPM is a contracts average revenue per minute, net of any commissions paid.

TABLE 3OUTLIER ANALYSIS SUMMARY STATISTICS
Number of contracts
Mean $

Median $

Std. dev.
$

Minimum $

Maximum $

Smaller Jails
Larger Jails

22
3

0.410
0.782

0.359
0.512

0.128
0.656

0.283
0.303

0.734
1.529

Total

25

0.455

0.370

0.255

0.283

1.529

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