§ 83.05 – How should I determine the APTL from my sample?

(a)    You must determine the sample APTL for a given sample as the ratio of sample total PMT over sample total UPT for the following cases:

(1)   for the entire sample,

(2)   by type of service days, or

(3)   by service group if applicable.

(b)   You must not determine the sample APTL as the average of the APTL across individual service units in the sample.

(c)    To determine the weighted sample APTL for an entire sample as required by question §83.03(c)(3), you should follow these steps:

(1)   Determine each group’s size in the number of service units actual operated.

(2)   Compute each group’s share of the number of service units actually operated.  These shares must sum to 1.

(3)   Determine each group’s sample size in the number of service units in the sample.

(4)   Determine each group’s sample total UPT.

(5)   Determine each group’s sample total PMT.

(6)   Compute each group’s sample average for UPT.

(7)   Compute each group’s sample average for PMT.

(8)   Sum the product of each group’s share of the number of service units actually operated and its sample average UPT.

(9)   Sum the product of each group’s share of the number of service units actually operated and its sample average PMT.

(10)           Compute the ratio of the result from (9) to the result from (8).  This ratio gives the weighted sample APTL.

(11)           Table 83.01 shows these steps with an example.

Table 83.01.  Example of Estimating Weighted Sample APTL

Step

 Description

Service Groups

Short Routes

Medium Routes

Long Routes

1

Group size in service units

109,685

331,033

35,325

2

Group size in shares

0.2304

0.6954

0.0742

3

Sample size

116

386

47

4

Sample total UPT

1,157

8,181

1,592

5

Sample total PMT

3,989

42,966

7,003

6

Sample average UPT

10.0

21.2

33.9

7

Sample average PMT

34.4

111.3

149.0

8

Weighted sample average UPT

19.55

9

Weighted sample average PMT

96.38

10

Weighted sample APTL

4.93