I. Parity measures

A. Statistical Tests

All statistical tests will be one-tailed tests.

1. Average-based Parity Measures

The Modified t-test will be used for all average-based parity measures as specified in:

Brownie, C., Boos, D., & Hughes-Oliver, J. (1990). Modifying the t and ANOVA F tests when treatment is expected to increase variability relative to controls. Biometrics, 46, 259-266.

The Modified t-test for the difference in means (averages) between the ILEC and the CLEC populations is:

t = (M_i-M_c)/[S_i*sqrt(1/N_c+1/N_i)]

Where:

M_c = the CLEC mean result

M_i = the ILEC mean result

S_i = the standard deviation of the results for the ILEC

N_c = the CLEC sample size

N_i = the ILEC sample size

sqrt = square root

For measures of time intervals, except for data where "zeros" are not possible, the raw score distribution will be normalized by taking the natural log of each score after a constant of 0.4 of the smallest unit of measurement is added to each score. For example, if the smallest unit of measurement is an integer, then the added constant would be 0.4:

x_tran = ln(x + 0.4)

Similarly, if the smallest unit of measurement is 0.01, then the added constant would be 0.004:

x_tran = ln(x + 0.004)

Results that are not measures of time intervals (e.g., Measure 34) will not be transformed.

The Modified t-test calculation for average parity measures will be structured so that a negative sign indicates "worst" performance. Specifically, when a lower value represents better performance, such as time to provision a service, the CLEC mean will be subtracted from the ILEC mean. Different performance measures may require reversing the means in the equation to have a negative sign indicate poorer performance.

The t-statistic will be converted to an _ (Type I error) probability using a t-distribution table or calculation. Degrees of freedom (df) will be based only on the ILEC sample size consistent with Brownie, et al. If the obtained _ value is less than the critical _ value, then the result will be deemed not in parity.

2. Proportion Parity Measures

Except for performance results that have numbers too large to calculate with the exact test, the Fisher's Exact Test will be used for all percentage or proportion parity measures as specified in:

Sheskin, D. (1997). Handbook of parametric and nonparametric statistical procedures. Boca Raton: CRC Press, pp. 221-225.

If the obtained _ value is less than the critical _ value, then the result will be deemed out-of-parity.

Performance results that are too large to calculate with the Fisher's exact test are those measures that exceed the following values:

1. For percentage-based measures where low values signal good service, Fisher's Exact Test shall be applied to all problems for which the CLEC numerator is less than 1000 "hits." The Z-test shall be applied to larger results.

2. For percentage-based measures where high values signal good service, the analysis is the same but is applied to the "misses" as opposed to the "hits." The Fisher's Exact Test shall be applied whenever the denominator minus the numerator is less than 1000 for the CLEC result. The Z-test shall be applied to larger results.

Such results will be calculated using the Modified Z-test for proportions as follows:

Z = (P_i-P_c)/sqrt[P_i(1-P_i)*(1/N_c+1/N_i)]

Where:

P_c = the CLEC proportion

P_i = the ILEC proportion

N_c = the CLEC sample size

N_i = the ILEC sample size

sqrt = square root

The Modified Z-test calculation for proportion parity measures will be structured so that a negative sign indicates "worst" performance. Specifically, when a higher value represents better performance, such as percent on-time tasks, the ILEC proportion will be subtracted from the CLEC proportion. Different performance measures may require reversing the means in the equation to have a negative sign indicate poorer performance.

The Z-statistic will be converted to an _ (Type I error) probability using a Z-distribution table or calculation. If the obtained _ value is less than the critical _ value, then the result will be deemed not in parity.

3. Rate-based Parity Measures

The Binomial Exact Test will be used for all rate parity measures. The Binomial Exact Test is specified in GTECs Exhibit C, Section 3, "Permutation Test for Rates", Equations 3.1 and 3.2 (Deliverable #7, Facilitated Work Group, April 2000).

4. Indexed-based Parity Measures

Measure 42 provides an index of parity performance that will be assessed by comparing ILEC and CLEC performance as follows:

Non-parity will be identified when the ILEC percentage minus the CLEC percentage exceeds 0.05 percentage points.

B. Critical Alpha Level for Parity Tests

The Type I error probabilities (alphas, _) obtained from the parity statistical tests will be compared to a critical alpha value of 0.10.

A performance result with _ equal to or less than 0.10 will be deemed a performance failure with no additional conditions.

A performance result with _ equal to or less than 0.20 and greater than 0.10 will be deemed a conditional failure. Additional conditions to determine failures will be specified in the final remedies plan.

C. Sample Sizes and Aggregation Rules

Statistical tests will be applied to the monthly performance results specified in D.99-08-020.

1. Average-based measures

For average-based performance results the following aggregation rules will be used:

(1) For each submeasure, the performance results for all samples with one to four cases will be aggregated with each other to form a single performance result.

(2) Statistical analyses and decision rules will be applied to determine performance subject to the performance remedies plan for all samples after the aggregation in step (1), regardless of sample size. For example, if samples with as few as one case remain after the aggregation, statistical analysis and decision rules will be applied to determine performance subject to the performance remedies plan to these samples, just as they are for larger samples.

2. Proportion and rate-based measures

All samples will be analyzed as they are reported without aggregation.

D. Measures without Retail Analogues.

In months where there are no retail analogue performance data, the prior six months of ILEC data be aggregated (to the extent that such data exist) and used in place of the data-deficient month. If the aggregate does not produce sufficient ILEC data, the submeasure not be evaluated for the month.

II. Benchmark Measures

For large samples, the actual performance will be compared to the benchmark nominal percentage according to the percentage set in the Joint Partial Settlement Agreement approved by the Commission. For small samples, maximum permitted "misses" shall be determined by small sample adjustment tables. Small samples are defined as follows:

90 percent benchmarks - 50 cases or less

95 percent benchmarks - 100 cases or less

99 percent benchmarks - 500 cases or less

Adjustment tables:

90% Benchmark		95% Benchmark		99% Benchmark
Sample size	Maximum permitted misses	Sample size	Maximum permitted misses	Sample size	Maximum permitted misses
1	0	1 to 3	0	1 to 19	0
2 to 9	1	4 to 19	1	20 to 97	1
10 to 20	2	20 to 40	2	98 to 202	2
21 to 31	3	41 to 63	3	203 to 319	3
32 to 44	4	64 to 88	4	320 to 445	4
45 to 50	5	89 to 100	5	446 to 500	5

The small sample adjustment tables shall be used in the following steps:

1. The number of performance "misses" for the CLEC industry-wide aggregate for each remedy plan benchmark submeasure will be compared to the number of permitted misses for all sample sizes covered by the related adjustment table. Industry aggregate performance will be identified as passing if the number of actual misses is less than or equal to the number of permitted misses, and identified as failing if otherwise.

2. For CLEC industry-wide aggregate sample sizes not covered by the related adjustment table, the actual performance percentage result will be compared to the benchmark nominal percentage value. Industry aggregate performance will be identified as passing if the actual performance percentage result is greater than or equal to the benchmark nominal percentage value, and identified as failing if otherwise.

3. For CLEC-specific analysis, results with sample sizes of four or less will be aggregated into a "small sample CLEC aggregate" for each submeasure. Each small sample CLEC aggregate performance result and all remaining non-aggregated CLEC performance results will be assessed.

4. For each submeasure where the CLEC industry-wide aggregate performance fails the benchmark, the actual performance percentage result for each small sample CLEC aggregate and each remaining non-aggregated CLEC result will be compared to the benchmark nominal percentage value. Each individual or aggregate performance result will be identified as passing if the actual performance percentage result is greater than or equal to the benchmark nominal percentage value, and identified as failing if otherwise.

5. For sample sizes covered by the related adjustment table where the CLEC industry-wide aggregate performance passes the benchmark, the following shall apply for each submeasure. For each benchmark submeasure, the number of performance "misses" for each small sample CLEC aggregate and each remaining non-aggregated CLEC will be compared to the number of permitted misses. CLEC performance will be identified as passing if the number of actual misses is less than or equal to the number of permitted misses, and identified as failing if otherwise.

6. For sample sizes not covered by the related adjustment table where the CLEC industry-wide aggregate performance passes the benchmark, the following shall apply. The actual performance percentage result for each small sample CLEC aggregate and each remaining non-aggregated CLEC result will be compared to the benchmark nominal percentage value. Each individual or aggregate performance result will be identified as passing if the actual performance percentage result is greater than or equal to the benchmark nominal percentage value, and identified as failing if otherwise.