Common use of Statistical Measurement Clause in Contracts

Statistical Measurement. 4.1 Qwest uses a statistical test, namely the modified “z-test,” for evaluating the difference between two means (i.e., Qwest and CLEC service or repair intervals) or two percentages (e.g., Qwest and CLEC proportions), to determine whether a parity condition exists between the results for Qwest and the CLEC(s). The modified z- tests shall be applicable if the number of data points are greater than 30 for a given measurement. For testing measurements for which the number of data points are 30 or less, Qwest will use a permutation test to determine the statistical significance of the difference between Qwest and CLEC. 4.2 Qwest shall be in conformance when the monthly performance results for parity measurements (whether in the form of means, percents, or proportions and at the equivalent level of disaggregation) are such that the calculated z-test statistics are not greater than the critical z-values as listed in Table 1, section 5.0. 4.3 Qwest shall be in conformance with benchmark measurements when the monthly performance result equals or exceeds the benchmark, if a higher value means better performance, and when the monthly performance result equals or is less than the benchmark if a lower value means better performance. The formula for determining parity using the modified z-test is: z = DIFF / σDIFF Where: DIFF = MQwest – MCLEC MQWEST = Qwest average or proportion MCLEC = CLEC average or proportion σDIFF = square root σQwest (1/ n CLEC + 1/ n Qwest)] σ2Qwest = calculated variance for Qwest nQwest = number of observations or samples used in Qwest measurement nCLEC = number of observations or samples used in CLEC measurement The modified z-tests will be applied to reported parity measurements that contain more than 30 data points. In calculating the difference between Qwest and CLEC performance, the above formula applies when a larger Qwest value indicates a better level of performance. In cases where a smaller Qwest value indicates a higher level of performance, the order is reversed, i.e., MCLEC - MQWEST. 4.3.1 For parity measurements where the number of data points is 30 or less, Qwest will apply a permutation test to test for statistical significance. Permutation analysis will be applied to calculate the z-statistic using the following logic: Calculate the modified z-statistic for the actual arrangement of the data Pool and mix the CLEC and Qwest data sets Perform the following 1000 times: Randomly subdivide the pooled data sets into two pools, one the same size as the original CLEC data set (nCLEC) and one reflecting the remaining data points, and one reflecting the remaining data points, (which is equal to the size of the original Qwest data set or nQWEST). Compute and store the modified z-test score (ZS) for this sample. Count the number of times the z-statistic for a permutation of the data is greater than the actual modified z- statistic. Compute the fraction of permutations for which the statistic for the rearranged data is greater than the statistic for the actual samples. If the fraction is greater than α, the significance level of the test, the hypothesis of no difference is not rejected, and the test is passed. The α shall be .05 when the critical z value is 1.645 and .15 when the critical z value is 1.04.

Statistical Measurement. 4.1 Qwest uses a statistical test, namely the modified “z-test,” for evaluating the difference between two means (i.e., Qwest and CLEC service or repair intervals) or two percentages (e.g., Qwest and CLEC proportions), to determine whether a parity condition exists between the results for Qwest and the CLEC(s). The modified z- tests shall be applicable if the number of data points are greater than 30 for a given measurement. For testing measurements for which the number of data points are 30 or less, Qwest will use a permutation test to determine the statistical significance of the difference between Qwest and CLEC. 4.2 Qwest shall be in conformance when the monthly performance results for parity measurements (whether in the form of means, percents, or proportions and at the equivalent level of disaggregation) are such that the calculated z-test statistics are not greater than the critical z-values as listed in Table 1, section 5.0. 4.3 Qwest shall be in conformance with benchmark measurements when the monthly performance result equals or exceeds the benchmark, if a higher value means better performance, and when the monthly performance result equals or is less than the benchmark if a lower value means better performance. The formula for determining parity using the modified z-test is: z = DIFF / σDIFF Where: DIFF = MQwest – MCLEC MQWEST = Qwest average or proportion MCLEC = CLEC average or proportion σDIFF = square root σQwest σQwest (1/ n CLEC + 1/ n Qwest)] σ2Qwest σ.2Qwest = calculated variance for Qwest nQwest = number of observations or samples used in Qwest measurement nCLEC = number of observations or samples used in CLEC measurement The modified z-tests will be applied to reported parity measurements that contain more than 30 data points. In calculating the difference between Qwest and CLEC performance, the above formula applies when a larger Qwest value indicates a better level of performance. In cases where a smaller Qwest value indicates a higher level of performance, the order is reversed, i.e., MCLEC - MQWEST. 4.3.1 For parity measurements where the number of data points is 30 or less, Qwest will apply a permutation test to test for statistical significance. Permutation analysis will be applied to calculate the z-statistic using the following logic: Calculate the modified z-statistic for the actual arrangement of the data Pool and mix the CLEC and Qwest data sets Perform the following 1000 times: Randomly subdivide the pooled data sets into two pools, one the same size as the original CLEC data set (nCLEC) and one reflecting the remaining data points, and one reflecting the remaining data points, (which is equal to the size of the original Qwest data set or nQWEST). Compute and store the modified z-test score (ZS) for this sample. Count the number of times the z-statistic for a permutation of the data is greater than the actual modified z- statistic. statistic Compute the fraction of permutations for which the statistic for the rearranged data is greater than the statistic for the actual samples. samples If the fraction is greater than α, the significance level of the test, the hypothesis of no difference is not rejected, and the test is passed. The α shall be .05 when the critical z value is 1.645 and .15 when the critical z value is 1.04.

Statistical Measurement. 4.1 Qwest uses a statistical test, namely the modified “z-test,” for evaluating the difference between two means (i.e., Qwest and CLEC service or repair intervals) or two percentages (e.g., Qwest and CLEC proportions), to determine whether a parity condition exists between the results for Qwest and the CLEC(s). The modified z- tests shall be applicable if the number of data points are greater than 30 for a given measurement. For testing measurements for which the number of data points are 30 or less, Qwest will use a permutation test to determine the statistical significance of the difference between Qwest and CLEC. 4.2 Qwest shall be in conformance when the monthly performance results for parity measurements (whether in the form of means, percents, or proportions and at the equivalent level of disaggregation) are such that the calculated z-test statistics are not greater than the critical z-values as listed in Table 1, section 5.0. 4.3 Qwest shall be in conformance with benchmark measurements when the monthly performance result equals or exceeds the benchmark, if a higher value means better performance, and when the monthly performance result equals or is less than the benchmark if a lower value means better performance. The formula for determining parity using the modified z-test is: z = DIFF / σDIFF Where: DIFF = MQwest – MCLEC MQWEST = Qwest average or proportion MCLEC = CLEC average or proportion σDIFF = square root σQwest σ Qwest (1/ n CLEC + 1/ n Qwest0/ x Xxxxx)] σ2Qwest Xxxxx σ2 = calculated variance for Qwest nQwest = number of observations or samples used in Qwest measurement nCLEC = number of observations or samples used in CLEC measurement The modified z-tests will be applied to reported parity measurements that contain more than 30 data points. In calculating the difference between Qwest and CLEC performance, the above formula applies when a larger Qwest value indicates a better level of performance. In cases where a smaller Qwest value indicates a higher level of performance, the order is reversed, i.e., MCLEC - MQWEST. 4.3.1 For parity measurements where the number of data points is 30 or less, Qwest will apply a permutation test to test for statistical significance. Permutation analysis will be applied to calculate the z-statistic using the following logic: Calculate the modified z-statistic for the actual arrangement of the data Pool and mix the CLEC and Qwest data sets Perform the following 1000 times: Randomly subdivide the pooled data sets into two pools, one the same size as the original CLEC data set (nCLEC) and one reflecting the remaining data points, and one reflecting the remaining data points, (which is equal to the size of the original Qwest data set or nQWEST). Compute and store the modified z-test score (ZS) for this sample. Count the number of times the z-statistic for a permutation of the data is greater than the actual modified z- statistic. statistic Compute the fraction of permutations for which the statistic for the rearranged data is greater than the statistic for the actual samples. samples If the fraction is greater than α, the significance level of the test, the hypothesis of no difference is not rejected, and the test is passed. The α shall be .05 when the critical z value is 1.645 and .15 when the critical z value is 1.04.

Statistical Measurement. 4.1 Qwest uses a statistical test, namely the modified “z-test,” for evaluating the difference between two means (i.e., Qwest and CLEC service or repair intervals) or two percentages (e.g., Qwest and CLEC proportions), to determine whether a parity condition exists between the results for Qwest and the CLEC(s). The modified z- tests shall be applicable if the number of data points are greater than 30 for a given measurement. For testing measurements for which the number of data points are 30 or less, Qwest will use a permutation test to determine the statistical significance of the difference between Qwest and CLEC. 4.2 Qwest shall be in conformance when the monthly performance results for parity measurements (whether in the form of means, percents, or proportions and at the equivalent level of disaggregation) are such that the calculated z-test statistics are not greater than the critical z-values as listed in Table 1, section 5.0. 4.3 Qwest shall be in conformance with benchmark measurements when the monthly performance result equals or exceeds the benchmark, if a higher value means better performance, and when the monthly performance result equals or is less than the benchmark if a lower value means better performance. The formula for determining parity using the modified z-test is: z = DIFF / σDIFF Where: DIFF = MQwest – MCLEC MQWEST = Qwest average or proportion MCLEC = CLEC average or proportion σDIFF = square root σQwest σ Qwest (1/ n CLEC + 1/ n Qwest)] σ2Qwest σ2Qwest = calculated variance for Qwest nQwest = number of observations or samples used in Qwest measurement nCLEC = number of observations or samples used in CLEC measurement The modified z-tests will be applied to reported parity measurements that contain more than 30 data points. In calculating the difference between Qwest and CLEC performance, the above formula applies when a larger Qwest value indicates a better level of performance. In cases where a smaller Qwest value indicates a higher level of performance, the order is reversed, i.e., MCLEC - MQWEST. 4.3.1 For parity measurements where the number of data points is 30 or less, Qwest will apply a permutation test to test for statistical significance. Permutation analysis will be applied to calculate the z-statistic using the following logic: Calculate the modified z-statistic for the actual arrangement of the data Pool and mix the CLEC and Qwest data sets Perform the following 1000 times: Randomly subdivide the pooled data sets into two pools, one the same size as the original CLEC data set (nCLEC) and one reflecting the remaining data points, and one reflecting the remaining data points, (which is equal to the size of the original Qwest data set or nQWEST). Compute and store the modified z-test score (ZS) for this sample. Count the number of times the z-statistic for a permutation of the data is greater than the actual modified z- statistic. Compute the fraction of permutations for which the statistic for the rearranged data is greater than the statistic for the actual samples. If the fraction is greater than α, the significance level of the test, the hypothesis of no difference is not rejected, and the test is passed. The α shall be .05 when the critical z value is 1.645 and .15 when the critical z value is 1.04.

Statistical Measurement. 4.1 Qwest uses a statistical test, namely the modified “z-test,” for evaluating the difference between two means (i.e., Qwest and CLEC service or repair intervals) or two percentages (e.g., Qwest and CLEC proportions), to determine whether a parity condition exists between the results for Qwest and the CLEC(s). The modified z- tests shall be applicable if the number of data points are greater than 30 for a given measurement. For testing measurements for which the number of data points are 30 or less, Qwest will use a permutation test to determine the statistical significance of the difference between Qwest and CLEC. 4.2 Qwest shall be in conformance when the monthly performance results for parity measurements (whether in the form of means, percents, or proportions and at the equivalent level of disaggregation) are such that the calculated z-test statistics are not greater than the critical z-values as listed in Table 1, section 5.0. 4.3 Qwest shall be in conformance with benchmark measurements when the monthly performance result equals or exceeds the benchmark, if a higher value means better performance, and when the monthly performance result equals or is less than the benchmark if a lower value means better performance. The formula for determining parity using the modified z-test is: z = DIFF / σDIFF DIFF Where: DIFF = MQwest – MCLEC MQWEST = Qwest average or proportion MCLEC = CLEC average or proportion σDIFF = square root σQwest (1/ n CLEC + 1/ n Qwest)] σ2Qwest Qwest 2 = calculated variance for Qwest nQwest = number of observations or samples used in Qwest measurement nCLEC = number of observations or samples used in CLEC measurement The modified z-tests will be applied to reported parity measurements that contain more than 30 data points. In calculating the difference between Qwest and CLEC performance, the above formula applies when a larger Qwest value indicates a better level of performance. In cases where a smaller Qwest value indicates a higher level of performance, the order is reversed, i.e., MCLEC - MQWEST. 4.3.1 For parity measurements where the number of data points is 30 or less, Qwest will apply a permutation test to test for statistical significance. Permutation analysis will be applied to calculate the z-statistic using the following logic: Calculate the modified z-statistic for the actual arrangement of the data Pool and mix the CLEC and Qwest data sets Perform the following 1000 times: Randomly subdivide the pooled data sets into two pools, one the same size as the original CLEC data set (nCLEC) and one reflecting the remaining data points, and one reflecting the remaining data points, (which is equal to the size of the original Qwest data set or nQWEST). Compute and store the modified z-test score (ZS) for this sample. Count the number of times the z-statistic for a permutation of the data is greater than the actual modified z- statistic. statistic Compute the fraction of permutations for which the statistic for the rearranged data is greater than the statistic for the actual samples. samples If the fraction is greater than α, the significance level of the test, the hypothesis of no difference is not rejected, and the test is passed. The α shall be .05 when the critical z value is 1.645 and .15 when the critical z value is 1.04.

Statistical Measurement. 4.1 Qwest uses a statistical test, namely the modified “z-test,” for evaluating the difference between two means (i.e., Qwest and CLEC service or repair intervals) or two percentages (e.g., Qwest and CLEC proportions), to determine whether a parity condition exists between the results for Qwest and the CLEC(s). The modified z- tests shall be applicable if the number of data points are greater than 30 for a given measurement. For testing measurements for which the number of data points are 30 or less, Qwest will use a permutation test to determine the statistical significance of the difference between Qwest and CLEC. 4.2 Qwest shall be in conformance when the monthly performance results for parity measurements (whether in the form of means, percents, or proportions and at the equivalent level of disaggregation) are such that the calculated z-test statistics are not greater than the critical z-values as listed in Table 1, section 5.0. 4.3 Qwest shall be in conformance with benchmark measurements when the monthly performance result equals or exceeds the benchmark, if a higher value means better performance, and when the monthly performance result equals or is less than the benchmark if a lower value means better performance. The formula for determining parity using the modified z-test is: z = DIFF / σDIFF DIFF Where: DIFF = MQwest – MCLEC MQWEST = Qwest average or proportion MCLEC = CLEC average or proportion σDIFF DIFF = square root σQwest Qwest (1/ n CLEC + 1/ n Qwest)] σ2Qwest Qwest 2 = calculated variance for Qwest nQwest = number of observations or samples used in Qwest measurement nCLEC = number of observations or samples used in CLEC measurement The modified z-tests will be applied to reported parity measurements that contain more than 30 data points. In calculating the difference between Qwest and CLEC performance, the above formula applies when a larger Qwest value indicates a better level of performance. In cases where a smaller Qwest value indicates a higher level of performance, the order is reversed, i.e., MCLEC - MQWEST. 4.3.1 For parity measurements where the number of data points is 30 or less, Qwest will apply a permutation test to test for statistical significance. Permutation analysis will be applied to calculate the z-statistic using the following logic: Calculate the modified z-statistic for the actual arrangement of the data Pool and mix the CLEC and Qwest data sets Perform the following 1000 times: Randomly subdivide the pooled data sets into two pools, one the same size as the original CLEC data set (nCLEC) and one reflecting the remaining data points, and one reflecting the remaining data points, (which is equal to the size of the original Qwest data set or nQWEST). Compute and store the modified z-test score (ZS) for this sample. Count the number of times the z-statistic for a permutation of the data is greater than the actual modified z- statistic. statistic Compute the fraction of permutations for which the statistic for the rearranged data is greater than the statistic for the actual samples. samples If the fraction is greater than α, the significance level of the test, the hypothesis of no difference is not rejected, and the test is passed. The α shall be .05 when the critical z value is 1.645 and .15 when the critical z value is 1.04.

Statistical Measurement. 4.1 Qwest uses a statistical test, namely the modified “z-test,” for evaluating the difference between two means (i.e., Qwest and CLEC service or repair intervals) or two percentages (e.g., Qwest and CLEC proportions), to determine whether a parity condition exists between the results for Qwest and the CLEC(s). The modified z- z-tests shall be applicable if the number of data points are greater than 30 for a given measurement. For testing measurements for which the number of data points are 30 or less, Qwest will use a permutation test to determine the statistical significance of the difference between Qwest and CLEC. 4.2 Qwest shall be in conformance when the monthly performance results for parity measurements (whether in the form of means, percents, or proportions and at the equivalent level of disaggregation) are such that the calculated z-test statistics are not greater than the critical z-values as listed in Table 1, section 5.0. 4.3 Qwest shall be in conformance with benchmark measurements when the monthly performance result equals or exceeds the benchmark, if a higher value means better performance, and when the monthly performance result equals or is less than the benchmark if a lower value means better performance. The formula for determining parity using the modified z-test is: z = DIFF / σDIFF Where: DIFF = MQwest – MCLEC MQWEST = Qwest average or proportion MCLEC = CLEC average or proportion σDIFF = square root σQwest σ Qwest (1/ n CLEC + 1/ n Qwest)] σ2Qwest = calculated variance for Qwest nQwest = number of observations or samples used in Qwest measurement nCLEC = number of observations or samples used in CLEC measurement The modified z-tests will be applied to reported parity measurements that contain more than 30 data points. In calculating the difference between Qwest and CLEC performance, the above formula applies when a larger Qwest value indicates a better level of performance. In cases where a smaller Qwest value indicates a higher level of performance, the order is reversed, i.e., MCLEC - MQWEST. 4.3.1 For parity measurements where the number of data points is 30 or less, Qwest will apply a permutation test to test for statistical significance. Permutation analysis will be applied to calculate the z-statistic using the following logic: Calculate the modified z-statistic for the actual arrangement of the data Pool and mix the CLEC and Qwest data sets Perform the following 1000 times: Randomly subdivide the pooled data sets into two pools, one the same size as the original CLEC data set (nCLEC) and one reflecting the remaining data points, and one reflecting the remaining data points, (which is equal to the size of the original Qwest data set or nQWEST). Compute and store the modified z-test score (ZS) for this sample. Count the number of times the z-statistic for a permutation of the data is greater than the actual modified z- statistic. Compute the fraction of permutations for which the statistic for the rearranged data is greater than the statistic for the actual samples. If the fraction is greater than α, the significance level of the test, the hypothesis of no difference is not rejected, and the test is passed. The α shall be .05 when the critical z value is 1.645 and .15 when the critical z value is 1.04.Qwest