


To:		Rochelle Boyd, U.S. Environmental Protection Agency, OAQPS

From:		Mark Bahner, RTI International 

Date:		August 23, 2012

Subject:	Clean Charge Cycles Statistical Analysis
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Background/Executive Summary
The proposed Secondary Aluminum NESHAP revisions published in the Federal Register on February 14, 2012 required that furnaces melting other than clean charge use "one or more" cycles of clean charge before being able to switch the furnace designation. The Aluminum Association and Alcoa commented that using one or more cycles of clean charge was not necessary because test data indicated that the first cycle of clean charge has emissions comparable to the second and third cycle of clean charge. This memorandum reports on the results of a statistical analysis of the data.

Based on a statistical analysis of the data, the Aluminum Association and Alcoa comment that there is no need to wait one or more cycles before switching furnace designations appears valid. There was not a statistically significant difference between mean or median emissions of the first cycle, second cycle, and third cycle.

All tables are presented at the end of this memorandum.
Test Data
Test data were provided by the Aluminum Association and Alcoa in their comments in April 2012, which were placed in the Secondary Aluminum NESHAP docket (EPA Docket ID No. EPA-HQ-OAR-2010-0544). These data included the first cycle emissions results and the average emissions for the first three runs. The data are shown in Table 1.

More detailed data were obtained fom Alcoa in July 2012. These data included not just the first cycle emissions and the average emissions for the first three runs, but also the emissions for the second cycle (run) and third cycle (run). The data are summarized in Table 2.

Statistical Analysis
Statistical tests were performed comparing mean and median values for the cycles, as shown in Table 3. 

Means were compared using a paired t-test. The null hypothesis is that there is no difference in the mean difference. The paired t-test first takes the difference of, for example, the first and second cycle, and calculates the mean of the differences, and tests if the mean of the differences is zero. The interpretation of the results is that a p-value <= 0.05 provides statistical evidence that the average of one cycle is different from the average of the other cycle. A p-value >= 0.05 does not provide evidence against the null hypothesis that the average of both cycles is the same. Based on the results in Table 2, there is no evidence that the averages of the cycles are different.

The paired t-test is based on a normality assumption:

For PM (lb/ton): The Shapiro-Wilk test was used to evaluate normality; p-values were 0.9388 (first cycle), 0.2385 (second cycle), and 0.3212 (third cycle). All values suggest that the first, second, and third cycle has a normal distribution.

For HCl (lb/ton): The Shapiro-Wilk test was used to evaluate normality; p-values were 0.022 (first cycle), 0.1572 (second cycle), and 1.061E-07 (third cycle). Results suggest that first cycle and third cycle data are not normal. For conclusions about the difference between these cycles the Wicoxon test should be used. Caution should be used given the small sample size.

The Wilcoxon signed rank test was used to evaluate the difference in the medians. This test is preferred if the assumption of normality doesn't hold. The same interpretation as described previously holds for p-values. 

Based on the results described above, there is no evidence that the means or medians of the cycles are different. 


Table 1. Data Provided by the Aluminum Association and Alcoa in April 2012 
(Docket ID No. EPA-HQ-OAR-2010-0544)


 
Table 2. Additional Data Provided by Alcoa


Table 3. Additional Data Provided by the Aluminum Association and Alcoa 
                                   Pollutant
                         Comparing the Mean (p-values)
                        Comparing the Median (p-values)
                                       
                          First Cycle vs Second Cycle
                                First Cycle vs
                                  Third Cycle
                          Second Cycle vs Third Cycle
                          First Cycle vs Second Cycle
                                First Cycle vs
                                  Third Cycle
                          Second Cycle vs Third Cycle
PM (lb/ton)
                                     0.473
                                     0.975
                                     0.888
                                       1
                                       1
                                     0.75
HCl (lb/ton)
                                     0.43
                                     0.422
                                     0.27
                                       1
                                      0.5
                                     0.371
D/F (lb/ton)
                                     0.659
                                     0.401
                                     0.506
                                       1
                                      0.5
                                       1

