California Code of Regulations
Title 22 - Social Security
Division 4.5 - Environmental Health Standards for the Management of Hazardous Waste
Chapter 16 - Recyclable Materials (Recyclable Hazardous Wastes)
Appendix A to IX - Statistics

A.1 Determination of Enrichment Factor

After at least 10 initial emissions tests are performed, an enrichment factor for each metal must be determined. At the 95% confidence level, the enrichment factor, EF95% s, is based on the test results and is statistically determined so there is only a 5% chance that the enrichment factor at any given time will be larger than EF95%. Similarly, at the 99% confidence level, the enrichment factor, EF99%, is statistically determined so there is only a 1% chance that the enrichment factor at any given time will be larger than EF99%.

For a large number of samples (n > 30), EF95% is based on a normal distribution, and is equal to:

EF95% = EF + zcs(1)

where:

For a 95% confidence level, zc is equal to 1.645.

For a small number of samples (n < 30), EF95% is based on the t - distribution and is equal to:

EF95% = EF + tc S (4)

where the standard deviation, S, is defined as:

tc is a function of the number of samples and the confidence level that is desired. It increases in value as the sample size decreases and the confidence level increases. The 95% confidence level is used in this method to calculate the "violation" kiln dust metal concentration limit; and the 99% confidence level is sometimes used to calculate the "conservative" kiln dust metal concentration limit. Values of tc are shown in table A-1 for various degrees of freedom (degrees of freedom = sample size-1) at the 95% and 99% confidence levels. As the sample size approaches infinity, the normal distribution is approached.

A.2 Comparison of Enrichment Factor Groups

To determine if the enrichment factors measured in the quarterly tests are significantly different from the enrichment factors determined in the initial Step 2 tests, the t-test is used. In this test, the value tmeas:

Table A-1. -T-Distribution

is compared to tcrit at the desired confidence level. The 95% confidence level is used in this method. Values of tcrit are shown in table A-1 for various degrees of freedom (degrees of freedom n1 + n2 - 2) at the 95% and 99% confidence levels. If tmeas is greater then tcrit, it can be concluded with 95% confidence that the two groups are not from the same population.

A.3 Rejection of Data

If the concentration of any hazardous metal in the "required" kiln dust sample exceeds the kiln dust metal concentration limit, the "spare" samples are analyzed. If the average of the combined "required" and "spare" values is still above the limit, a statistical test is used to decide if the upper value can be rejected.

The "Q-test" is used to determine if a data point can be rejected. The difference between the questionable result and its neighbor is divided by the spread of the entire data set. The resulting ratio, Q meas, is then compared with rejection values that are critical for a particular degree of confidence, where Q meas is:

The 90% confidence level for data rejection is used in this method. Table A-2 provides the values of Qcrit at the 90% confidence level. If Q at the 90% confidence level. If Qmeas is larger than Qcrit, the data point can be discarded. Only one data point from a sample group can be rejected using this method.

Table A-2. -Critical Values for Use in the Q-Test

Note: Authority cited: Sections 25150, 25159,25159.5, 25245,58004 and 58012, Health and Safety Code. Reference: Sections25159 and 25159.5, Health and Safety Code; and 40 CFR part 266, Appendix IX. Authority cited: Sections 25150, 25159, 25159.5,25245, 58004 and 58012, Health and Safety Code. Reference: Sections25159 and 25159.5, Health and Safety Code; and 40 CFR part 266, Appendix IX.