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

Current through Register 2024 Notice Reg. No. 28, July 12, 2024
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
_
n-1 or n1 +
							 n2-2
t95
t99
_
1
6.31
31.82
2
2.92
6.96
3
2.35
4.54
4
2.13
3.75
5
2.02
3.36
6
1.94
3.14
7
1.90
3.00
8
1.86
2.90
9
1.83
2.82
10
1.81
2.76
11
1.80
2.72
12
1.78
2.68
13
1.77
2.65
14
1.76
2.62
15
1.75
2.60
16
1.75
2.58
17
1.74
2.57
18
1.73
2.55
19
1.73
2.54
20
1.72
2.53
25
1.71
2.48
30
1.70
2.46
40
1.68
2.42
60
1.67
2.39
120
1.66
2.36
8
1.645
2.33
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
n
Qcrit
3
0.94
4
0.76
5
0.64
6
0.56
7
0.51
8
0.47
9
0.44
10
0.41
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.