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# Appendix 4: Applied research services technical bulletin 13

## An assessment of the precision of emission rates

This bulletin reports the results of a statistical analysis of the results of 387 emissions tests on 42 wood-burning heaters tested to New Zealand Standard 7403:1992 (Australia Standard 4013:1992) in our laboratory. Emission rates vary from test to test as a result of variations in factors such as fuel loading and the way in which the logs burn in a particular test. To allow comparison of the results at different control settings and between different heaters, the results at each control setting for a given heater were divided by the average emissions rate for that control setting and heater.

As can be seen from the graphs in Figure A3 (below), the distributions of results are very close to being normal.

Figure A3: Distribution of normalised emissions rates from 387 test runs

Analysis of the data gives the following information (Table A3).

##### Table A3: Analysis of 384 test runs

Control setting

Mean

Median

Standard deviation

Number of tests

Low

1

0.99

0.284

128

Medium

1

0.97

0.287

122

High

1

0.99

0.289

134

Overall

1

384

This data indicates that the variability is largely independent of the control setting.

During testing to NZS 7403 (AS4013), three test cycles are carried out at each of three control settings (a total of nine runs) and the results are averaged to reduce the effect of variability on the precision of the final result. The number of tests carried out is a compromise between the costs of testing and the desire to reduce the effect of variability on the precision of the result.

The data can be used to give an indication of the amount that a test result could vary from the 'true' result (the 'true' result being the average of a very large number of test cycles). This is a useful factor to know when comparing results on a given heater under different conditions, or when comparing a test result to a legislative standard. Most statistics texts (Battacharyya GK, Johnson RA, 1977) give details of the calculations.

For example, if the true value of the emissions rate is 1.00, we can be 95% certain that the average of nine runs will lie between 0.81 and 1.19. Table A4 shows the 95% confidence interval for this and other numbers of runs.

##### Table A4: Confidence intervals

Number of runs

Range of results at 95% confidence

1

0.58

0.42-1.58

2

0.41

0.59-1.41

3

0.33

0.67-1.33

4

0.19

0.81-1.19