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Appendix 2: Estimating the emissions from NES-compliant wood burners

Nine NES-compliant burners were tested on several occasions and their emissions measured. To estimate the total emissions from all NES-compliant burners in a population, the mean emissions from an NES-compliant burner (estimated from the sample) should be multiplied by the estimate of the number of NES-compliant burners in the population and by an estimate of the average household usage. The mean should be used when carrying out this exercise because the aim is to estimate the total emissions, and this cannot be determined from the median emissions.

The mean emissions of an NES-compliant burner should be estimated as the sum of the mean emissions of each burner divided by the sample size, in this case:

X bar equals the sum of lower case x bar sub i, where i ranges from 1 to 9. Divide this sum by nine.

where x bar sub i. is the mean emissions of burner i.

This estimation method avoids biasing the overall mean estimate toward the mean of the burner with the most observations.

Table A2: Mean emissions (g/kg) of individual wood burners

Burner

1

2

3

4

5

6

7

8

9

Mean

Mean emissions

4.25

4.63

11.21

4.22

4.89

2.97

3.75

2.33

3.63

4.65

Even though the distribution of emissions from new burners (in real-life situations) is skewed, we can use Student’s t-distribution to obtain a confidence interval for the mean. The Central Limit Theorem and robustness studies indicate that the mean of nine observations is close to a normal distribution, even when the underlying distribution is skewed (Moore, 2004). We use the t-distribution to estimate the confidence interval, however, because the standard deviation is unknown. A 95% confidence interval for the mean emissions of new burners is:

X bar plus or minus t sub 8 multiplied by s divided by the square root of 9, equals 4.65 plus or minus 2.306 multiplied by 2.58 divided by 3, equals 4.65 plus or minus 1.98.

This confidence interval is accurate if the sample of NES-compliant burners is representative of the population of NES-compliant burners (that is, if the brands and models used in the sample testing are similar to the brands and models used in the population).

Comparing the mean emissions of pre-1994 wood burners and NES-compliant wood burners

To compare the mean emissions of old and new burners, a two-sample t-test was done comparing the mean emissions of the nine new burners and 12 old burners. Although the emission distributions are skewed, the t-test is still appropriate for these sample sizes because the test is quite robust to skewedness in distributions (Moore, 2004). The mean emissions of the old burners, 14.01, was significantly higher than that of the new burners, 4.65. Using the SPSS statistical package the p-value was 0.003 for the unequal variances t-test. A 95% confidence interval for the difference in means is 3.88 to 14.83.

The p-value is the probability of seeing as large a difference in means as 14.01 4.65 = 9.36, or larger if the means were equal (by chance this may happen due to randomly sampling high-emission old burners and low-emission new burners). The p-value indicates that the probability of seeing this large a difference is 0.003, or about 1 in 300. This probability is low enough to state that the difference is unlikely to be due to chance, and is likely to be due to a real difference in the mean emissions. If the p-value is less than 0.05, we say that there is a “statistically significant difference”.

The confidence interval estimates the difference in means (9.35) but adds a statement of how confident we are in the estimate. We can say we are 95% confident that the difference in means is somewhere between 3.88 and 14.83 (note that the point estimate 9.35 is right in the middle of the interval). This can be used to estimate how much the emissions would decrease if you switched out, say, 1,000 old wood burners for NES-compliant wood burners: you can be 95% confident that the total emissions would decrease by between 3,880 g/kg and 14,830 g/kg.