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Appendix 2: Estimating the emissions from wood-pellet burners

Four wood-pellet burners were tested on 28 occasions and their emissions measured. One burner was determined to be working improperly and its emissions were unusually high. To estimate the total emissions from all pellet burners in a population, the mean emissions from a pellet burner (estimated from the sample) should be multiplied by the estimate of the number of appliances in the population and by an estimate of the average household usage. The mean should be used in this exercise because the aim is to estimate the total emissions. The total emissions cannot be determined from the median emissions of a new burner.

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 four observations is close to a normal distribution, even when the underlying distribution is skewed.3 We use the t-distribution to estimate the confidence interval because the standard deviation is unknown.

This confidence interval is accurate if the sample of the pellet burners is representative of the population of pellet burners; that is, if the brands and models used in the sample testing are similar to the brands and models used in the population.

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

Burner

1

2

3

4

Mean (with burner #2)

Mean (without burner #2)

Mean emissions

1.54

11.35

1.09

1.65

3.91

1.43

The 95% confidence interval for the mean was calculated, as follows. With burner number 2:

 X bar plus or minus t sub 3, multiplied by s divided by the square root of 4, equals 3.91 plus or minus 3.182 multiplied by 4.97 divided by 2, equals 3.91 plus or minus 7.90.

Without burner number 2:

X bar plus or minus t sub 2 multiplied by s divided by the square root of 3, equals 1.43 plus or minus 4.303 multiplied by 0.30 divided by the square root of 3, equals 1.43 plus or minus 0.74.

Since improperly functioning burners are likely to occur in practice, but at a lower rate than 25%, the true mean emissions of wood-pellet burners is likely to be somewhere between the two estimates.


3 Moore D. 2004. The Basic Practice of Statistics. New York: WH Freeman & Company.