Appendix 2 Statistical Comparison of Annual Means

CONTENTS

A2.1	Introduction
A2.2	Long Term Trends
A2.3	Previous Work

A2.1 Introduction
First it is important to clarify several definitions. An annual mean is the mean taken across any annual period. For convenience this is usually done across a calendar year, and is commonly referred to as a fixed annual mean. The use of the term "maximum annual running mean" is misleading, as the period across which the running mean is being considered is not specified. The term is intended to refer to the maximum annual running mean from a dataset consisting of one year of running means (which requires two years worth of data). In addition, periods are quoted as time ending- i.e. running means from 01/01/94 - 01/01/95 through until
31/12/94 - 31/12/95 would give the maximum running annual mean for 1995. The "fixed" average across the period 01/01/1995 to 31/12/1995 (inclusive) is labelled as 1995.

So, the comparison between a "fixed" annual mean, and the maximum value from a dataset of one years worth of annual running means may be visualised as follows:-

1995	á
	Average taken across all
	instantaneous values	à "Fixed Annual" Mean
1996	â

1994	­
	½	­
	½	½	­
	½	½	½	­
	¯	½	½	½	­
1995		¯	½	½	½	­
			¯	½	½	½	­
				¯	½	½	½
					¯	½	½
						¯	½	à Maximum value from a "years
1996							¯	worth" of annual running means

(annual running means generated from instantaneous values)

Due to the large amounts of data involved, the "fixed" annual mean, and the maximum value from a dataset of one years worth of annual running means were calculated from daily average data, rather than instantaneous values. This is considered to have little impact on the results. Only days with data capture in excess of 75% were used, and only annual periods with data capture in excess of 75% were used.

A2.2 Long Term Trends
There is a complicating factor which arises during this comparison. If the measured concentrations are generally falling with time, then the annual running means are expected to decrease with time. As a result the relationship between the two parameters skewed. The maximum running annual mean would be expected to occur towards the start of the annual period (in the above example: the mean from January '94 to January '95). The "fixed" annual average will give a lower value.

A2.3 Previous Work
Work conducted in the report "Investigation into the use of Surrogate Pollutant Statistics for Local Authority Air Quality Review and Assessment" (Draft- March 1998 A Loader, P Willis and G Broughton) considered Benzene and 1,3-Butadiene data from several sources across the period 1994 to 1996. The following conclusions were reached:-

"The benzene maximum running annual mean can be accurately estimated from fixed annual mean measurements".

"The 1,3-butadiene maximum running annual mean can accurately be predicted from fixed annual mean measurements."

The following relationships were arrived at:-

Benzene
Max. Annual Running Mean = 1.1015 Annual Calendar Mean + 0.0198
(R² = 0.9328)

1,3-Butadiene
Max. Annual Running Mean = 1.0075 Annual Calendar Mean + 0.0291
(R² = 0.7907)


A2.4 Results
Results from the current statistical analysis are shown in Figure A2.1 and Figure A2.2. In summary the following relationships were found:-

Benzene
Max. Annual Running Mean = 1.102 Annual Calendar Mean - 0.004
(R² = 0.960)

1,3-Butadiene
Max. Annual Running Mean = 1.022 Annual Calendar Mean + 0.016
(R² = 0.933)


The following summarises the date corresponding to the maximum value of the running means across the sites and years used for the statistical analysis above. It appears that an unusually high proportion of the dates for benzene occur at the start of the calendar year, indicating that concentrations are falling (see Section A2.2 above). This trend for 1,3-butadiene is less evident. However, without further, more in depth, statistical analysis it is not possible to confirm whether this trend is significant.

Table A2a Date for Max. Running Annual Mean - Benzene

Site Name	1994	1995	1996	1997	1998 (to21/08)
Belfast	01-Jan	02-Jan	07-Apr	04-Dec	01-Jan
Birmingham	06-Jan	12-Dec	07-Oct	07-Nov	01-Jan
Bristol	24-Dec	31-Dec	07-Apr	12-Nov	01-Jan
Cardiff	08-Jan	03-Jan	16-Apr	04-Dec	06-Jan
Edinburgh	01-Jan	29-Dec	11-Apr	31-Jan	01-Jan
Harwell		03-Jan	17-Apr	05-Dec	28-Apr
Leeds		05-Jan	26-Sep	04-Dec	01-Jan
London UCL	08-Jan	03-Jan	08-Oct	13-Nov	01-Jan
London Eltham	08-Jan	04-Feb	08-Oct	13-Nov	01-Jan
Liverpool		12-Dec	02-Jan	23-Dec	01-Jan
Middlesbrough	12-Nov	01-Jan	23-Apr	09-Nov	03-Jan
Marylebone Rd					15-Feb
Southampton		14-Sep	05-Jan	13-Nov	01-Jan

Table A2b Date for Max. Running Annual Mean - 1,3-Butadiene

Site Name	1994	1995	1996	1997	1998 (to21/08)
Belfast	27-Dec	12-Dec	07-Apr	04-Dec	24-May
Birmingham	24-Dec	12-Dec	07-Oct	07-Jun	08-Mar
Bristol		31-Dec	04-Apr	20-Aug	03-Jul
Cardiff	24-Dec	02-Jan	22-Apr	20-Feb	27-Jul
Edinburgh	14-Dec	29-Dec	02-Apr	31-Jan
Harwell			18-Oct	24-Jan
Leeds		29-Dec	03-Sep	31-Jul
London UCL	11-Nov	01-Jan	17-Apr	29-Jan	01-Mar
London Eltham		12-Dec	29-Feb	13-Nov	07-Jan
Liverpool			06-Dec	13-May
Middlesbrough		29-Aug	09-Apr	19-Feb
Marylebone Rd
Southampton			04-Jul	28-Jan