Annex 8- Coronel Analysis VER 1 DGO English translation

CDM Coronel, First Verification
Statistical Report of biogas fraction with periodical measurements
1. Introduction
This report is intended to verify whether the methodology used by CDM Coronel project obtains a
confidence level of 95% in the measurement of the biogas methane level according to the
applicable methodology:
The fraction of methane in biogas (wCH4,y) should be measured with a continuous analyzer or,
alternatively, with periodic measurements with a 95% of confidence level, using calibrated portable
gas meters and taking a number of statistically valid samples [...].'
2. Methodology used to analyze 95% confidence level
o
The first sheet in Excel, (Idec Report 95% per day) is a summary from 95% confidence intervals
for the CH4 percentage average each day from December 16th, 2007 up to June 29th, 2008.
o
For some days with excessive data missing, these were replaced according to agreement. For
these cases, sample size is indicated as follows 24(*).
o
From the second sheet on: Dec 2007 to June 2008, complete the "Statistical Indicators" to build
the corresponding confidence intervals of 95% for each day ... With these data the first daily
report sheet is obtained.... Formulas are implicit in every cell of these new indicators..
o
Summary of the necessary statistical indicators to form the 95% daily Idec are:
1. Average and standard sample deviation are obtained for every day, which statistical symbols are:
Y
s= Standard deviation Sample Average
Sample average
2. Both the average and the standard sample deviation estimate the true average and standard
deviation of CH4 percentage actually destroyed in the day. For these cases symbols are:
µ = True Average (Population)
σ
= True Standard deviation (Population)
3. With the sample data, it is intended to estimate a 95% of confidence interval (IdeC) for
µ population average. It means to solve the following statistical form:
(
)
P Y − µ < d = 95% (1)
That is, the µ population average is expected to be estimated by estimator Y obtained from a
sample so that:
The probability that the distance between the estimate Y and the actual µ value to be
less than certain "d" value called " estimation mistake (or sampling error) (or accuracy)
is equal to 0.95
4. As the sample size is small (most are 24) and the σ standard deviation is unknown, the solution
(1) is based on the "t de Student" table
s < µ < y + t n −1 * s
1
y − t 0n,−975
*
0 , 975
n
n
(2)
This is the formula to be used to obtain Idec, the low limit (LI) and Top Limit (TL), which duly
programmed in Excel file attached.
s
1
LI = y − t 0n,−975
*
n
s
1
LS = y + t 0n,−975
*
n
5. SUMMARY OF REPORT STATISTICAL INDICATORS
y = Average = PrAverage
omedio de
la sample
muestra
of the
µ = Mean = PrPopulation
omedio de la
Población
Verdadero
del díaday
que
es desconocid
o
= Pr omedio
average
= actual
average
of unknown
which
is
estimated by average of sample Y
y que se estima por el promedio de la muestra y
n = Sample size = Tamaño
de24
la samples
muestra (usualmente 24)
Usually
Usually 24 samples
s = S Standard
tan dard Deviation
= Desviación
Estándar de la muestra
deviation
of the sample
95% = Confidence Level = Nivel de Confianza usado en este proyecto
s
n
= S tan dard Error = Error Estándar = Error Típico
1
Percentiltabla
for t‘student
t table’
t 0n,−975
de student
= Percentil
1
t 0n,−975
*
s
n
1
y − t 0n,−975
*
1
y + t 0n,−975
*
Precision
= Estimation Error = Error
de estimación = Error de muestreo = Pr ecisión
s
n
s
n
Inferior del
ervalo
= Límite
int of
95% de confianza
Low interval
limit
95%del
confidence
for µ para µ
Top interval
f 95%
µ
= Límite
Superiorlimit
del int
ervaloconfidence
del 95% defor
confianza
para µ
Bibliography
STATISTICS APPLIED in the administration and economy, David K. Hildebrand and R. Lyman Ott,
Addison Wesley Iberoamericana.
Walpole, R.E. and Myers, R.H. Probability and Statistics for Engineers and Scientists. Mc.Millan.
Excel, By following Excel commands the necessary indicators can be obtained to build confidence intervals
for the average population (Statistical concepts are implicitly defined in the user’s manual)
Commands
Ø Tools
Ø Data Analysis
Ø Descriptive statistics
Ø Input range: data screen
Ø Output Range: Mark cell for indicators
Ø Statistical Summary: Mark this option
Ø Confidence Interval for average: Mark this option with 95% confidence.
Useful output to build the confidence interval for µ average will be
Media
Common fault
Account
Confidence Level
(95,0%)
Sample Average
Standard fault
Sample Sizw(n)
Estimation fault
Conclusion Report
Based on the 197 daily samples size n = 24 (or approximate), from each day between December
16th 2007 and June 29 2008, a confidence interval was obtained for actual µ daily average of CH4
methane gas, therefore:
"It can be stated that for every of these 197 days, the corresponding interval obtained
contains, with a 95% confidence level, the real daily average of methane gas CH4"
Rafael Águila
Professor of Mathematics of the ‘Pontifica Universidad católica de Chile’ (Santiago)
Master en Mathematics Estadistics of the ‘Centro Interamericano de la Enseñanza de la Estadística’,
‘CIENES’