quality-indicators-2017

QUALITY INDICATORS 2017
The value of indicator T1 can be presented in different forms; for this purpose the standard error, the coefficient
of variation and the confidence interval are most frequently used.
The standard error of the estimate is equal to the square root of the sampling error, i.e.:
se( Y
ˆ
) Var ˆ ( Y
ˆ
)
.
The coefficient of variation is defined as the ratio between the standard error of the estimate and the estimate
itself:
se(
Y
ˆ
)
cv( Y
ˆ
)
Y
ˆ
.
The coefficient of variation is usually expressed as a percentage.
At a 95% confidence level, the lower ( I
SM
calculated as follows:
I Y
ˆ
1,96 se(
Y
ˆ
SM
)
,
I Y
ˆ
1,96 se(
Y
ˆ
ZM
)
.
) and the upper ( I
ZM
) limits of the confidence interval can be further
3.3.3 Explanation and calculation examples
The estimation of sampling errors of statistical results is a complex and extensive problem from both theoretical
and practical standpoints. The simple formulas presented in Section 3.2 only apply in simple random sampling,
which is rarely used in practice. By using more complex sampling designs or more demanding (non-linear)
estimators, theoretical results are much more demanding and sometimes cannot be expressed in an exact
analytical form.
The approaches applied to the calculation of the sampling error can be roughly divided into three groups:
Analytical approach. For the calculation of the sampling error, direct or approximate formulas are used
(usually on the basis of a linearisation method).
Resampling approach. A set of subsamples is selected by means of an appropriate procedure; for each
subsample an appropriate estimate is calculated; the variability of estimates obtained from different
subsamples will then serve for the estimate of the sampling error.
Appropriate model approach. The sampling error is expressed as a function of known parameters (or
more easily measured parameters). These parameters may be: the estimate itself, the random error
assuming simple sampling, the sampling error for the entire sample – the model provides an estimate for
the domain, etc.
Example: Let us say that after we have implemented a statistical survey in which the mean value of variable Y
is estimated on the basis of a simple random sampling without replacement, we get the data shown in the table
below:
Population size
( N )
Sample Size ( n )
Mean Estimate
(Yˆ )
Population Variance
Estimation
2
( s )
10,000 500 800 50,000
In accordance with the above-stated formulas, we then calculate:
500 50000
Var ( Y
ˆ
) (1 ) 0.95100
95
10000 500
se ( Y
ˆ
) 95 9.75
12