10.1.2023
Third period
Third period
z2 ×N3 ×σew3 !
n3 ¼ ðTE – AEÞ
2
H1
∑h¼1
– z2 ×
H2 N2h1 2 N2h2 2 :seh1  – z2 ×∑h¼1 :s nh1 nh2 eh2
!
EN
ðz×N3 ×σe3 Þ n3 ¼ 2 2 2 ðTE – AEÞ  – z2 ×N1 ×s2e1  – z2 ×N2 ×s2e2 n1 n2
2
H3
σew3 ¼ ∑h¼1 ðNh3 :σ2eh3 Þ
Extrapolation of errors
In the framework of application of the off-the-shelf methodologies laid down in this Regulation, a single extrapolation method, ratio estimation, applies for SRS referred to in Article 5(1), point (b), and equal probability selection referred to in Article 6(1), point (b), for the purpose of simplification and legal certainty.
This does not limit the application of other extrapolation methods by the audit authorities under Article 79 of Regulation (EU) 2021/1060.
Projected/extrapolated error (SRS/equal probability selection): For the exhaustive strata, the projected error is the sum of the errors found in the units belonging to the strata: n1
n2
n3
Projected/extrapolated error (SRS/equal probability selection): For the exhaustive strata, the projected error is the sum of the errors found in the units belonging to the strata: H1
EEe ¼ ∑i¼1 E1i þ ∑i¼1 E2i þ ∑i¼1 E3i
H2
nh2
H2
nh3
EEe ¼ ∑h¼1 ∑i¼1 Eh1i þ ∑h¼1 ∑i¼1 Eh2i þ ∑h¼1 ∑i¼1 Eh3i
For the non-exhaustive strata, the projected error is:
For the non-exhaustive strata, the projected error is: H1
EEs ¼ BV1 ×
nh1
Official Journal of the European Union
Notes: Whenever different approximations for the standard-deviations of each period cannot be obtained/are not applicable, the same value of standard deviation may be applied to all periods.
In such a case σew1þ2þ3 is just equal to the single standard-deviation of errors σe .
The parameter σ refers to the standard-deviation obtained from auxiliary data (e.g. historical data) and s refers to the standard-deviation obtained from the audited sample.
In the formulas, whenever s is not available, it may be substituted by σ.
See also notes above for the two-period simple random sampling as regards the use of the standard approach to the recalculation of the sample size and the global approach referred to in Article 5(6).
n1
n2
n3
1
2
3
∑i¼1 E1i þ BV × ∑i¼1 E2i þ BV × ∑i¼1 E3i n n n 2 3 ∑i¼1 BV1i ∑i¼1 BV2i ∑i¼1 BV3i
nh1
nh2
nh3
∑i¼1 Ei þ ∑H BV × ∑i¼1 Ei þ ∑H N × ∑i¼1 Ei n n h2 h¼1 h¼1 h3 nh3 ∑i¼1 BVi ∑i¼1 BVi 2
h1
3
h2
The projected error at the level of population is the sum of the two components above.
L 7/21
The projected error at the level of population is the sum of the two components above.
EEs ¼ ∑h¼1 BVh1 ×