```Statistical Sampling in Audit for NSO
Equal Probability Sampling
Comptroller and Auditor General of India
1
Statistical Sampling in Audit for NSO
Simple Random Sampling
A procedure of sampling will be called SRS
if, in sample of size n,all the possible
combinations of n elementary units that may
be formed from the population of N
elementary units have the same probability
of being included.
Comptroller and Auditor General of India
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Statistical Sampling in Audit for NSO
Simple Random Sampling
1. Simple Random Sampling With
Replacement (SRSWR)
2. Simple Random Sampling With
Out Replacement (SRSWOR)
Comptroller and Auditor General of India
3
Statistical Sampling In audit for NSO
SRSWR
 A sample is said to be selected by SRSWR
By n draws if :
(a) At each draw each unit in the
population has the same chance of being
selected.
(b) A unit selected at a draw is returned
to the population in the next draw.
Comptroller and Auditor General of India
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Statistical Sampling In audit for NSO
SRSWR
 The sample mean is the unbiased estimate of population mean.
Symbolically :
n
1
Yˆ  y   yi , where yi observation of i th sam ple
n i 1
Estim ateof population total , Yˆ  N y
2
s
Estim ateof V (Yˆ )  v( y ) 
n
2 2
n
N
s
1
2
2
Estim ateof V (Yˆ ) 
, where s 
(
y

y
)

i
n
n  1 i 1
Estim ateof c.v(Yˆ )  c.v(Yˆ )  y s n
Comptroller and Auditor General of India
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Statistical Sampling In audit for NSO
SRSWOR
 A sample is said to be selected by SRSWOR
if :
(a) At each draw each unit in the
population has the same chance of being
selected.
(b) A unit selected at a draw is removed
from the population in the next draw.
Comptroller and Auditor General of India
6
Statistical Sampling In audit for NSO
SRSWOR
 The sample mean is the unbiased estimate of population mean.
 Symbolically :
n
1
Yˆ  y   yi , where yi observation of i th sam ple
n i 1
Estim ateof population total , Yˆ  N y
( N  n) s 2
ˆ
Estim ateof V (Y ) 
Nn
2
n
N
(
N

n
)
s
1
2
2
Estim ateof V (Yˆ ) 
, where s 
(
y

y
)
 i
n
n  1 i 1
Estim ateof c.v(Yˆ )  ( N  n ) s
nN y
Comptroller and Auditor General of India
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Statistical Sampling In audit for NSO
Systematic Random Sampling
 The sample is chosen by selecting a random
start and then picking every Ith element in
succession from the sampling frame (list of
sample units). Where I=N/n.
Two types of Sys. Random Sampling
 Linear Systematic Sampling
 Circular Systematic Sampling
Comptroller and Auditor General of India
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Statistical Sampling In audit for NSO
LSS
 Random Start between 1 to I .Let it be r.
 Then select r,r+I,r+2I,r+3I ….
 Stop when n samples are selected or the
sample list is exhausted.
 We may not select exactly n number of
samples
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Statistical Sampling In audit for NSO
CSS
 Random Start between 1 to N.Let it be r.
 Then select r,r+I,r+2I,r+3I ….
 Stop when n samples are selected .
 If at any stage r+kI > N .Then subtract N
from it as N-(r+kI) and select that number
and proceed further.
 Always select exactly n number of samples
Comptroller and Auditor General of India
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Statistical Sampling In audit for NSO