Statistical Sampling in Audit for NSO Comptroller and Auditor General of India1 Equal Probability Sampling.

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Presentation transcript:

Statistical Sampling in Audit for NSO Comptroller and Auditor General of India1 Equal Probability Sampling

Statistical Sampling in Audit for NSO Comptroller and Auditor General of India2 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.

Statistical Sampling in Audit for NSO Comptroller and Auditor General of India3 Simple Random Sampling 1. Simple Random Sampling With Replacement (SRSWR) 2. Simple Random Sampling With Out Replacement (SRSWOR)

Statistical Sampling In audit for NSO Comptroller and Auditor General of India4 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.

Statistical Sampling In audit for NSO Comptroller and Auditor General of India5  The sample mean is the unbiased estimate of population mean. Symbolically : SRSWR

Statistical Sampling In audit for NSO Comptroller and Auditor General of India6 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.

Statistical Sampling In audit for NSO Comptroller and Auditor General of India7  The sample mean is the unbiased estimate of population mean.  Symbolically : SRSWOR

Statistical Sampling In audit for NSO Comptroller and Auditor General of India8 Systematic Random Sampling  The sample is chosen by selecting a random start and then picking every I th 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

Statistical Sampling In audit for NSO Comptroller and Auditor General of India9 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

Statistical Sampling In audit for NSO Comptroller and Auditor General of India10 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

Statistical Sampling In audit for NSO Comptroller and Auditor General of India11 Advantages of Sys. Ran. Sampling  If the sampling units are arranged in a manner unrelated to the character under interest this method will yield quite similar result to SRS.  If the ordering of the elements is related to the characteristics of interest this method increases the representative ness of the sample  It is less costly and easier to implement.