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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 2 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 4 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 5 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 7 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 8 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 Comptroller and Auditor General of India 9 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 10 Statistical Sampling In audit for NSO 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. Comptroller and Auditor General of India 11