Statistical Sampling in Audit for NSO Equal Probability

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 : 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 : 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+2 I, r+3 I …. ¬ 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+2 I, r+3 I …. ¬ Stop when n samples are selected. ¬ If at any stage r+k. I > N. Then subtract N from it as N-(r+k. I) 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