Vijay Koshti Statistics ( Statistical concepts and related articles)

    Unit 2: Other sampling Methods   2.1 Systematic Sampling The systematic sampling technique is operationally more convenient than simple random sampling. It also ensures, at the same time that each unit has an equal probability of inclusion in the sample. In this method of sampling, the first unit is selected with the help of random numbers, and the remaining units are selected automatically according to a predetermined pattern. This method is known as systematic sampling. Suppose the N units in the population are numbered 1 to N in some order. Suppose further that N is expressible as a product of two integers n and k, so that N=nk.   To draw a sample of size n:   1. Select a random number between 1 and k. 2. Suppose it is i. 3. Select the first unit, whose serial number is i. 4. Select every k th unit after i th unit. The sample will contain I, i+k, i+2k,i+3k,.....,i+(n-1)k   serial number units. Thus, the first unit is selected at...

  1.3 Stratified Sampling   Introduction:   An important objective in any estimation problem is to obtain an estimator of a population parameter which can take care of the salient features of the population. If the population is homogeneous with respect to the characteristic under study, then the method of simple random sampling will yield a homogeneous sample, and in turn, the sample mean will serve as a good estimator of the population mean. Thus, if the population is homogeneous with respect to the characteristic under study, then the sample drawn through simple random sampling is expected to provide a representative sample. Moreover, the variance of the sample mean not only depends on the sample size and sampling fraction but also on the population variance. In order to increase the precision of an estimator, we need to use a sampling scheme which can reduce the heterogeneity in the population. If the population is heterogeneous with respect to the characteristic ...