Sampling methods

Sampling methods
    The various methods of sampling can be grouped under

    Random sampling
    • Under this method, every unit of the population at any stage has equal chance (or) each unit is drawn with known probability. It helps to estimate the mean, variance etc of the population.
    • When the successive draws are made with placing back the units selected in the preceding draws, it is known as sampling with replacement. When such replacement is not made it is known as sampling without replacement. When the population is finite sampling with replacement is adopted otherwise SWOR is adopted.

    Mainly there are many kinds of random sampling. Some of them are.
    1. Simple Random Sampling
    2. Systematic Random Sampling
    3. Stratified Random Sampling
    4. Cluster Sampling

    Simple Random sampling(SRS)
    • The basic probability sampling method is the simple random sampling. It is the simplest of all the probability sampling methods. It is used when the population is homogeneous.When the units of the sample are drawn independently with equal probabilities. The sampling method is known as Simple Random Sampling(SRS). Thus if the population consists of N units, the probability of selecting any unit is 1/N.

    A theoretical definition of SRS is as follows
    • Suppose we draw a sample of size n from a population of size N. There are NCn possible samples of size n. If all possible samples have an equal probability 1/NCn of being drawn, the sampling is said be simple random sampling.
    There are two methods in SRS
      1. Lottery method
      2. Random no. table method
    Lottery method
    • This is most popular method and simplest method. In this method all the items of the universe are numbered on separate slips of paper of same size, shape and color. They are folded and mixed up in a drum or a box or a container. A blindfold selection is made. Required number of slips is selected for the desired sample size. The selection of items thus depends on chance.

    • For example, if we want to select 5 plants out of 50 plants in a plot, we number the 50 plants first. We write the numbers from 1-50 on slips of the same size, role them and mix them. Then we make a blindfold selection of 5 plants. This method is also called unrestricted random sampling because units are selected from the population without any restriction. This method is mostly used in lottery draws. If the population is infinite, this method is inapplicable. There is a lot of possibility of personal prejudice if the size and shape of the slips are not identical.

    Random number table method
    • As the lottery method cannot be used when the population is infinite, the alternative method is using of table of random numbers. There are several standard tables of random numbers. But the credit for this technique goes to Prof. LHC. Tippet(1927). The random number table consists of 10,400 four-figured numbers. There are various other random numbers. They are fishers and Yates(19380 comprising of 15,000 digits arranged in twos. Kendall and B.B Smith(1939) consisting of 1,00,000 numbers grouped in 25,000 sets of 4 digit random numbers, Rand corporation(1955) consisting of 2,00,000 random numbers of 5 digits each etc.,

    Merits
    • There is less chance for personal bias.
    • Sampling error can be measured.
    • This method is economical as it saves time, money and labour.
    Demerits
    • It cannot be applied if the population is heterogeneous.
    • This requires a complete list of the population but such up-to-date lists are not available in many enquires.
    • If the size of the sample is small, then it will not be a representative of the population.

    Stratified Sampling
    When the population is heterogeneous with respect to the characteristic in which we are interested, we adopt stratified sampling. When the heterogeneous population is divided into homogenous sub-population, the sub-populations are called strata. From each stratum a separate sample is selected using simple random sampling. This sampling method is known as stratified sampling.
    • We may stratify by size of farm, type of crop, soil type, etc.
    • The number of units to be selected may be uniform in all strata (or) may vary from stratum to stratum.
    There are four types of allocation of strata
    1. Equal allocation
    2. Proportional allocation
    3. Neyman’s allocation
    4. Optimum allocation

    If the number of units to be selected is uniform in all strata it is known as equal allocation of samples.     If the number of units to be selected from a stratum is proportional to the size of the stratum, it is known as proportional allocation of samples. When the cost per unit varies from stratum to stratum, it is known as optimum allocation. When the costs for different strata are equal, it is known as Neyman’s allocation.

    Merits
    • It is more representative.
    • It ensures greater accuracy.
    • It is easy to administrate as the universe is sub-divided.

    Demerits
    • To divide the population into homogeneous strata, it requires more money, time and statistical experience which is a difficult one.
    • If proper stratification is not done, the sample will have an effect of bias.

Last modified: Sunday, 18 March 2012, 4:20 PM