Type I & I Errors
Unit 6 Case Study Method
9. Economy: It should be another criterion in choosing the sampling method. It means achieving the desired level of precision at minimum
7.5 Methods of Sampling
7.5.1 Probability or Random Sampling
Probability sampling is based on the theory of probability. It is also known as random sampling. It provides a known nonzero chance of selection for each population element. It is used when generalization is the objective of study, and a greater degree of accuracy of estimation of population parameters is required. The cost and time required is high hence the benefit derived from it should justify the costs.
The following are the types of probability sampling:
i) Simple Random Sampling: This sampling technique gives each element an equal and independent chance of being selected. An equal chance means equal probability of selection. An independent chance means that the draw of one element will not affect the chances of other elements being selected. The procedure of drawing a simple random sample consists of enumeration of all elements in the population.
1. Preparation of a List of all elements, giving them numbers in serial order 1, 2, B, and so on, and
2. Drawing sample numbers by using (a) lottery method, (b) a table of random numbers or (c) a computer.
Suitability: This type of sampling is suited for a small homogeneous population.
Advantages: The advantage of this is that it is one of the easiest methods, all the elements in the population have an equal chance of being selected, simple to understand, does not require prior knowledge of the true composition of the population.
Disadvantages: It is often impractical because of non-availability of population list or of difficulty in enumerating the population, does not ensure proportionate representation and it may be expensive in time and money. The amount of sampling error associated with any sample drawn can easily be computed. But it is greater than that in other probability samples of the same size, because it is less precise than other methods.
ii) Stratified Random Sampling: This is an improved type of random or probability sampling. In this method, the population is sub-divided into homogenous groups or strata, and from each stratum, random sample is drawn. E.g., university students may be divided on the basis of discipline, and each discipline group may again be divided into juniors and seniors. Stratification is necessary for increasing a sample’s statistical efficiency, providing adequate data for analyzing the various sub-populations and applying different methods to different strata. The stratified random sampling is appropriate for a large heterogeneous population. Stratification process involves three major decisions. They are stratification base or bases, number of strata and strata sample sizes.
Stratified random sampling may be classified into:
a) Proportionate stratified sampling: This sampling involves drawing a sample from each stratum in proportion to the latter’s share in the total population. It gives proper representation to each stratum and its statistical efficiency is generally higher. This method is therefore very popular. E.g., if the Management Faculty of a University consists of the following specialization groups:
Specialization stream
No. of students Proportion of each stream
Production strata sample sizes would be:
Strata Sample size
Advantages: Stratified random sampling enhances the representativeness to each sample, gives higher statistical efficiency, easy to carry out, and gives a self-weighing sample.
Disadvantages: A prior knowledge of the composition of the population and the distribution of the population, it is very expensive in time and money and identification of the strata may lead to classification of errors.
b) Disproportionate stratified random sampling: This method does not give proportionate representation to strata. It necessarily involves giving over-representation to some strata and under-representation to others. The desirability of disproportionate sampling is usually determined by three factors, viz, (a) the sizes of strata, (b) internal variances among strata, and (c) sampling costs.
Suitability: This method is used when the population contains some small but important subgroups, when certain groups are quite heterogeneous, while others are homogeneous and when it is expected that there will be appreciable differences in the response rates of the subgroups in the population.
Advantages: The advantages of this type is it is less time consuming and facilitates giving appropriate weighing to particular groups which are small but more important.
Disadvantages: The disadvantage is that it does not give each stratum proportionate representation, requires prior knowledge of composition of the population, is subject to classification errors and its practical feasibility is doubtful.
iii) Systematic Random Sampling: This method of sampling is an alternative to random selection. It consists of taking kth item in the population after a random start with an item form 1 to k. It is also known as fixed interval method. E.g., 1st, 11th, 21st ……… Strictly speaking, this method of sampling is not a probability sampling. It possesses characteristics of randomness and some non-probability traits.
Suitability: Systematic selection can be applied to various populations such as students in a class, houses in a street, telephone directory etc.
Advantages: The advantages are it is simpler than random sampling, easy to use, easy to instruct, requires less time, it’s cheaper, easier to check, sample is spread evenly over the population, and it is statistically more efficient.
Disadvantages: The disadvantages are it ignores all elements between two kth elements selected, each element does not have equal chance of being selected, and this method sometimes gives a biased sample.