The procedure of selecting a sample may be broadly classified under the following two heads: 1. Non-Probability Sampling Methods 2. Probability Sampling.
1. Non-Probability Sampling Methods:
The common feature in non-probability sampling methods is that subjective judgments are used to determine the populations that are contained in the sample.
We classify non-probability sampling into four groups:
1. Convenience Samples.
2. Judgment Samples.
3. Quota Samples.
4. Snowball Samples.
(A) Convenience Samples:
I. These types of samples are used primarily for reasons of convenience.
II. It is used for exploratory research and speedy situations.
III. It is often used for new product formulations or to provide gross-sensory evaluations by using employees, students, peers, etc.
Convenience sampling is extensively used in marketing studies and otherwise.
This would be clear from the following examples:
1. Suppose a marketing research study aims at estimating the proportion of Pan (Beetle leaf) shops in Delhi, which store a particular drink Maaza. It is decided to take a sample of size 150. What the investigator does is to visit 150 Pan shops near his place of office as it is very convenient to him and observe whether a Pan shop stores Maaza or not.
This is definitely not a representative sample, as most Pan Shops in Delhi had no chance of being selected. It is only those Pan shops which were near the office of the investigator has a chance of being selected.
2. As another example a researcher might visit a few shops to observe what brand of vegetable oil people are buying so as to make inference about the share of a particular brand he is interested in.
(B) Judgment Samples:
It is that sample in which the selection criteria are based upon your (researcher’s) personal judgment that the members of the sample are representative of the population under study.
It is used for most test markets and many product tests conducted in shopping malls. If personal biases are avoided, then the relevant experience and the acquaintance of the investigator with the population may help to choose a relatively representative sample from the population. It is not possible to make an estimate of sampling error as we cannot determine how precise our sample estimates are.
Judgment sampling is used in a number of cases, some of which are: Suppose we have a panel of experts to decide about the launching of a new product in the next year. If for some reason or the other, a member drops out, from the panel, the chairman of the panel may suggest the name of another person whom he thinks has the same expertise and experience to be a member of the said panel. This new member was chosen deliberately a case of Judgment sampling.
The method could be used in a study involving the performance of salesmen. The salesmen could be grouped into top grade and low grade performer according to certain specified qualities. Having done so, the sales manager may indicate who in his opinion, would fall into which category. Needless to mention this is a biased method. However in the absence of any objective data, one might have to resort to this type of sampling.
(C) Quota Samples:
This is a very commonly used sampling method in marketing research studies. Here the sample is selected on the basis of certain basic parameters such as age, sex, income and occupation that describe the nature a population so as to make of it representative of the population.
The Investigators or field workers are instructed to choose a sample that conforms to these parameters. The field workers are assigned quotas of the number of units satisfying the required characteristics on which data should be collected.
However, before collecting data on these units the investigators are supposed to verify that the units qualify these characteristics. Suppose we are conducting a survey to study the buying behavior of a product and it is believed that the buying behaviour is greatly influenced by the income level of the consumers.
We assume that it is possible to divide our population into three income strata such as high- income group, middle-income group and low-income group. Further it is known that 20% of the population is in high-income group, 35% in the middle-income group and 45% in the low- income group. Suppose it is decided to select a sample of size 200 from the population.
Thus the samples of size 40, 70 and 90 should come from high income, middle income and low income groups respectively. Now the different field workers are assigned quotas to select the sample from each group in such a way that a total sample of 200 is selected in the same proportion. For example- selection is done by non-probability means; and is based upon the researcher’s judgment of appropriate demographics.
(D) Snowball Sampling:
I. It is that samples in which the selection of additional respondents (after the first small group of respondents is selected) is based upon referrals from the initial set of respondents.
II. It is used to sample low incidence or rare populations.
III. It is done for the efficiency of finding the additional, hard-to-find members of the sample.
Advantages of Non-Probability Samples:
I. It is much cheaper to probability samples.
II. It is acceptable when the level of accuracy of the research results is not of utmost importance.
III. Less research time is required than probability samples.
IV. It often produces samples quite similar to the population of interest when conducted properly.
Disadvantages of Non Probability Samples:
I. You cannot calculate sampling error. Thus, the minimum required sample size cannot be calculated which suggests that you (researcher) may sample too few or too many members of the population of interest.
II. You do not know the degree to which the sample is representative of the population from which it was drawn.
III. The research results cannot be projected (generalized) to the total population of interest with any degree of confidence.
2. Probability Sampling Methods:
Probability sampling is the scientific method of selecting samples according to some laws of chance in which each unit in the population has some definite pre-assigned probability of being selected in the sample.
The different types of probability sampling are:
I. Where each unit has an equal chance of being selected.
II. Sampling units have different probabilities of being selected.
III. Probability of selection of a unit is proportional to the sample size.
Simple Random Sampling:
It is the technique of drawing a sample in such a way that each unit of the population has an equal and independent chance of being included in the sample. In this method an equal probability of selection is assigned to each unit of population at the first draw. It also implies an equal probability of selecting in the subsequent draws.
Thus in simple random sample from a population of size N, the probability of drawing any unit in the first draw is 1/N .The probability of drawing a second unit in the second draw is 1/N.
1. The probability of selecting a specified unit of population at any given draw is equal to the probability of its being selected at the first draw.
Selection of a Simple Random Sample:
We know all know simple random sample refers to that method of selecting a sample in which each and every unit of population is given independent and equal chance to be included in the sample. But, random sample does not depend only upon selection of units but also on the size and nature of the population.
One procedure may be good and simple for a small sample but it may not be good for the large population. Generally, the method of selecting a sample must be independent of the properties of sampled population. Proper precautions should be taken to ensure that your selected sample is random.
Random selection is best for two reasons – it eliminates bias and statistical theory is based on the idea of random sampling. We can select a simple random sample through use of tables of random numbers, computerized random number generator or lottery method.
Thus, the three methods of drawing simple random sample are:
a. Mechanical method and using tables of random numbers,
b. Sealed envelopes (lottery system) etc.
This method is the simplest method of selecting a random sample. We will illustrate it by means of example for better understanding. Suppose, we want to select “r” candidates out of “n”. We assign the numbers from 1 to n i.e. to each and every candidate; we assign only one exclusive number.
These numbers are then written on n slips which are made as homogeneous as possible in shape, size, colour, etc. These slips are then put in a bag and thoroughly shuffled and then “r” slips are drawn one by one. The “r” candidates corresponding to numbers on the slips drawn will constitute a random sample.
This method of selecting a simple random sample is independent of the properties of population. Generally in place of slips you can also use cards. We make one card corresponding to one unit of population by writing on it the number assigned to that particular unit of population.
The pack of cards is a miniature of population for sampling purposes. The cards are shuffled a number of times and then a card is drawn at random from them. This is one of the most important reliable methods of selecting a random sample.
Mechanical Randomization or Random Numbers Method:
The explained method of lottery is very time consuming and cumbersome to use if population is very large. Thus the most practical and inexpensive method of selecting a random sample consists in the use of random numbers tables, which has been constructed that each of the digits 0,1,2,3,4,5,6,7,8,9 appear with approximately the same frequency and independently of each other. If we have to select a simple random sample from a population of size N (d”99) then the numbers can be combined two by two to give pairs from 00 to 99.
Similarly if Nd”999 or Nd”9999 and so on, then combining the digits three by three ( or four by four and so on ), we get numbers from 000 to 999 or (0000 to 9999) and so on. Since each of the digits 0,1,2,3,4,5,6,7,8,9 appear with approximately the same frequency and independently of each other, so does each of the pairs 00 to 99 or triplets from 000 to 999 or quadruplets 0000 to 9999 and so on.
Thus, the method of drawing the random sample consists in the following steps:
(i) Identify the N units in the population with the numbers from 1 to N
(ii) Select at random, any page of the random number tables and pick up the numbers in any row or column or diagonal at random.
(iii) The population units corresponding to the number of unit selected in step ii comprises the random sample.
a. Tippets (1927) Random Number Table:
(Tracts for computers No. 15 Cambridge University Press) Tippet number tables consist of 10,400 four digit numbers, giving in all 10,400 x 4, i.e., 41600 digits selected at random from the British Census Report of surveys.
Merits and Limitations of Simple Random Sampling:
1. Since samples units are selected at random providing equal chance to each and every unit of population to be selected, the element of subjectivity or personal bias is completely eliminated. Therefore, we can say that simple random sample is more representative of population than purposive or judgment sampling.
2. You can ascertain the efficiency of the estimates of the parameters by considering the sampling distribution of the statistic (estimates).
One measure of calculating precision is sample size. Sample mean becomes an unbiased mean of population mean or a more efficient estimate of population mean as sample size increases.
1. The selection of simple random sample requires an up-to-date frame of population from which samples are to be drawn. Although it is impossible to have complete knowledge about each and every units of population; if population happens to be very large. This restricts the use of simple random sample.
2. A simple random sample may result in the selection of the sampling units, which are widely spread geographically and in such a case the administrative cost of collecting the data may be high in terms of time and money.
3. Sometime, a simple random sample might give most non-random looking results,
4. For a given precision, simple random sample usually requires larger sample size as compared to stratified random sampling.