Non-probability Sampling Quota Sampling

This is stratified-cum-purposive or judgment sampling and thus enjoys the benefits of both. It aims at making the best use of stratification without incurring the high costs involved in probabilistic methods. There is considerable saving in time and money as the simple units may be selected that they are close together. If carefully experienced by skilled and experienced investigators who are aware of the limitations of judgment sampling and if proper controls are imposed on the investigators, this sampling method may give reliable results.

Purposive or Judgment Sampling

A desired number of sampling units are selected deliberately so that only important items representing the true characteristics of the population are included in the sample.

A major disadvantage of this sampling is that it is highly subjective, since the selection of the sample depends entirely on the personal convenience and beliefs.

Example: In the case of socio-economic survey on the standard of living from people in Chennai, if the researcher wants to show that the standard has gone down, he may include only individuals from the low income stratum of the society in the samples and exclude people from rich areas.

Other Forms of Sampling

Snow Ball Sampling : This method is used in the cases where information about units in the population is not available. If a researcher wants to study the problem of the weavers in a particular region, he may contact the weavers who are known to him. From them, he may collect the addresses of other weavers in the various parts of the region he selected. From them again he may collect the information on other known weavers to him. By repeating like this for several times, he will be able to identify and contact the majority of weavers from a selected region. He could then draw a sample from this group. This method is useful only when individuals in the target group have contact with one another, and also willing to reveal the names of others in the group.

Spatial Sampling : Some populations are not static and moving from place to place but staying at one place when an event is taking place. In such case the whole population in a particular place is taken into the sampling and studied.

Example: The number of people living in Dubai may vary depending on many factors.

Saturation Sampling : Sometimes if all members of population is need to be studied so as to get a picture of entire population. The sampling method that requires a study of entire population is called Saturation Sampling. This technique is more familiar in Socio metric studies where in distorted results will be produced even if one person is left out.

Example: In case of analyzing the student's behavior of one particular class room, all the students in the class room must be examined.

From the above discussion on sampling methods, normally one may resort to simple random sampling since biasness is generally eliminated in this type of sampling. At the same time, purposive sampling is considered more appropriate when the universe happens to be small and a known characteristic of it is to be studied intensively. In situations where random sampling is not possible then it is advisable to use necessarily a sampling design other than random sampling.

Determination of Sample size

Determination of appropriate sample size is crucial part of any business research. The decision on proper sample size tremendously requires the use of statistical theory. When a business research report is been evaluated, the evaluation start with the question of 'how big is the sample size?'

Having discussed various sampling designs it is important to focus the attention on Sample Size. Suppose we select a sample size of 30 from the population of 3000 through a simple random sampling procedure, will we able to generalize the findings to the population with confidence? So in this case what is the sample size that would be required to carry out the research?

It is the known fact that larger the sample size, the more accurate the research is. In fact this is the fact based on the statistics. According to this fact, increasing the sample size decreases the width of the confidence interval at a given confidence level. When the standard deviation of the population is unknown, a confidence interval is calculated by using the formula:

Confidence Interval,

μ = X ± KSx

where,

Sx = S / Sqrt(n)

In sum, choosing the appropriate sampling plan is one of the important research design decisions the researcher has to make. The choice of a specific design will depend broadly on the goal of research, the characteristics of the population, and considerations of cost.

Issues of Precision and Confidence in determining Sample size

We now need to focus attention on the second aspect of the sampling design issue—the sample size. Suppose we select 30 people from a population of 3,000 through a simple random sampling procedure. Will we be able to generalize our findings to the

population with confidence? What is the sample size that would be required to make reasonably precise generalizations with confidence? What do precision and confidence mean?

A reliable and valid sample should enable us to generalize the findings from the sample to the population under investigation. No sample statistic (X, for instance) is going to be exactly the same as the population parameter (Sx), no matter how sophisticated the probability sampling design is. Remember that the very reason for a probability design is to increase the probability that the sample statistics will be as close as possible to the population parameters.

Precision

Precision refers to how close our estimate is to the true population characteristic.

Usually, we would estimate the population parameter to fall within a range, based on the sample estimate.

Example: From a study of a simple random sample of 50 of the total 300 employees in a workshop, we find that the average daily production rate per person is 50 pieces of a particular product (X = 50). We might then (by doing certain calculations, as we shall see later, be able to say that the true average daily production of the product (X) would lie anywhere between 40 and 60 for the population of employees in the workshop. In saying this, we offer an interval estimate, within which we expect the true population mean production to be (μ = 50 ± 10). The narrower this interval, the greater is the precision. For instance, if we are able to estimate that the population mean would fall anywhere between 45 and 55 pieces of production (μ = 50 ± 5) rather than 40 and 60 (μ

= 50 ± 10), then we would have more precision. That is, we would now estimate the mean to lie within a narrower range, which in turn means that we estimate with greater exactitude or precision.

Precision is a function of the range of variability in the sampling distribution of the sample mean. That is, if we take a number of different samples from a population, and take the mean of each of these, we will usually find that they are all different, are normally distributed, and have a dispersion associated with them Even if we take only one sample of 30 subjects from the population, we will still be able to estimate the variability of the sampling distribution of the sample mean. This variability is called the standard error, denoted by 'S'. The standard error is calculated by the following formula:

Sx = S / Srqt(n) where,

S = Standard deviation of the sample n = Sample size

Sx = Standard error or the extent of precision offered by the sample.

In sum, the closer we want our sample results to reflect the population characteristics, the greater will be the precision we would aim at. The greater the precision required, the larger is the sample size needed, especially when the variability in the population itself is large.

Confidence

Whereas precision denotes how close we estimate the population parameter based on the sample statistic, confidence denotes how certain we are that our estimates will really hold true for the population. In the previous example of production rate, we know we are more .precise when we estimate the true mean production (μ) to fall somewhere between 45 and 55 pieces, than somewhere between 40 and 60.

In essence confidence reflects the level of certainty with which we can state that our estimates of the population parameters, based on our sample statistics will hold true.

The level of confidence can range from 0 to 100%. A 95% confidence is the

conventionally accepted level for most business research, most commonly expressed by denoting the significance level as p = .05. In other words, we say that at least 95 times out of 100, our estimate will reflect the true population characteristic.

In sum, the sample size n, is a function of 1. The variability in the population

2. Precision or accuracy needed 3. Confidence level desired

4. Type of sampling plan used, for example, sample random sampling versus stratified random sampling

It thus becomes necessary for researchers to consider at least four points while making decisions on the sample size needed to do the research:

(1) Much precision is really needed in estimating the population characteristics interest, that is, what is the margin of allowable error?

(2) How much confidence is really needed, i.e. how much chance can we take of making errors in estimating the population parameters?

(3) To what extent is there variability in the population on the characteristics investigated?

(4) What is the cost-benefit analysis of increasing the sample size?

Determining the Sample Size

Now that we are aware of the fact that the sample size is governed by the extent of precision and confidence desired, how do we determine the sample, retired for our research? The procedure can be illustrated through an example:

Suppose a manager wants to be 95% confident that the withdrawals in a bank will be within a confidence interval of ±$500. Example of a simple of clients indicates that the average withdrawals made by them have a standard deviation of $3,500. What would be the sample size needed in this case?

We noted earlier that the population mean can be estimated by using the formula:

μ = X ± KSx

Given, S = 3500. Since the confidence level needed here is 95%, the applicable K value is 1.96 (t-table). The interval estimate of ±$500 will have to encompass a dispersion of (1.96 x standard error). That is,

The sample size needed in the above is 188. Let us say that this bank has the total clientele of only 185. This means we cannot sample 188 clients. We can, in this case, apply the correction formula and see what sample size would be needed to have the same level of precision and confidence given the fact that we have a total of only 185 clients. The correction formula is as follows:

where,

N = total number of elements in the population = 185 n = sample size to be estimated = ?

Sx = Standard error of estimate of the mean = 255.10 S = Standard deviation of the sample mean = 3500 Applying the correlation formula,

we find that

255.10 = 3500 × √n × √185-n/184 the value of n to be 94.

We would now sample 94 of the total 185 clients.

To understand the impact of precision and/or confidence on the sample size, let us try changing the confidence level required in the bank withdrawal exercise which needed a sample size of 188 for a confidence level of 95%. Let us say that the bank manager now wants to be 99% sure that the expected monthly withdrawals will be within the interval of ±$500. What will be the sample size now needed?

The sample has now to be increased 1.73 times (from 188 to 325) to increase the confidence level from 95% to 99%.It is hence a good idea to think through how much precision and confidence one really needs, before determining the sample size for the research project.

So far we have discussed sample size in the context of precision and confidence with respect to one variable only. However, in research, the theoretical framework has several variables of interest, and the question arises how one should come up with a sample size when all the factors are taken into account.

Krejcie and Morgan (1970) greatly simplified size decision by providing a table that ensures a good decision model. The Table provides that generalized scientific guideline for sample size decisions. The interested student is advised to read Krejcie and Morgan (1970) as well as Cohen (1969) for decisions on sample size.

Importance of Sampling Design and Sample Size

It is now possible to see how both sampling design and the sample size are important to establish the representativeness of the sample for generality. If the appropriate

sampling design is not used, a large sample size will not, in itself, allow the findings to be generalized to the population. Likewise, unless the sample size is adequate for the desired level of precision and confidence, no sampling design, however sophisticated, can be useful to the researcher in meeting the objectives of the study.

Hence, sampling decisions should consider both the sampling design and the sample size. Too large a sample size, however (say, over 500) could also become a problem in as

much as we would be prone to committing Type II errors. Hence, neither too large nor too small sample sizes help research projects.

Roscoe (1975) proposes the following rules of thumb for determining sample size:

1. Sample sizes larger than 30 and less than 500 are appropriate for most research.

2. Where samples are to be broken into sub samples; (male/females, juniors/ seniors, etc.), a minimum sample size of 30 for each category is necessary.

3. In multivariate research (including multiple regression analyses), the sample size should be several times (preferably 10 times or more) as large as the number of variables in the study.

4. For simple experimental research with tight experimental controls (matched pairs, etc.), successful research is possible with samples as small as 10 to 20 in size.

KEY TERMS

1. "What is Sample Design"? What all are the points to be considered to develop a sample design?

2. Explain the various sampling methods under probability sampling.

3. Discuss the non probability sampling methods.

4. What are the importance of sample size and sampling design?

5. Discuss the other sampling methods.

6. Explain why cluster sampling is a probability sampling design.

7. What are the advantages and disadvantages of cluster sampling?

8. Explain what precision and confidence are and how they influence sample size.

9. The use of a convenience sample used in organizational research is correct because all members share the same organizational stimuli and go through almost the same kinds of experience in their organizational life. Comment.

10. Use of a sample of 5,000 is not necessarily better than one of 500. How would you react to this, statement?

11. Non-probability sampling designs ought to be preferred to probability sampling designs in some cases. Explain with an example

End of Chapter -LESSON – 11