Quantitative Methods:

Module 6:  Sampling Methods

 

Introduction

Population

Complete set of conceivable observations

Sample

Subset of population

 

In practice information is nearly always collected form samples for a  Wide variety of reasons

Ø      Economic Advantage

Ø      Timeliness

Ø      Size and accessibility

Ø      Observation and destruction

 

Applications of Sampling:

Ø      Opinion poll,

Ø      Quality control,

Ø      Checking invoices

 

Ideas Behind Sampling

Ø      Sample should be representative of product representation, Sampling Methods

Random Sampling Methods

Simple Random

Variation on Simple Random Sampling

Ø      Multi-Stage Sample

Ø      Cluster Sample

Ø      Stratified Sample

Ø      Weighting

Ø      Probability

Ø      Variable

Ø      Area

Judgment Sampling

Ø      Systematic

Ø      Convenience

Ø      Quota

 

Random Sampling

Simple Random Sample:

Each member of Population has an equal chance of being selected.  I.e. draw names from a hat. 

Multi-stage sample

Population is split into groups, and then subgroups. A random sample is taken at each stage of the breakdown.

Cluster sample:

 Closely linking with multi-stage sampling in that the population is divided into groups, subgroups but, the difference is that at the final stage each individual of the chosen groups is included in the final sample

Stratified sample:

 Sample contains same % of breakdown of subgroups as in population. Prior knowledge of this break down is used to make the sample more representative.

Weighting:

Is a way of recognizing  the existence of stratification  in the population after the sampling has been carried out. The measurements made on individual elements of the population are weighted so that the net effect is as if the proportions of each stratum in the sample had been the same as those in the population.

Probability Sample

In simple random sampling, each element of the population has an equal chance of being selected for that sample. There are circumstances when it is desirable for elements to have differing chances to be selected.

Variable Sample

 Some special sub-population is over-sampled i.e. deliberately over-represented.

Area Sample

An artificial breaking down of the population to make sampling easier. (The population is split into geographical areas).

 

Judgment Sampling

Ø      Involves a significant degree of personal judgment

Systematic Sampling:

The sample is taken at regular intervals from the population. (Example: For a sample of 1000 out of a population of 50000, every 50th on the list would be chosen.)

Convenience Sampling

Sampling is taken the easiest way possible. (For instance, medically, a blood sample is usually taken from the arm.)

Quota Sampling

Frequently used in market research interviews in order to overcome interview bias

Accuracy of Samples

Stratified sampling improves accuracy, but in simple random sampling, the accuracy can be calculated.

Difficulties in Sampling

Sampling Frame

The complete list from which the sample is selected. In practice, this list is often different from the population at large.

Non-Response

Can bias the sample, because the input of the non-responses may be atypical of the population, and other members of the sample. Reducing non-response can be expensive.

Bias

The tendency to over or underrepresented elements of the population.

Other sources include

Ø      Inaccurate measurement i.e. physical inaccuracy thermometer calibrated one degree to high

Ø      Interviewer bias – interviewer induces bias answers from question asked

Ø      Interviewee bias – interviewee injects the bias false claims

Ø      Instrument bias – means of collecting data such as a questionnaire.

 

Sample Size

Ø      What level of Accuracy is needed in the results?

Ø      Use Statistical Theory to calculate the sample size – which is related to accuracy

Ø      Random sample, it is possible to say, with 95% accuracy, how close the calculated sample statistic is to the actual population.

Ø      Accuracy increases with the square root of the sample size. (Example: increasing the sample from 100 to 400 --a factor of 4, halves the error [Ö4 =2]. )

Ø      Collect the largest sample that the available budget allows. 

Ø      Small population sizes impact accuracy of samples, for instance, in a population of 50, the first selection has a 1/50 chance of being picked, the second has a 1/49, the third, 1/48. Random sampling requires that each member of the population has an equal chance of being selected. This is not true for small populations (for large populations, the differences are negligible.)

Ø      Sampling with replacement: Downside--elements could be selected twice.

Ø      Use a different theory for calculating accuracy and sample size.

Key Message

1) Sampling is a trade off between accuracy and expense.

2) The larger the sample size, the closer the accuracy will be to maximum (but, possible that measurement errors could swamp sampling errors.)

3) Applications:

a) Opinion polls

b) Market research of consumer attitudes and preferences

c) Medical investigations

d) Agriculture

e) Accounting

f) Quality control

g) Information systems

4) Sample size is dependent upon objectives and required accuracy, not related to population size.