1. Chapter 9 SELECTING A SAMPLE

2. Definition
Sampling: is the process of selecting a few (a sample) from a bigger group, the sampling population, to become the basis for estimating or predicting the prevalence of an unknown piece of information, situation or outcome regarding the bigger group.
Sample: is a subgroup of population you are interested in.

3. Adv. & Disad. Of Sampling Process
Advantages
Saves time
Saves financial and human resources
Disadvantages
Unable to find out the information about the population’s characteristics of interest to you but you only estimate or predict them
The possibility of an error in your estimation exists

4. Sampling in Qualitative Research
In qualitative research the issue of sampling has little significance as the main aim of most qualitative inquires is either to explore or describe the diversity in situation, phenomenon or issue.
Qualitative research does not make attempt to either quantify or determine the extent of diversity.
You can select one individual as a sample and describe whatever the aim of your inquiry is.

5. To explore the diversity in qualitative research you need to reach what is known as ‘saturation point’ in terms of findings.
For instance, you go on interviewing or collecting information as long as you keep discovering new information.
When you find that you are not obtaining any new data or the new information can be ignored, you are assumed to have reached ‘saturation point’.
Keep in mind that ‘saturation point’ is a subjective judgment which you, as researcher, decide.

6. Sampling Terminology Term Definition Population/study population
The large general group of many cases from which a researcher draw a sample and are usually denoted by the letter (N)
Sample
A smaller set of cases a researcher selects from a larger group and generalizes to the population
Sample size
The number of selected cases from larger population from who you obtain the required information and is usually denoted by the letter (n)
Sampling design/strategy
The method you use to select your sample
Sampling unit/ sampling element
The name for a case or single unit to be selected
Sampling frame
The list of units composing a population from which a sample is selected
Sample statistics
Information obtained from your respondents
Population parameters/population mean
A characteristic of the entire population that is estimated from a sample
Saturation point
When you reach a stage where no new information is coming from you respondents

7. Principles of Sampling
Average age of four people: A, B, C & D.
A is 18 yrs, B is 20, C is 23 & D is 25
Average age is : 21.5 ( = 86 divided by 4)
By selecting a sample of two we can estimate their average age.
And we can have six possible combinations of two:
1. A & B
2. A & C
3. A & D
4. B & C
5. B & D
6. C & D
Principle One: In a majority of cases of sampling there will be a difference between the sample statistics and the true population mean, which is attributable to the selection of the units in the sample

8. Difference between Sample average & population Average (2 cases)
Population mean
Difference bet 1 & 2 1
19.0
21.5
-2.5 2
20.5
-1.5 3
0.0 4 5
22.5
+1.0 6
24.0
+2.5
1. A & B
2. A & C
3. A & D
4. B & C
5. B & D
6. C & D

9. Principle Two:
The greater the sample size, the more accurate will be the estimate of the true population mean
Average age of four people: A, B, C & D.
A is 18 yrs, B is 20, C is 23 & D is 25
Average age is : 21.5 ( = 86 divided by 4)
By selecting a sample of three we can estimate their average age.
And we can have four possible combinations of three:
1. A + B+C
2. A + B+D
3. A + C+D
4. B + C+D

10. Difference between Sample & Population Average (3 cases)
Sample average
Population mean
Difference bet 1 & 2 1
20.33
21.5
-1.17 2
21.00
-0.5 3
22.00
+0.5 4
22.67
+1.17
1. A + B+C
2. A + B+D
3. A + C+D
4. B + C+D

11. Principle Three: The greater the difference in the variable under study in a population for a given sample size, the greater will be the difference between the sample statistics and the true population mean
A is 18 yrs, B is 26, C is 32 & D is 40
Average age is: 29 ( = 116 divided by 4)

12. Difference between Sample Statistics & Population Mean (2 cases)
Sample average
Population mean
Difference bet 1 & 2 1 22
29.00
-7.00 2 25
-4.00 3 29
0.00 4 5 33
+4.00 6 36
+7.00
1. A & B
2. A & C
3. A & D
4. B & C
5. B & D
6. C & D

13. Difference between Sample and Population Average (3 cases)
Sample average
Population mean
Difference bet 1 & 2 1
25.33
29.00
--3.67 2
28.00
-1.00 3
30.00
+1.00 4
32.66
+3.66
1. A + B+C
2. A + B+D
3. A + C+D
4. B + C+D

14. Factors affecting the inferences of sample
The size of the sample
The extent of variation in the sampling population

15. Aims in selecting a sample
To achieve maximum precision in your estimates within a given sample size
To avoid bias in the selection of your sample
Bias in the selection of a sample can occur if:
Sampling is done by a non-random method
The sampling frame does not cover the sampling population accurately and completely
A section of a sampling population is impossible to find or refuses to cooperate

17. Random/probability sampling Designs
Each element in the population has an equal and independent chance of selection in the sample.
Equal : means the probability of selection of each element in the population is the same.
That is, the choice of an element in the sample is not influenced by other considerations such as personal preference.
Independent : means that the choice of one element is not dependent upon the choice of another element in the sampling
That is, the selection or rejection of one element does not affect the inclusion or exclusion of another.
A sample can only be considered a random/probability sample and representative of the population under study if these conditions are met. If not, bias can be introduced into the study.

18. Advantages of Random/Probability Samples
As they represent the total sampling population, the inferences drawn from such samples can be generalized to the total sampling population.
Some statistical tests based upon the theory of probability can be applied only to data collected from random samples. Some of these tests are important for establishing conclusive correlations.

19. Method of drawing a random sample
The fishbowl draw
Computer program
A table of random numbers

20. Procedure for using a table of random numbers
Identify the total number of elements in the study population.
The total number of elements in a study population may run up to four or more digits.
Number each element starting from 1.
If the table for random numbers is on more than one page, choose the starting page by a random procedure.
Again select a column or row that will be your starting point with a random procedure and proceed from there in a predetermined direction
Corresponding to the number of digits to which the total population runs, select the same number, randomly, of columns or rows of digits from the table
Decided on your sample size
Select the required number of elements for your sample from the table
If you happen to select the same number twice, discard it and go to the next

23. Difference Systems of Drawing a Random Sample
Sampling without replacement
Sampling with replacement

24. Type of Specific Random/Probability Sampling Designs
Simple random sampling (SRS)
Stratified random sampling
Cluster sampling

25. Procedure for Selecting Simple Random Sampling
Identify by a number all elements or sampling units in the population
Decide on the sample size (n)
Select (n) using either the fishbowl draw, the table of random numbers or a computer program

26. Stratified Random Sampling
In this sampling the researcher attempts to stratify the population in such a way that population within a stratum is homogeneous with respect to the characteristic on the basis of which it is being stratified.
It is important that the characteristics chosen as the basis of stratification are clearly identifiable in the study population
For example, it is much easier to stratify a population on the basis of gender than on the basis of age, income or attitude.
Once the sampling population has been separated into non-overlapping groups you select the required number of elements from each stratum, using the simple random sampling technique.

27. Types of stratified Random Sampling
Proportionate stratified sampling : the number of elements from each stratum in relation to its proportion in the total population is selected.
Disproportionate stratified sampling: consideration is not given to the size of the stratum.

28. Cluster Sampling
Based on the ability of the researcher to divide the sampling population into groups, called cluster, and then to select elements within each cluster, using the SRS technique.
Depending on the level of clustering, sometimes sampling may be done at different levels. These levels constitute the different stages (single, double or multi-stage cluster sampling).

29. Non-random/non-probability Sampling Designs
These are used when the number of elements in a population is either unknown or cannot be individually identified.
In such situations the selection of elements is dependent upon other considerations.

30. Types of Non-random/non-probability Sampling Designs
Quota sampling
Accidental sampling
Judgmental or purpose sampling
Snowball sampling

31. Quota Sampling
The researcher is guided by some visible characteristic, such as gender or race, of the study population
The sample is selected from a location convenient to the researcher, and whenever a person with this visible relevant characteristic is seen that person is asked to participate in the study.
The process continues until the researcher has been able to contact the required number of respondents (quota).

32. Quota Sampling Advantages: Disadvantages:
It is the least expensive way of selecting a sample
You do not need any information, such as a sampling frame, the total number of elements, their location, or other information about the sampling population
It guarantees the inclusion of the type of people you need
Disadvantages:
The resulting sample is not a probability one, the findings cannot be generalized to the total sampling population
The most accessible individuals might have characteristics that are unique to them and hence might not be truly representative of the total sampling population

33. Accidental sampling
Whereas quota sampling attempts to include people possessing an obvious/visible characteristic, accidental sampling makes no such attempt.
The method of sampling is common among market research and newspaper reporters.
It has same advantages and disadvantages as quota sampling.
As you are guided by any obvious characteristics, some people contact may not have the required information

34. Judgmental or purpose sampling
Is the judgment of the researcher as to who can provide the best information to achieve the objectives of the study.
The researcher only goes to those people who in his/her opinion are likely to have the required information and be willing to share it.
This type of sampling is extremely useful when you want to construct a historical reality, describe phenomenon or develop something about which only a little is known.

35. Snowball sampling Is the process of selecting a sample using networks.
To start with, a few individuals in a group or organization are selected and the required information is collected from them.
They are then asked to identify other people in the group or organization, and the people selected by them become a part of the sample.
This process continued until the required number or a saturation point bas been researched.
This method is useful for studying communication patterns, decision making or diffusion of knowledge within a group.

37. Mixed Sampling Design : Systematic Sampling Design
Systematic Sampling has the characteristics of both random and non-random sampling designs
In systematic sampling the sampling frame is first divided into a number of segments called intervals.
If the first interval is the fifth element, the fifth element of each subsequent interval will be chosen

38. Procedure for Selecting a Systematic Sample
Prepare a list of all the elements in the study population (N)
Decide on the sample size (n)
Determine the width of the interval (k)
= total population
sample size
Using the SRS, select an element from the first interval (nth order)
Select the same order element from each subsequent interval

40. Calculation of sample Size
Depends on what you want to do with the findings and what type of relationships you want to establish.
In qualitative research the question of sample size is less important as the main focus is to explore or describe a situation, issue, process or phenomenon.

41. Calculation of sample Size
In quantitative research and particularly for cause-and-effect studies, you need to consider the following:
At what level of confidence do you want to test your results, findings or hypotheses?
With what degree of accuracy do you wish to estimate the population parameters?
What is the estimated level of variation (standard deviation, with respect to the main variable you are studying, in the study population?

42. Calculation of sample Size
The size of the sample is important for testing a hypothesis or establishing an association, but for other studies the general rule is the larger the sample size, the more accurate will be your estimates.
In practice, your budget determines the size of your sample.
Your skills in selecting a sample, within the constraints of your budget, lie in the way you select your elements so that they effectively and adequately represent your sampling population.

43. END Of CHAPTER 9