SAMPLING DESIGN

PROBABILITY SAMPLING & NON-PROBABILITY SAMPLING

Prepared By,Sagar Gadekar

A population is the set of data of all possible measurements (or observations) of individuals or items.

E.g.. the heights of all students in a junior college, the lengths of life of all the light bulbs produced by a manufacturer.

A sample is a set of data chosen from a population and is a subset of the population.

A sampling unit is an individual member of a sample. A sampling frame is a list of all members of a

population. A parameter is a characteristic of the population. Examples are population mean, population variance

and population proportion. A statistic is a characteristic of the sample. Examples are sample mean, sample variance and

sample proportion.

Definition of Sampling:

Measuring a small portion of something and then making a general statement about the whole thing.

Process of selecting a number of units for a study in such a way that the units represent the larger group from which they are selected.

Why We Need Sampling (Purposes and Advantages of Sampling)

1. Sampling makes possible the study of a large, heterogeneous (different characteristics) population.

- The universe or population to be studied maybe too large or unlimited that it is almost impossible to reach all of them. Sampling makes possible this kind of study because in sampling only a small portion of the population maybe involved in the study, enabling the researcher to reach all through this small portion of the population.

Why We Need Sampling (Purposes and Advantages of Sampling)

2. Sampling is for economy.- Research without sampling

may be too costly. Sampling reduces the study population to a reasonable size that expenses are greatly reduced.

3. Sampling is for speed.- Research without sampling

might be too time consuming.

Why We Need Sampling (Purposes and Advantages of Sampling)

4. Sampling is for accuracy.- If it takes too long a time

to cover the whole study population, there maybe inaccuracy. The research must be finished within a reasonable period of time so that the data are still true, valid and reasonable.

Why We Need Sampling (Purposes and Advantages of Sampling)

5. Sampling saves the sources of data from being all consumed.

- The act of gathering data may consume all the sources of information without sampling. In such a case, there is no more data to apply the conclusion to.

Disadvantages of Sampling (Defective Sampling)

1. If sampling is biased, or not representative, or too small, the conclusion may not be valid and reliable.

2. In research, the respondents to a study must have a common characteristics which is the basis of the study.

3. If the population is very large and there are many sections and subsections, the sampling procedure becomes very complicated.

4. If the researcher does not possess the necessary skill and technical knowhow in sampling procedure.

WHAT IS A GOOD SAMPLE? The sample must be valid. Validity depends on 2 considerations:

1. Accuracy – bias is absent from the sample(ex. A company is thinking of lowering its price for its soap bar product. After making a survey in the sales of their product in a known mall they concluded that they will not cut down the price of the soap bar since there was an increased in sales compared to last year. Bias is present in this study since the company based its decision for the sales of a known mall which have consumers who can afford high price products. They did not consider the sales of their products in other area wherein they have middle class or low class consumers.)

WHAT IS A GOOD SAMPLE?2. Precision – sample represents the population

(ex. Customers who visited a particular dress shop are requested to log in their phone numbers so that they will receive information for discounts and new arrivals. Management wish to study customers satisfaction for that shop. By means of interviewing through phone they get comments and reactions of their client. Samples used are not an exact representative of the population since it is limited only to those customers who log in their phone numbers and they did not consider customers without phone numbers indicated.

SAMPLING DESIGN1. What is the target population?

- Target population is the aggregation of elements (members of the population) from which the sample is actually selected.

2. What are the parameters of interest?- Parameters are summary description of a given variable in a population.

3. What is the sampling frame?- Sampling frame is the list of elements from which the sample is actually drawn. Complete and correct list of population members only.

4. What is the appropriate sampling method? - Probability or Non-Probability sampling

method

SAMPLING DESIGN5. What size sample is needed?

There are no fixed rules in determining the size of a sample needed. There are guidelines that should be observed in determining the size of a sample.

When the population is more or less homogeneous and only the typical, normal, or average is desired to be known, a smaller sample is enough. However, if differences are desired to be known, a larger sample is needed.

When the population is more or less heterogeneous and only the typical, normal or average is desired to be known a larger sample is needed. However, if only their differences are desired to be known, a smaller sample is sufficient.

SAMPLING DESIGN The size of a sample varies inversely as the

size of the population. A larger proportion is required of a smaller population and a smaller proportion may do for a bigger population.

For a greater accuracy and reliability of results, a greater sample is desirable.

In biological and chemical experiments, the use of few persons is more desirable to determine the reactions of humans.

When subjects are likely to be destroyed during experiment, it is more feasible to use non-humans.

SAMPLING DESIGNExample: A Company would like to make a study in the quality

of digital cameras it manufactured. 1. Target population – consumers of digital cameras2. Parameters of interest – quality of digital cameras

(scale of 1 to 5 , 5 being the most satisfactory)3. Sampling frame – database of stores in which

digital cameras are sold, usually customers gives information about them for warranty purposes

4. Sampling method – Probability sampling (Stratified sampling).

5. Size of sample – it is more on heterogeneous population, average responses would like to know by the manufacturer, so large proportion will be needed from the population.

STEPS IN COMPUTING THE SIZE OF A SAMPLE

1. Determine the size of the target population. 2. Decide on the margin of error. As much as

possible the margin of error should not be higher than 5%. Probably 3% is an ideal one.

3. Use the formula n = N 1 + Ne2 (pagoso , et al.

p.46)n = sample size

N = the size of the population e = the margin of error4. Compute the sample proportion by dividing

the result in number 3 by the population.

STEPS IN COMPUTING THE SIZE OF A SAMPLE

1. Population is 5,3462. Margin of error is 3%3. Using the formula n = ___5,346_ 1+ 5346(.03)2

n = 9204. Sample proportion (%) = 920 / 5346 = 17%

General Types of Sampling

1. Probability sampling

The sample is a proportion (a certain percent) of the population and such sample is selected from the population by means of some systematic way in which every element of the population has a chance of being included in the sample.

PROBABILITY SAMPLING Randomization is a feature of the

selection process rather than an assumption about the structure of the population.

More complex, time consuming and more costly

General Types of Sampling

2. Non-probability sampling

The sample is not a proportion of the population and there is no system in selecting the sample. The selection depends upon the situation.

NON-PROBABILITY SAMPLING

No assurance is given that each item has a chance of being included as a sample

There is an assumption that there is an even distribution of characteristics within the population, believing that any sample would be representative.

TYPES OF PROBABILITY SAMPLING

A. PURE RANDOM SAMPLING

This type of sampling is one in which every one in the population of the inquiry has an equal chance of being selected to be included in the sample.

Also called the lottery or raffle type of sampling.

This may be used if the population has no differentiated levels, sections, or classes.

Done with or without replacement

PURE RANDOM SAMPLING

main advantage of this technique of sampling is that, it is easy to understand and it is easy to apply too.

disadvantage is that, it is hard to use with too large a population because of the difficulty encountered in writing the names of the persons involved.

PURE RANDOM SAMPLING Steps in selecting sample using a table of random

numbers: Define the population Determine the desired sample size List all the members of the population Assign each of the individuals on the list a

consecutive number from zero to the required number, ex. 01-89 or 001-249

Select an arbitrary number in the table of random numbers (Close your eyes and point)

For the selected number, look at only the appropriate number of digits

If the selected number corresponds to the number assigned to any individual in the population, then that individual is in the sample

Repeat the steps until the desired sample size is reached.

B. SYSTEMATIC SAMPLING

A technique of sampling in which every kth name (old system of counting off) in a list may be selected to be included in a sample.

Also called as interval sampling, there is a gap or interval, between each selected unit in the sample.

Used when the subjects or respondents in the study are arrayed or arranged in some systematic or logical manner such as alphabetical arrangement and geographical placement from north to south.

SYSTEMATIC SAMPLING

Steps in systematic sampling: Define the population Determine the desired sample size Obtain a list (preferably randomized) of the

population Determine what K is equal to by dividing the size

of the population by the desired sample size Select some random place at the top of the

population list Starting at that point, take every Kth name on

the list until desired sample size is reached If the end of the list is reached before the

desired sample is reached, go back to the top of the list.

SYSTEMATIC SAMPLING

k = skip interval = population size sample size population size = 64

sample size = 8

k = 8

SYSTEMATIC SAMPLING

Main advantage is that it is more convenient, faster, and more economical

Disadvantage is that the sample becomes biased if the persons in the list belong to a class by themselves whereas the investigation requires that all sectors of the population are to be involved.

C. STRATIFIED SAMPLING

The process of selecting randomly, samples from the different strata of the population used in the study.

Advantage is that it contributes much to the representative of the sample

Steps involves in stratified sampling: Define the population Determine the desired sample size Identify the variable and subgroups (strata) for which

you want to guarantee appropriate representation (either proportion or equal)

Classify all members of the population as members of one of the identified subgroups

Randomly select (using table of random numbers) an appropriate number of individuals from subgroups.

STRATIFIED SAMPLINGExample: A call center company wants to seek suggestions of

their agents for a new marketing strategy for their new services.

1. Population 5,000 agents. 2. Desired sample size 500 3. Variable of interest is age and there are three subgroups

under 30, 30 to 45 and over 45 4. We classify the agents into the subgroups 20% or 1,000 are under age 30 65% or 3,250 are age 30 to 45 15% or 750 are over age 45 5. We want 500 agents. Since we want proportional

representation. 20% of the sample (100) under age 30 65% (325) should be age 30 to 45 15% (75) should be over age 45 Therefore, using table of random numbers, 100 of the 1000 under age 30 are selected 325 of the 3250 age 30 to 45 are selected 75 of the 750 over age are selected

D. CLUSTER SAMPLING Also called as multistage cluster sampling

Used when the population is so big or the geographical area of the research is so large.

Advantage : efficiency

Disadvantage: reduced accuracy or representativeness, on the account of the fact that in every stage there is a sampling error.

CLUSTER SAMPLING

Steps in cluster sampling: Define the population Determine the desired sample size Identify and define a logical cluster Obtain, or make a list of all clusters in the

population Estimate the average number of

population members per cluster Determine the number of clusters needed

by dividing the sample size by the estimated size of the cluster

Randomly select the needed number of clusters (using a table of random numbers)

Include in the sample all population members in selected cluster

CLUSTER SAMPLING Same example in the stratified sampling:1. Population 5,000 agents2. Desired sample size 5003. Logical cluster is a branch4. 50 branches all over the country5. Although the branch vary in number of

agents , there is an average of 100 agents per branch.

6. The number of clusters (branch) needed equals the desired sample size, 500 divided by the average size of a cluster, 100. Thus, the number of branch needed is 5.

7. Therefore, we randomly select 5 of the 50 branch

8. All the agents in each of the 5 selected branch are in the sample.

TYPES OF NON-PROBABILITY SAMPLING

A. ACCIDENTAL SAMPLING /CONVENIENCE SAMPLING No system of selection but only those whom

the researcher or interviewer meet by chance are included in the sample.

Process of picking out people in the most convenient and fastest way to immediately get their reactions to a certain hot and controversial issue.

ACCIDENTAL / CONVENIENCE SAMPLING

Not representative of target population because sample are selected if they can be accessed easily and conveniently.

Advantage : easy to use

Disadvantage: bias is present

It could deliver accurate results when the population is homogeneous.

ACCIDENTAL / CONVENIENCE SAMPLING

Examples:

The female moviegoers sitting in the first row of a movie theatre

The first 100 customers to enter a department store

The first three callers in a radio contest

Use of volunteers

B. PURPOSIVE SAMPLING

The respondents are chosen on the basis of their knowledge of the information desired.

TYPES OF PURPOSIVE SAMPLING

1. QUOTA SAMPLING Specified number of persons of certain types

are included in the sample.

Advantage over accidental sampling is that many sectors of the population are represented. But its representativeness is doubtful because there is no proportional representation and there are no guidelines in the selection of the respondents.

PURPOSIVE SAMPLING

2. JUDGEMENT SAMPLING Sample is taken based on certain

judgements about the overall population.

Critical issue: objectivity “how much can judgement be relied upon to arrive at a typical sample?”

Advantage: reduced cost and time involved in acquiring the sample