Samplels & Sampling Techniques

Population

sample

Sampling

The Research Locals This portion of the

presentation contains a description of the place where the respondents are to be obtained. It includes a brief description of the location whether urban or rural; city or country; provincial; commercial or agricultural; and the regional or local characteristics.

This study shall be conducted in the Cordillera Administrative Region (CAR) which covers the provinces of Abra, Apayao, Benguet, Ifugao, Kalinga and Mountain Province and the City of Baguio. The CAR provinces belong to three (3) income classifications. Benguet province is second class, Abra, Apayao, Kalinga and Ifugao are considered as third class while Mt. Province is classified as fourth class province. In this study, one province from each income classification and the City of Baguio shall be selected as the source of data and information. Benguet province shall represent the second class province, Mt. Province shall be picked up to represent the fourth class province while Abra shall represent the third class provinces due to accessibility purposes and to the close association of its upland areas to the provinces of Apayao and Kalinga.

Example

Bradfield et al (1980) define “sampling” as the process of measuring a small portion of something followed by a general statement about the whole thing.

A sample is a collection of individuals selected from a larger population

For a study to produce a valid and reliable result, sufficient representatives of samples and appropriate sampling techniques should be adopted.

Sampling is the process of getting a

representative part of the population being studied. A representative of the samples is determined in a manner that the characteristics, properties and variations are reflected.

Population

Sample

A sample is any sub-aggregate drawn from the population (Fergusson, 1976). Ary et al defines sampling as the process involving the taking a part of the population.

It is pointed out that a good sampling is an effective means of reducing the number of persons contacted to get a relatively accurate picture of the sample population’s attitude and opinion (Orth, 1976).

Sampling The process of selecting a

portion of the target population in such a way that the individuals chosen represent, as nearly as possible, the characteristics of the target population

The Population and Sample Size

• A population refers to a group to which an investigator

would like the result to be generalized. Hence, it is a larger group about which a generalization is made (Gay, 1976). It also refers to “all members of any well-defined class of people, events or objects” (Kerlingen, 1973).

• A sample is a small group taken from a larger population composed of members being studied. A good example size should be a representative of the population and should be adequate in size to be reliable. If all members of the population have an equal chance of being selected, then the sample is a representative of the population.

Slovin (1960) presents a formula to determine the size of a sample as follows:

Where: n=______N______

1 + (N)(e) ²

n= Sample Size

N=Population Size

Example: In your study, the size of your population is 10, 000. What is the size of

your sample if you allow 2% margin of error? Using above captioned formula the sample size could be computed as follows:

n=______10,000_______

1 + 10,000(.02) ²

= ______10,000_______

1 + 10, 000(.0004)

=_____10,000______

1 + 4

= ____10,000____

5

= 2,000

Therefore, your representative sample size is 2,000 out of 10,000

Therefore, your representative sample size is 2,000 out of 10,000

This formula is not applicable to a small population. Pagoso et al

(1980), presents a Table below showing the sample size for specified

margins of error, indicating the margins of error that are not applicable

to population sizes as indicated by “NH” as follows

Population Margin of Error

1% 2% 3% 4% 5% 10%

500 NA NA NA NA 222 83

1,500 NA NA 638 441 316 94

2,500 NA 1,250 769 500 345 96

3,000 NA 1,364 811 517 353 97

4,000 NA 1,538 870 541 364 98

5,000 NA 1,667 909 556 370 98

6,000 NA 1,765 938 566 375 98

7,000 NA 1,842 959 574 378 99

8,000 NA 1,908 976 580 381 99

9,000 NA 1,908 989 584 383 99

10,000 5,000 2,000 1,020 588 388 99

50,000 8,333 2,333 1,087 617 387 100

Depending upon the type of research use, Gay (1978) as cited by Sevilla et al (1978) offers some minimum acceptable sizes as follows:

1. Descriptive Research, 20% for a smaller

population as small as 500 and below and 10% of the population for a larger population as large as 1,000.

2. Experimental Research, 30 per group as minimum although 15 subjects are acceptable (Sevilla et al, 1988).

3. Ex post facto or causal comparative group – 15 subjects per research

3. Experimental research – 15 subjects per group. Some believe that 30 per group should be considered minimum

Lynch et al 1972, and cited by Ardoles, 1992, suggested the

formula below to determine the sample size: n= NZ² x p (1-p) _ Where: n= Sample Size Nd² + Z² p (1-p) N= Population

Z= the value of the normal variables (1.96) for a reliability level of 0.95 p= the largest possible proportion (0.50)

For instance, if the population size in your research is 10,000 and the desired reliability is 0.95, with 0.05 as allowable sampling error and the proportion of a target population with a certain characteristics important to the study is 0.50. What is the size of the population?

The sample size could be computed as follows:

n= 10,000 (1.96) ² x 0.50 (1-0.50)

= 10,000 (3.84) x 0.50(0.50)

10,000 (.0025) + 3.84 x 0.50(0.50)

= 38,400 x 0.25

25 + 3.84 x 0.25

= 9,600

25 + 0.96

= 9,600

25.96

= 369.79 or 370

Pagoso et al, proposed the formula for computing the size of the sample as:

n=____N____

1 + (N)(e) ²

Where: n= the size of the sample

N= the size of the Population

e= the margin of error (should not be higher than 5%)

which is ideally 3%

Example: If the population is 10,000 and the margin of error to be adopted is 3%, the size of the population is computed as follows:

n=____10,000_____

1 + 10,000 (.03) ²

=_____10,000_____

1 + 10,000 (.0009)

=_____10,000_____

1+ 9

=_____10,000_____

10

N = 1,000

Department Total

Number

10% Sample

Size

Elementary 6,000 0.1 600

Secondary 3,000 0.1 300

College 1,000 0.1 100

10,000 1,000

Then: The sample proportion should be computed

using this formula: n = 1,000 =0.1 N 10,000 Hence: Every sub-group is represented accordingly

in the sample.

Sampling Error The fluctuation of a statistic from one sample

to another drawn from the same population. (Can be estimated with probability sampling. Note: the larger the sample, the less sampling error.

There are basically two types of sampling, namely:

1. Probability Sampling

A probability sampling is a type of sampling wherein the selection of samples is done with the members of the population having equal chance to be selected as part of the representative sample. It is further classified into the following sub-types: simple random, stratified random, cluster, systematic sampling, selective sampling

Sampling procedures use some form of randomization to select samples from the population

2. Non Probability Sampling

Using other than random Procedures such as: convenience sampling, purposive sampling, quota sampling

It is further classified into the following sub-types:

a) Simple Random Sampling In this type of sampling every member of the population has

an equal chance of being chosen to be included in the sample. It is the simplest probability sampling which is usually done by using lottery or raffle method of getting the representative samples of the population. This method is easily done by listing numerically all the names of the members of the population from the first to the last member. Write their individual numbers in small pieces of paper, then place these in a box and draw them after shaking the box very well until the total desired samples are obtained.

b) Stratified Sampling This is the selection of samples from the different classes

or strata of the population involved in the research. Each class is treated as a different population. A simple random sampling is then used in each class with proportionate and equal percentage of representation from each stratum.

An example is when a study is conducted with

Groups of respondents were the residents grouped as Commercial, Industrial and Residential of Urdaneta City for the year 2012 and 2013

Application for Business, Building, and Occupancy Permit

The first groups of respondents were the eighteen (18) BFP personnel of Urdaneta City who are the implementers of the Fire Code of the Philippines. The other groups of respondents were the residents grouped as Commercial, Industrial and Residential of Urdaneta City who applied for Business, Building, and Occupancy Permit for the year 2006 and 2007. The numbers of applicants were: Commercial - N=251, Industrial – N=190, and Residential – N=56. The representative sample by group was determined using the Slovin formula (Parel, 1984). The computed samples by group were: Commercial (n=113), Industrial (n=86) and Residential (n=25) yielding a total of 224.

The formula is shown below. n = ______N_______ 2 1 + N e Where: n = sample; N = population; e = standard error.

Stratified sampling is a strategy for selecting samples in such a way that specific subgroups or strats will have a sufficient number of representatives within the sample to provide ample number of sub analysis of the members of these subgroups

C. Stratified sampling

Cluster sampling refers to the selection of members of a sample rather than individual. It is sampling in which groups, not individual, are randomly selected.

use in multi stage sampling process Used when target population is very large Can results in more sampling error Statistical analysis more complicated

D. Cluster sampling

Cluster sampling may be used when it is either impossible or impractical to compile an exhaustive list of the elements that make up the target population. Usually, however, the population elements are already grouped into subpopulations and lists of those subpopulations already exist or can be created.

To conduct a cluster sample, the researcher first selects groups or clusters and then from each cluster, selects the individual subjects either by simple random sampling or systematic ransom sampling or, if the cluster is small enough, the researcher may choose to include the entire cluster in the final sample rather than a subset from it.

For example, let’s say the target population in a study was church members in Region 1. The researcher could, however, create a list of churches in the region 1, choose a sample of churches, and then obtain lists of members from those churches.

Method Best when

Simple random sampling Whole population is available.

Stratified sampling (random within target groups)

There are specific sub-groups to investigate (eg. demographic groupings).

Systematic sampling (every nth person)

When a stream of representative people are available (eg. in the street).

Cluster sampling (all in limited groups) When population groups are separated and access to all is difficult, eg. in many distant cities.

Probability methods This is the best overall group of methods to use as you

can subsequently use the most powerful statistical

analyses on the results.

Non Probability Sampling

a) Quota Sampling This method involves the taking of the desired

number of respondents with the required characteristics proportionate to the population under study.

Sample This is selecting interviewees in proportion to the consumer profile within your target market. A good example of this appears below, where the percentage of buyers for each gender of chocolate reflects the respondent quote

Researcher uses some knowledge of the population to build some representativeneness into sampling plan.

Divides population into different strata and samples from each of them

Usually better than convenience

b) Convenience or Accidental Sampling This sampling technique

involves the conduct of a study wherein respondents are selected based on the convenience of the researcher.

Involves the use of the most convenient and readily available subjects for the sample.

Example: man on on the street interviews; teachers uses students.

Convenience sampling is the most widely used yet weakest form of sampling. There is no way to evaluate all of the biases that may be operating

Two basic principles in random sample:

• Equi probability - equally likely to occur; having equal probability.

• independence

The table of random samples is considered the most systematic technique in getting sample units at random The lottery or fishball technique is another type of random sampling The lottery or fishball technique use either sampling without replacement or with replacement

Snowball sampling

Variations of above, used when subjects are hard to find. One subject recommends another. Even more prone to bias

Purposive Sampling “Judgmental Sampling”

• Respondents are selected deliberately depending on the intentions of the researcher as well as objectives of the study

• Proceeds on the belief that researcher knows enough about the population and its element to handpick the sample.

Quota methods For a particular analysis and valid results, you can determine the number

of people you need to sample.

In particular when you are studying a number of groups and when sub-

groups are small, then you will need equivalent numbers to enable

equivalent analysis and conclusions.

Method Best when

Quota sampling (get only as many

as you need)

You have access to a wide

population, including sub-groups

Proportionate quota sampling (in

proportion to population sub-

groups)

You know the population

distribution across groups, and

when normal sampling may not

give enough in minority groups

Non-proportionate quota sampling

(minimum number from each sub-

group)

There is likely to a wide variation

in the studied characteristic within

minority groups

Selective methods Sometimes your study leads you to target particular groups.

Method Best when

Purposive sampling (based on

intent) You are studying particular groups

Expert sampling (seeking 'experts') You want expert opinion

Snowball sampling (ask for

recommendations)

You seek similar subjects (eg.

young drinkers)

Modal instance sampling (focus on

'typical' people)

When sought 'typical' opinion may

get lost in a wider study, and when

you are able to identify the 'typical'

group

Diversity sampling (deliberately

seeking variation)

You are specifically seeking

differences, eg. to identify sub-

groups or potential conflicts

Convenience methods Good sampling is time-consuming and expensive. Not all

experimenters have the time or funds to use more accurate

methods. There is a price, of course, in the potential limited

validity of results.

Method Best when

Snowball sampling (ask for recommendations)

You are ethically and socially able to ask and seek similar subjects.

Convenience sampling (use who's available)

You cannot proactively seek out subjects.

Judgment sampling (guess a good-enough sample)

You are expert and there is no other choice.

Ethnographic methods When doing field-based observations, it is often impossible to

intrude into the lives of people you are studying. Samples

must thus be surreptitious and may be based more on who is

available and willing to participate in any interviews or studies.

Method Best when

Selective sampling (gut feel) Focus is needed in particular

group, location, subject, etc.

Theoretical sampling (testing a

theory)

Theories are emerging and

focused sampling may help

clarify these.

Convenience sampling (use

who's available)

You cannot proactively seek out

subjects.

Judgment sampling (guess a

good-enough sample)

You are expert and there is no

other choice.

http://changingminds.org/explanations/research/sampling/quota_sampling.htm

Rivera, Jr M and Rivera Roela Victoria Practical Guide to Thesis and Dissertation Katha Publishing Inc. Quezon City, Philippines (2007) Jennifer Villanueva Types of Descriptive Research http://www.slideshare.net/jeanniferbvillanuev a/types-of-descriptive-research (2013)