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Norton university

Research MethodTopic:

Determination of sample size

Facilitated by: Dr. pheak sothea

DEPARTMENT: MDM

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batch : 16Semester : 2session : weekendroom ; e206Academic year : 2009-2010

DATE OF PRESENTATION18/07/2010

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Group Members

• CHEA SOKTA• LY VANNY• ROS VANNARY• UNG RAKSMEY• SOK TENG • RORNG ROTHA• TANG SITHARITH

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Content of PresentationA. Reviewing some basic terminology

B. Population Parameters and Sample Statistics

C. Making Data Usable

D. Sample Distribution, and Sampling Distribution

E. Sample Size

F. Determining Sample Size

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A. Reviewing Some Basic Terminology

• A population is the entire collection of things under consideration.

parameter is a summary measure computed to describe a characteristic of the population

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• A sample is a portion of the population selected for analysis

Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.

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Population versus Sample

•A population is a collection of all possible individuals, objects, or measurements of interest.

•A sample is a portion, or part, of the population of interest

Types of Statistics

• Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.

• Inferential Statistics: A decision, estimate, prediction, or generalization about a population, based on a sample.

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Types of Variables

A. Qualitative or Attribute variable - The characteristic being studied is nonnumeric.

Examples: Gender, religious affiliation, type of automobile owned, state of birth, eye color are examples.

B. Quantitative variable - Information is reported numerically.

Examples: Balance in your checking account, minutes remaining in class, or number of children in a family.

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B. Population Parameters & Sample Statistics

• Population Parameters are summary descriptors (e.g., incidence proportion, mean, variance) of variables of interest in the population.

• Sample Statistics are descriptors of the relevant variables computed from sample data.

Sample Statistics are used as estimators of population parameters. They are the basis of our inferences about the population.

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C. Making Data Usable

1111Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc..

SecondaryData Compilation

Observation

Experimentation

Print or Electronic

Survey

PrimaryData Collection

Making Data Usable

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Collecting the Data

Raw Data

Analyzing and Interpreting

Qualitative Data Quantitative Data

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D. Sample Distribution and Sampling Distribution

The sample distribution is the distribution

resulting from the collection of actual data.

A major characteristic of a sample is that it

contains a finite (countable) number of scores,

the number of scores represented by the letter

N.

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For example, suppose that the following data were collected

32 35 42 33 36 38 37 33 38 36 35 34 37 40 38 36 35 31 37 36 33

36 39 40 33 30 35 37 39 32 39 37 35 36 39 33 31 40 37 34 34 37

These numbers constitute a sample distribution. Using the procedures discussed in on frequency distributions, the following relative frequency polygon can be constructed to picture this data:

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Sampling Distribution

• Note the "-ING" on the end of SAMPLE. It looks and sounds similar to the SAMPLE DISTRIBUTION, but, in reality the concept is much closer to a population model.

• The sampling distribution is a distribution of a sample statistic. It is a model of a distribution of scores, like the population distribution, except that the scores are not raw scores, but statistics.

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• In statistics, a sampling distribution is the distribution of a given statistic based on a random sample of size n. It may be considered as the distribution of the statistic for all possible samples of a given size.

• The sampling distribution depends on the underlying distribution of the population, the statistic being considered, and the sample size used.

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• For example, suppose that a sample of size

sixteen (N=16) is taken from some population. The mean of the sixteen numbers is computed. Next a new sample of sixteen is taken, and the mean is again computed. If this process were repeated an infinite number of times, the distribution of the now infinite number of sample means would be called the sampling distribution of the mean.

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• Every statistic has a sampling distribution. For example, suppose that instead of the mean, medians were computed for each sample. The infinite number of medians would be called the sampling distribution of the median.

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E. Sample Size

What is sample size?- Specific size of the group or groups being studied in your research;- Number of participants planned to be included in your study;- In research terms, a sample is a group of people (individual persons, things), determine using specific criteria to be representative of a large population, who are chosen for observation and/or interviewing.

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1. Define the target population

2. Define the sampling frame

3. Select a sampling technique (s)

4. Determine the sample size

5. Execute the sampling process

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Sampling with replacement

Sampling without replacementA sampling technique in

which an element can be included in the sample

more than once

A sampling technique in which an element cannot

be included in the sample more than once

Probability sampling Non-probability sampling

Sampling technique that do not use chance selection

procedures, rather they rely on the personal judgment of the

researchers

A sampling procedure in which each element of the population has a fixed probabilistic chance of being selected for the sample

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Non-probability Probability

Conveniencesampling

Judgmentalsampling

Quotasampling

Snowballsampling

Simple randomsampling

Systematicsampling

Stratifiedsampling

Clustersampling

Other samplingtechniques

Proportionate Disproportionate

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Non-Probability Sampling

Convenience sample

Purposive sample

Snow-ball sample

That attempts to obtain a sample of convenient element. The selection of sampling units is left primarily to the interviewer The population elements are purposively selected based on the judgment of the researcher

An initial group of respondents is selected randomly. Subsequent respondents are selected based on the referrals or information provided by the initial respondents.

Quota sampleIs a two-stage restricted judgmental sampling. The 1st stage consists of developing control categories or quotas of population elements. In the 2nd stage, sample elements are selected based on convenience or judgment

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Probability Sampling

Simple random sampling

Systematic sampling

Stratified sampling

Cluster sampling

Multi-stage clustersampling

For small population, with possible assigned number

For big population, make a sampling interval with impossible assigned number

Different type of population, making a strata

Complex population Sampling frame is not available, making a cluster

Complex population, Sample selected from stages of cluster

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F. Determine of Sample Size

How to Determine Sample Size-To calculate your sample size you will need certain information;- Depend on the statistical test you plan to use;- Desirable effect size to determine sample size;- Define the alpha level you want to use for the statistical test.

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Determine of Sample Size

Assume that a researcher has set the alpha level a priori at .05,plans to use a seven point scale, has set the level of acceptable error at 3%, and has estimated the standard deviation of the scale as 1.167

Where t = value for selected alpha level of .025 in each tail = 1.96

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Determine of Sample Size

Where s = estimate of standard deviation in the

population = 1.167.

(estimate of variance deviation for 7 point scale

calculated by using 7 [inclusive range of scale]

divided by 6 [number of standard deviations

that include almost all (approximately 98%) of

the possible values in the range]).

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Determine of Sample Size

Where d = acceptable margin of error for mean

being estimated = .21.

(number of points on primary scale * acceptable

margin of error; points on primary scale = 7;

acceptable margin of error = .03 [error

researcher is willing to except]).

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Determine of Sample Size

=(t)2 * (s)2 /(d)2

= (1.96)2* (1.167)2/(7*.03)2

= 118

Therefore, for a population of 1,679, the

required sample size is 118.

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Determine of Sample Size

Sample Size Calculator

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THANK YOU INDEED FOR YOUR ATTETION AND

PARTICIPAITON