Note: The Slides were taken from Elementary Statistics: A Handbook of Slide Presentation prepared by Z.V.J. Albacea, C.E. Reano, R.V. Collado, L.N. Comia and N.A. Tandang in 2005 for the Institute of Statistics, CAS, UP Los Banos
Training on Teaching Basic Statistics for Tertiary Level Teachers
Summer 2008
BASIC CONCEPTS IN SAMPLING AND
SAMPLING TECHNIQUES
TEACHING BASIC STATISTICS ….
Session 3.2
Sampling Process
Sample
Data
Universe
Inferences/Generalization(Subject to Uncertainty)
INFERENTIAL STATISTICS
TEACHING BASIC STATISTICS ….
Session 3.3
Basic Terms
UNIVERSE – the set of all entities under study
VARIABLE – attribute of interest observable on each entity in the universe
POPULATION – the set of all possible values of the variable
SAMPLE – subset of the universe or the population
TEACHING BASIC STATISTICS ….
Session 3.4
SAMPLING – the process of selecting a sample
PARAMETER – descriptive measure of the population
STATISTIC – descriptive measure of the sample
INFERENTIAL STATISTICS – concerned with making generalizations about parameters using statistics
Basic Terms
TEACHING BASIC STATISTICS ….
Session 3.5
WHY DO WE USE SAMPLES?
1. Reduce Cost
2. Greater Speed or Timeliness
3. Greater Efficiency and Accuracy
4. Greater Scope
5. Convenience
6. Necessity
7. Ethical Considerations
TEACHING BASIC STATISTICS ….
Session 3.6
TWO TYPES OF SAMPLES
1. Probability sample
2. Non-probability sample
TEACHING BASIC STATISTICS ….
Session 3.7
Samples are obtained using some objective chance mechanism, thus involving randomization.
They require the use of a complete listing of the elements of the universe called the sampling frame. (Session_5_DEFINING A SAMPLING FRAME.pptx)
PROBABILITY SAMPLES
TEACHING BASIC STATISTICS ….
Session 3.8
The probabilities of selection are known.
They are generally referred to as random samples.
They allow drawing of valid generalizations about the universe/population.
PROBABILITY SAMPLES
TEACHING BASIC STATISTICS ….
Session 3.9
Samples are obtained unevenly, selected purposively or are taken as volunteers.
The probabilities of selection are unknown.
NON-PROBABILITY SAMPLES
TEACHING BASIC STATISTICS ….
Session 3.10
They should not be used for statistical inference.
They result from the use of judgment sampling, accidental sampling, purposively sampling, and the like.
NON-PROBABILITY SAMPLES
TEACHING BASIC STATISTICS ….
Session 3.11
BASIC SAMPLING TECHNIQUES
Simple Random Sampling
Stratified Random Sampling
Systematic Random Sampling
Cluster Sampling
Slide No. 3.20
TEACHING BASIC STATISTICS ….
Session 3.12
SIMPLE RANDOM SAMPLING
Most basic method of drawing a probability sample
Assigns equal probabilities of selection to each possible sample
Results to a simple random sample
TEACHING BASIC STATISTICS ….
Session 3.13
STRATIFIED RANDOM SAMPLING
The universe is divided into L mutually exclusive sub-universes called strata.
Independent simple random samples are obtained from each stratum.
TEACHING BASIC STATISTICS ….
Session 3.14
ILLUSTRATION
C
D
B
A
B
Slide No. 3.13
TEACHING BASIC STATISTICS ….
Session 3.15
Steps in Stratified Random Sampling
1. Identify and define the population (sampling frame)
2. Determine the desired sample size3. Identify the variable and subgroups (strata) for
which you want to guarantee appropriate representation (either proportional or equal)
4. Classify all members of the population as members of one of the identified subgroups
5. Randomly select the individuals from each subgroup (using the table of random numbers or lottery)
TEACHING BASIC STATISTICS ….
Formula: with
= sample size of subgroup kn = Total sample size (determined using the specified methods) = Population size of subgroup kN = Total population size
Session 3.16
1 1
L L
h hh h
N N n n
Computation of Sample Size in SRS
TEACHING BASIC STATISTICS ….
Session 3.17
Example: The researcher would like to conduct a study on administrators’ performance in State Colleges and Universities in Caraga from which the distribution of population is given in the table. Suppose the researcher would like to get 80 samples.
State University/ College
Number of Administrators
State University/ College
Number of Administrators
SUC1 7 SUC5 36
SUC2 9 SUC6 29
SUC3 14 SUC7 15
SUC4 45 SUC8 25
Computation of Sample Size in SRS
TEACHING BASIC STATISTICS ….
Session 3.18
Advantages of Stratification
1. It gives a better cross-section of the population.
2. It simplifies the administration of the survey/data gathering.
3. The nature of the population dictates some inherent stratification.
4. It allows one to draw inferences for various subdivisions of the population.
5. Generally, it increases the precision of the estimates.
TEACHING BASIC STATISTICS ….
Session 3.19
SYSTEMATIC SAMPLING
Adopts a skipping pattern in the selection of sample units
Gives a better cross-section if the listing is linear in trend but has high risk of bias if there is periodicity in the listing of units in the sampling frame
Allows the simultaneous listing and selection of samples in one operation
TEACHING BASIC STATISTICS ….
Session 3.20Population
Systematic Sample
ILLUSTRATION
TEACHING BASIC STATISTICS ….
Session 3.21
CLUSTER SAMPLING
It considers a universe divided into N mutually exclusive sub-groups called clusters.
A random sample of n clusters is selected and their elements are completely enumerated.
It has simpler frame requirements.
It is administratively convenient to implement.
Slide No. 3.19
Slide No. 3.11
TEACHING BASIC STATISTICS ….
Session 3.22
ILLUSTRATIONPopulation
Cluster Sample
Slide No. 3.18
TEACHING BASIC STATISTICS ….
Steps in Cluster Sampling
Identify and define the population (sampling frame)
Determine the desired sample size
Identify and determine a logical cluster
List all clusters that comprise the population
Estimate the average population per cluster
Determine the number of clusters needed by dividing the sample size by the estimated average population per cluster
Randomly select the needed number of clusters
All members in the selected cluster are included as sample units
Session 3.23
TEACHING BASIC STATISTICS ….
Example of Cluster Sampling
Let us see how the superintendent would get a sample of teachers if cluster sampling were used.
1. The population is 5000 teachers in the superintendent’s school system.
2. The desired sample size is 500.
3. A logical cluster is a school.
4. There are 100 schools in the list.
5. Although the schools vary in the number of teachers, there is an average number of teachers per school.
Session 3.24
TEACHING BASIC STATISTICS ….
Example of Cluster Sampling
6. Suppose the average number of teachers per school is 50. So the number of clusters (schools) needed is:
7. There are 10 schools in the sample, which will be selected randomly from the 100 schools.
8. All teachers in each of the 10 schools are in the sample (if the desired sample size is not reached, add one cluster from the population, which will be chosen randomly from the 90 schools left).
Session 3.25
TEACHING BASIC STATISTICS ….
Session 3.26
SIMPLE TWO-STAGE SAMPLING
In the first stage, the units are grouped into N sub-groups, called primary sampling units (psu’s) and a simple random sample of n psu’s are selected.
Illustration:
A PRIMARY SAMPLING UNIT
TEACHING BASIC STATISTICS ….
Session 3.27
SIMPLE TWO-STAGE SAMPLING
In the second stage, from each of the n psu’s selected with Mi elements, simple random sample of mi units, called secondary sampling units ssu’s, will be obtained.
Illustration:
A SECONDARY SAMPLING UNIT
SAMPLE
Accidental or Incidental SamplingGetting a subject of study that is
only available during the period Quota Sampling
Getting a sample of subject of study using through quota system
Ex. All PolSci students of the different HEI’s in Caraga
Non-Probability Sampling Techniques
Purposive SamplingThe researcher simply picks out the
subjects that are representatives of the population depending on the purpose of the study
Non-Probability Sampling Techniques
TEACHING BASIC STATISTICS ….
End of Presentation
Session 3.30