Session basic concepts_in_sampling_and_sampling_techniques

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


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


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


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


Session 3.6

TWO TYPES OF SAMPLES

1. Probability sample

2. Non-probability sample


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


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


Session 3.9

Samples are obtained unevenly, selected purposively or are taken as volunteers.

The probabilities of selection are unknown.

NON-PROBABILITY SAMPLES


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


Session 3.11

BASIC SAMPLING TECHNIQUES

Simple Random Sampling

Stratified Random Sampling

Systematic Random Sampling

Cluster Sampling

Slide No. 3.20


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


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.


Session 3.14

ILLUSTRATION

C

D

B

A

B

Slide No. 3.13


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)


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


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


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.


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


Session 3.20Population

Systematic Sample

ILLUSTRATION


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


Session 3.22

ILLUSTRATIONPopulation

Cluster Sample

Slide No. 3.18


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


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


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


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


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


End of Presentation

Session 3.30

Session basic concepts_in_sampling_and_sampling_techniques

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