CHAPTER 5EDUCATIONAL RESEARCH

SELECTING A SAMPLE

LEARNING OUTCOMES:

To Define sampling in both:

QUALITATIVE RESEARCH &QUANTITATIVE RESEARCH

KEY TERMS: SAMPLE, POPULATION, QUANTITATIVE, QUALITATIVE,

SAMPLEA sample is a selected group (that when properly selected) provides information the same as the population.

The representation of the information from the sample group is intended to be the same as the population.

POPULATIONThe entire group of interest which the

researcher would like to get their study results

from. A population may be of any size, and usually

begins with the word “ALL”

Every member of the population has an equal and independent chance of

selection for the sample.

The researcher has no control over the selection.

PROBABILITY IS EQUALIZED

ERROR & BIAS ARE MINIMALIZED

Generally, it is not possible to conduct an experiment on all the units of a population. An entire population is usually not available.

To save the time and money of the researcher, a portion of the population is used.

The results collected from a study on a sample are generalizable to the entire population.

Why do a sample, and not a whole population?

RANDOM SAMPLING STRATEGIES

SIMPLE STRATIFIED

CLUSTERSYSTEMATIC

SIMPLE RANDOM SAMPLINGEveryone in the population has an equal chance

of selection for the sample.

The researcher has no control over the selection.

The selection of an individual does not effect the selection of any other individual (independent)

• You should have at least 30 samples.• The sample size should be less than 10% of the

entire sample.

Random Numbers

The sample size formula for the infinite population is given as :

The number of observation in a given sample population is known as Sample size. The sample size plays an important part in any study which helps us to find the difference between the population from the given sample. Sample size can be smaller and larger, but the larger sample size gives us the more accurate results and in the lower case it is denoted by 'n' and the sample size in upper case is denoted by 'N' .

Sample Size Problems

Back to Top Below are few problems based on Sample size:

Solved Examples

Question 1: Find the Sample size for finite and infinite population, when percentage of 4300 population is 5, confidence level 95 and confidence interval is 0.04? Solution: From the given data: Z = 3.8416 ( from the z table, we the value of confidence level, that is 1.96) by applying given data in the formula

SS = Z2p(1−p)C2

SS = (1.96)20.5(1−0.5)0.042 = 600.25

SS=600 (after rounding to nearest whole numbers) Now lets calculate the sample size for the finite population.

New SS = SS1+(SS−1Pop)

New SS = 6001+(600−14300) New SS = 527 Question 2: Find the Sample size for finite and infinite population using the given data below, when percentage of 7800 population is 5, confidence level 90 and confidence interval is 0.04? Solution:

From the given data: Z= 2.7060( from the z table, we the value of confidence level, that is 1.645) by applying given data in the formula SS = Z2p(1−p)C2

SS = (1.645)20.5(1−0.5)0.042 = 422.812 SS = 423 (after rounding to nearest whole numbers) Now lets calculate the sample size for the finite population. New SS = SS1+(SS−1Pop)

New SS = 4231+(423−17800) = 401.28 New SS = 401 (after rounding to nearest whole numbers)

THE SAMPLE SIZE FORMULA FOR THE FINITE POPULATION IS GIVEN AS :

Here,SS = Sample size.Z = Given z value

p = Percentage of populationC = Confidence level

Pop = Population 

STRATIFIED RANDOM SAMPLING

Stratified RS is a way to guarantee representation of relevant subgroups within

a sample.Population are subdivided into subgroups

(strata) on a certain variable. From each group proportional or equal

numbers of subjects are selected randomly to form a sample

STEPS IN STRATIFIED RS

1. Identify and define the population.2. Determine the desired sample size.3. Identify the variables and subgroups

(strata).4. Classify all members of the population

into subgroups.5. Randomly select an equal or

proportional number of individuals from each subgroup (using table of random

numbers).

CLUSTER SAMPLING intact groups (clusters), not GROUPS are

randomly selected.

All the individuals of the selected clusters are included.

May be the only feasible method of selecting a sample when the researcher is unable to obtain a list of all members of an intended

population.

CLUSTER: STEPS1.Identify and define the population.2.Determine the desired sample size.3.Identify and define a logical cluster.

4.List all clusters.5.Estimate the average number of population

members per cluster.6.Divide the sample size by the estimated size of cluster to determine the number of

clusters.7.Randomly select the needed number of

clusters.8.Include all population members in each

selected cluster.

SYSTEMATIC SAMPLINGSelecting every Kth individual from the list

of the population.K = Number of Individuals on the

list/Number of individuals desired for the sample

All members don’t have an independent chance of selection.

It is considered random sampling if the list of the population is randomly ordered.

Process may cause certain subgroups of the population to be excluded from the

sample* NOT USED VERY OFTEN

STEPS: SYSTEMATIC SAMPLING

1. Identify and define the population.2.Determine the desired sample size.

3.Obtain a list of the population.4.Determine K by dividing the size of the population by the desired sample size.5.Start at some random place in the

population list.6.Take ever K th individual on the list.

7.If the end of the list is reached before the desired sample is reached, go back to the top

of the list.

NONRANDOM SAMPLING STRATEGIES

CONVENIENCE SAMPLINGPURPOSIVE SAMPLING

QUOTA SAMPLING

AKA: non-probability sampling.

Independent or biased free selection of the individuals will not happen.

Useful when the population can’t be described.

CONVENIENCE SAMPLING

AKA accidental Sampling or haphazard sampling.

Sample includes available individuals; “whoever is available”

Volunteers Pre-existing groups

Difficult to describe the population from which the sample was drawn and to whom results can be generalized

PURPOSIVE SAMPLINGAKA judgment sampling.

Selection based on the researcher’s experience and knowledge of the individuals being sampled.

Researcher select the criteria to select the individuals.

Main weakness is the imperfections in the researcher’s criteria.

QUOTA SAMPLING

Process based on required, exact numbers, or quotas of individuals or groups with varying characteristics.

Mostly used in wide-scale survey research when listing all members of the population is not possible.

Data obtained from easily accessible individuals.

People who are less accessible are underrepresented due to their own unavailability.

QUALITATIVE SAMPLINGINTENSITY SAMPLING

HOMOGENOUS SAMPLINGCRITERION SAMPLINGSNOWBALL SAMPLINGRANDOM PURPOSIVE

SAMPLING

QUALITATIVE SAMPLING

In qualitative research the sampling is mainly purposive. Selecting process designed to select a small number of individuals that will be good key informants. “QUALITY instead of Quantity”

The researcher first identifies the potential participants of the research.

Participants are selected on some criteria according to their knowledge, experience, characteristics and willingness

Intensity Sampling- good and poor, experienced and inexperiencedHomogenous Sampling- similar

subjects in experience, perspective & outlook

Criterion Sampling- according to some specific criterion

Snowball Sampling- first select small number, then get additional people

from them. Random Purposive Sampling- Select

more participants than needed.

Intact groups are randomly selected:

a. Simple Samplingb. stratified Samplingc. cluster samplingd. systematic

Intact groups are randomly selected:

a. Simple Samplingb. stratified Samplingc. cluster sampling *d. systematic

Everyone has an equal chance of being selected:

a. Simple Samplingb. stratified Samplingc. cluster samplingd. systematic

Everyone has an equal chance of being selected:

a. Simple Sampling *b. stratified Samplingc. cluster samplingd. systematic

Similar subjects in experience, perspective, & outlook:

a. Intensityb. Homogenousc. Criterion Sampling d. Snowballe. Random Purpose

Similar subjects in experience, perspective, & outlook:

a. Intensity b. Homogenous *

c. Criterion Sampling

d. Snowball e. Random Purpose

Select more participants than needed:

a. Intensity b. Homogenous c. Criterion

Sampling d. Snowball *

e. Random Purpose

Good & Poor, Experienced & Inexperienced:

a. Intensity b. Homogenous

c. Criterion Sampling d. Snowball

e. Random Purpose

Good & Poor, Experienced & Inexperienced:

a. Intensity * b. Homogenous c. Criterion

Sampling d. Snowball

e. Random Purpose