Sampling

Sampling

A sample is a small number of

individuals representing a larger

group.

Samples and Populations

 A sample in a research study is a relatively

small number of individuals about whom

information is obtained. The larger group

to whom the information is then

generalized is the population.

Why use samples?

 Although the best data comes from

studying an entire population, samples are

used because they are smaller and less

unwieldy. It can be too time consuming

and expensive to study an entire

population.

Defining the population

Whether a researcher is drawing a sample

or is studying an entire population, the

population needs to be defined. This

helps focus the research.

Target vs. accessible populations

 The target population is the population a

researcher would like to generalize to.

Often this isn’t possible, so the accessible

population is used. For example, a

researcher might want to target all male

elementary teachers in the United States,

but actually collects data from the male

elementary teachers in Hawaii.

Random vs. nonrandom sampling

 Random sampling is completely based on

chance. For example, one might identify

all members of a population, (n=250) write

their names on separate pieces of paper,

and then draw 25 names out of a hat to

determine who is actually to be included in

the study.

Nonrandom sampling

 In a nonrandom sample, members are

selected on the basis of a particular set of

characteristics, rather than a random

chance of being included.

Simple random sample

 In a simple random sample, each and

every member of a population has an

equal and independent chance of being

selected.

Table of random numbers

 A table of random numbers is used to

identify the people to be included in a

sample. These are usually found in

statistics books, or can be generated by

some calculators and computers.

Stratified random sample

 In stratified random sampling, subgroups

within a target population are identified to

be included in proportion to the numbers in

which they exist in the population. For

example, a researcher studying

aggressive behavior in dog breeds found

in Hawaii would want to include a sample

of registered breeds in the proportion they

are found in the state.

Cluster sampling

 In situations where simple random

sampling isn’t possible, as is often the

case in schools, groups or clusters are

identified for inclusion in research. For

example, a researcher might choose to

study all of the students in some specific

classes.

Two stage random sampling

 This technique combines random

sampling with cluster sampling. It allows a

bigger group to be targeted for

generalization.

Systematic sampling with a random

start

 In this procedure, a random number is

generated to identify the first member

selected for a sample, and then every nth

member of the population is selected for

inclusion. For example, the first member

selected in a population of 500 might be #

412, and then every 7th person is chosen:

419, 426, 433, 440, 447, and so on. When

you pass 500, you loop back to the

beginning.

Sampling ratio

 This is the proportion of individuals

selected for a study. For example, you

might select to study ten percent of the

population. The ratio is defined as the

sample size divided by the population size.

Convenience sample

 When it isn’t possible to draw a random or

systematic nonrandom sample, a

researcher might choose to study the

individuals who are available. This is

known as a convenience sample.

Purposive sampling

 A purposive sample is one identified on

the basis of specific characteristics

identified by the researcher. For example,

if a researcher wanted to study all of the

foreign-born teachers in a school district,

he or she would try to identify all of those

individuals and include only them.

External validity

 Since the entire point of sampling is to

generalize the results to a larger

population, researchers need to be sure

their work actually does represent the

population. The extent to which

information can be generalized to a larger

population is known as external validity.

Representative samples

 A representative sample provides the most

accurate portrayal of the population being

studied.

Replication studies

 A replication study follows the format of a

previous study, but uses a new group of

subjects or a new set of conditions or both.

Ecological generalizability

 This term refers to the degree to which a

study can be generalized to a different set

of conditions. For example, researchers

studying rural schools might have difficulty

generalizing their results to urban schools.

Data

 Data is a plural word that refers to the

kinds of information researchers collect.

Data should be followed by a plural verb,

such as “Data are” or “Data were”.

Instrumentation

 The process of preparing to collect data is

called instrumentation. It involves the

selection of the method by which data will

be collected, as well as the procedures

and conditions for collecting them.

Validity

 This term refers to the defensibility of the

inferences a researcher can make from a

study using an instrument.

Reliability

 Reliability refers to consistency of results.

If a study is repeated, will it yield similar

findings? A good example of reliability

might be having three different people

grading students’ essays. Will all three of

them agree on what constitutes an A, B,

C, etc? Or will their scoring vary widely?

If there is a large variety, the grades would

not be reliable.

Objectivity

 This characteristic refers to the absence of

subjective bias on the part of the

researcher. For example, political analyst

with a particular ideological bent might

conduct a poll differently from one who

has no affiliation.

Different types of instruments

 Researcher instruments are used by the

researcher to collect data; a tally sheet or rubric

are examples.

 Subject instruments are completed by the

subject. A survey questionnaire is an example.

 Informant instruments are completed by

knowledgeable participants providing

information in addition to that collected by

researchers and given by subjects.

Selecting instruments

 Instruments may be selected in one of two

ways. Either a researcher locates one that

has been developed by another person, or

he/she designs a new one. The

advantage of selecting existing ones is

that they have often been field tested for

reliability and validity.

Collecting data

 Data may be collected in a variety of ways.

Respondents might give written

responses, or they might perform a task.

Doing a miscue analysis on a student is an

example of a performance analysis.

Rating scales

 The difference between observation and rating

is that when a researcher rates a subject, he or

she is making a judgment of some type. On the

other hand, when a researcher makes an

observation, he or she is merely recording

behavior and not judging it. For example, a

rating might be that a girl made 3 baskets in 20

attempts, thus scored 2 on a scale of poor to

good on free throws, while an observation would

just note the number of baskets/attempts.

Researcher instruments

 Interview schedules

 Tally sheets

 Performance checklists

 Anecdotal records

 Time-and-motion logs

Subject instruments

 Questionnaires

 Self-checklists

 Attitude scales

 Personality inventories

 Achievement tests

 Aptitude tests

 Performance tests

 Projective devices

 Sociometric devices

Scores

 Raw scores are the initial scores obtained

on a test. The number right out of a total

number of questions is an example.



 Derived scores have been scaled to show

their relative position with respect to other

raw scores.

Derived scores

 Percentile ranks

 Age/grade equivalence

 Standard scores

Norm-referenced vs. Criterion

referenced

 A norm-referenced test is developed to

provide scores that replicate a normal

curve among the population tested. Thus,

among a population taking the test, half of

the people should score above average

and half below.

 A criterion referenced test is based on a

goal and an identified percentage is

targeted to reach that goal.

Measurement scales

 A nominal scale, the simplest scale, identifies

groups by a number, e.g. “1” for male and “2” for

female.

 An ordinal scale provides an rating from most to

least. A Likert scale is an ordinal scale.

 An interval scale is an ordinal scale that has the

addition of equal distances between the points.

IQ is measured using an interval scale.

 A ratio scale is an interval with a true zero and is

rarely used in educational measurement.