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CHAPTER

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Sampling

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Sampling

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What Is a Sample?

One of the mos t impo r tant steps in the research p rocess is

to select the sample of individu als who w il l part ic ipate (be

observed or quest ioned) as a part of the stud y. Sampl ing

refers to the proc ess of select ing these individuals.

A sample in a research study refers to any group on which

in format ion is obtained. The larger group to wh ich one

hopes to apply the resu lts is cal led the popu lat ion.

Samp le (statist ics ) Population (parameters)

X

s

m

s

Fraenkel p.96

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Samples and Populations

When i t is p oss ib le, researchers would p refer to

stud y the ent i re populat ion in wh ich they areinterested. Usual ly, however, this is dif f icul t to do .

Most popu lat ion s o f interest are large, diverse, and

scattered over a large geog raphic area. Find ing , let

alone con tact ing, al l members can be t ime-

consum ing and expensive. For that reason, of

necess ity, researchers o ften select a sample to

study.

A populat ion can be any size and it w i l l have at least

one (and sometimes several) character ist ic (s) thatsets it of f from any other popu lat ion. Not ice that a

popu lat ion is alwaysallof the ind iv iduals who

possess a certain character ist ic (or set of

ch aracterist ic s). Fraenkel p. 97

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Samples and Populations (contd)

In educational research , the popu lat ion o f interest is

usual ly a grou p o f persons (students, teachers, or

other indiv iduals) who possess certain

character ist ic s. In some cases, however, the

popu lat ion may be def ined as a grou p o f

classrooms, schools, or even faci l i ties.

Target populat ion the actual popu lat ion to which a

researcher would l ik e to general ize rarely available

ideal choice

Accessib le populat ion the populat ion to wh ich a

researcher isableto general izerealist ic cho ice

Fraenkel p. 97

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Random versus Nonrandom Sampling

Random sampl ing i ts intent isto select arepresentat ive

sample from the popu lat ion

Fraenkel p. 98

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Representative vs. Non-representative Samples

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Random Sampling Methods

Simple Random Sample asample in which each and

every member of the

popu lat ion has an equal and

independent chance of being

selected

Fraenkel p. 99

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Part of a Table of Random Numbers (Table 6.1)

011723 223456 222167 032762 062281 565451912334 379156 233989 109238 934128 987678

086401 016265 411148 251287 602345 659080

059397 022334 080675 454555 011563 237873

666278 106590 879809 899030 909876 198905

051965 004571 036900 037700 500098 046660063045 786326 098000 510379 024358 145678

560132 345678 356789 033460 050521 342021

727009 344870 889567 324588 400567 989657

000037 121191 258700 088909 015460 223350

667899 234345 076567 090076 345121 121348042397 045645 030032 657112 675897 079326

987650 568799 070070 143188 198789 097451

091126 021557 102322 209312 909036 342045

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Random Sampling Methods

Strat i f ied Random Sample a pro cessin which cer tain subgroups, orstrata,

are selected fo r the sample in the same

propo rt ion as they exist in the

populat ion

This requires the researcher to know

some informat ion about the peop le in

the populat ion

Fraenkel p. 100

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Selecting a Stratified Sample (Figure 6.2)

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Random Sampling Methods (contd)

Clus ter Random Sampl ing theselect ion of g roups , or c lus ters, of

subjects rather than ind iv iduals

Two-Stage Random Sampl ing acombinat ion of c luster random

samp l ing w i th indiv idual random

sampl ing

Fraenkel p. 100-101

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Random Sampling Methods (Figure 6.3)

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Nonrandom Sampling Methods

Systemat ic Sampl ing every nth indiv idu al in the

popu lat ion l ist is selected for inclus ion in the sample

If the ini t ial ind ividual is selected random ly then th is

method is technica lly known as systemat ic sampl ing

with a random star t .

The sampling interval is the distance in the l ist

between each o f the ind ividu als selected. It is

determ ined by d iv id ing the population size by the

desired samp le size.

The samp l ing rat io is the proport ion o f thepopu lat ion that is selected for the sample. It is

determ ined by d iv id ing the sample size by the

popu lat ion size.Fraenkel p. 102-103

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Nonrandom Sampling Methods (contd)

Convenience Sampl ing a group of ind iv iduals who

(convenient ly ) are avai lable for study. In general ,

these samples canno t be cons idered representat ive

of any popu lat ion and shou ld be avoided i f at al l

possib le. If th is is the on ly type of sample the

researcher can use, then they should be extremelycareful to include demographic inform at ion and

other character ist ics o f the samp le that was studied.

The stud y shou ld also be repl icated w ith a num ber of

sim i lar samp les to decrease the likelihood that the

resu l ts ob tained were simp ly a one-t ime occu rrence.

Fraenkel p. 103

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Convenience Sampling (Figure 6.4)

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Nonrandom Sampling Methods (contd)

Purposive Sampl ing a samp l ing m ethod in

which the researcher selects the sample

based on prev ious know ledge of a

popu lat ion. This is di f ferent from

convenience sampl ing in that researchers dono t simply study whoever is avai lable, bu t

use their judgment to select a sample that

they bel ieve, based on p rior info rmation , w i l l

pro vide the data they need.

Fraenkel p. 103-105

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Nonrandom Sampling Method (Figure 6.5)

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Sample Size

A samp le sho uld b e as large as the researcher can

ob tain w ith a reasonable expenditure of t ime andenergy.

Type of Study Minimum Sample SizeDescriptive 100

Exper imental or

Causal/Comparative

30 in each grou p

Correlational 50

Fraenkel p.106-109

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External Validity: Generalizing from a Sample

Bo th the nature of the samp le and the env ironmental

condi t ions the sett ing - with in wh ich a stud y takes

place must be considered in th ink ing about

generalizabi l i ty. The extent to wh ich the results of a

stud y can be general ized determ ines theexternal

val idi tyof the study.

Popu lat ion generalizibi l i tyrefers to th e degree to

wh ich a sample represents the popu lat ion of

interest . If the resul ts o f a stud y only apply to the

grou p being s tudied, and i f that group is fai r ly smallor is narrowly def ined, the usefulness o f any

f inding s is ser ious ly l imi ted. This is wh y try ing to

f ind arepresentat ive sampleis so impor tant .

Fraenkel p. 109

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External Validity: Generalizing from a Sample (contd)

One aspect o f general izabi l i ty th at is oft en

overlooked in methods or treatment studies isthat wh ich pertains to the teachers, counselors,

adminis trators, or others who admin ister the var ious

treatments. A study that random ly selects students

bu t no t teachers is only enti t led to general ize theoutcomes to the populat ion of s tudents - i f taugh t by

the same teachers. To general ize to other teachers,

the samp le of teachers must also be selected

random ly and must be suff ic ient ly large.

The best samp l ing plan is of no value if informat ion

is m issing on a sizable port ion of the in i t ial sample.

Fraenkel p. 110

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External Validity: Generalizing from a Sample (contd)

Do researchers always want to general ize? No, no t i f

the resu lts o f an invest igat ion are of interest on ly as

appl ied to a part icular group o f peop le at a part icu lar

t ime, and where all of the members o f the group are

inc luded in the study.

Random sampl ing is somet imes not feasib le wh ich

makes much of the research in educat ion subject to

cr i t ic ism.

Repl icat ion of a stu dy can g ive a researcher more

conf idence about general izing th eir f inding s despi te

the lack of a random samp le.

Fraenkel p. 109

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Ecological Generalizability

Ecological general izabi l i ty refers to the degree to

wh ich resul ts of a study can be extended to other

sett ings or condi t ions . Researchers must make

clear the nature of the environmental condi t ions

the sett ing - under wh ich a stud y takes place.

Only when outcom es have been shown to be simi lar

throu gh repl icat ion acros s speci f ic environmental

condi t ion s can we generalize acros s these

cond i t ions.

Fraenkel p. 111

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Population as Opposed to Ecological Generalizing (Figure 6.6)