This document discusses sampling and sample size determination. It defines key terms like population, population element, census, and provides reasons for using a sample such as cost, speed, accuracy, and avoiding destruction of test units. It outlines the steps in sampling which include defining the target population, selecting a sampling frame, choosing between probability or non-probability sampling, determining the sampling unit, and addressing sources of error. It then discusses different probability and non-probability sampling methods like simple random sampling, systematic sampling, stratified sampling, cluster sampling, convenience sampling, judgment sampling, quota sampling, and snowball sampling. Factors to consider when determining sample size are discussed such as population variance or heterogeneity, acceptable error or confidence interval, confidence level.

1. SSaammpplliinngg aanndd SSaammppllee
SSiizzee DDeetteerrmmiinnaattiioonn

2. TTeerrmmss
 SSaammppllee
 PPooppuullaattiioonn
 PPooppuullaattiioonn eelleemmeenntt
 CCeennssuuss

3. WWhhyy uussee aa ssaammppllee??
 CCoosstt
 SSppeeeedd
 AAccccuurraaccyy
 DDeessttrruuccttiioonn ooff tteesstt uunniittss

4. SStteeppss
 DDeeffiinniittiioonn ooff ttaarrggeett ppooppuullaattiioonn
 SSeelleeccttiioonn ooff aa ssaammpplliinngg ffrraammee ((lliisstt))
 PPrroobbaabbiilliittyy oorr NNoonnpprroobbaabbiilliittyy ssaammpplliinngg
 SSaammpplliinngg UUnniitt
 EErrrroorr
–– RRaannddoomm ssaammpplliinngg eerrrroorr ((cchhaannccee
fflluuccttuuaattiioonnss))
– NNoonnssaammpplliinngg eerrrroorr ((ddeessiiggnn eerrrroorrss))

5. TTaarrggeett PPooppuullaattiioonn
((sstteepp 11))
 WWhhoo hhaass tthhee iinnffoorrmmaattiioonn//ddaattaa yyoouu
nneeeedd??
 HHooww ddoo yyoouu ddeeffiinnee yyoouurr ttaarrggeett
ppooppuullaattiioonn??
-- GGeeooggrraapphhyy
-- DDeemmooggrraapphhiiccss
-- UUssee
-- AAwwaarreenneessss

6. Operational DDeeffiinniittiioonn
 AA ddeeffiinniittiioonn tthhaatt ggiivveess mmeeaanniinngg ttoo aa
ccoonncceepptt bbyy ssppeecciiffyyiinngg tthhee aaccttiivviittiieess
nneecceessssaarryy ttoo mmeeaassuurree iitt..
- EEgg.. SSttuuddeenntt,, eemmppllooyyeeee,, uusseerr,, aarreeaa,, mmaajjoorr
nneewwss ppaappeerr..
WWhhaatt vvaarriiaabblleess nneeeedd ffuurrtthheerr ddeeffiinniittiioonn??
((IItteemmss ppeerr ccoonnssttrruucctt))

7. SSaammpplliinngg FFrraammee
((sstteepp 2))
 LLiisstt ooff eelleemmeennttss
 SSaammpplliinngg FFrraammee eerrrroorr
– EErrrroorr tthhaatt ooccccuurrss wwhheenn cceerrttaaiinn ssaammppllee
eelleemmeennttss aarree nnoott lliisstteedd oorr aavvaaiillaabbllee aanndd
aarree nnoott rreepprreesseenntteedd iinn tthhee ssaammpplliinngg ffrraammee

8. PPrroobbaabbiilliittyy oorr
NNoonnpprroobbaabbiilliittyy ((sstteepp 33))
PPrroobbaabbiilliittyy SSaammppllee::
– AA ssaammpplliinngg tteecchhnniiqquuee iinn wwhhiicchh eevveerryy
mmeemmbbeerr ooff tthhee ppooppuullaattiioonn wwiillll hhaavvee aa
kknnoowwnn,, nnoonnzzeerroo pprroobbaabbiilliittyy ooff bbeeiinngg
sseelleecctteedd

9.  NNoonn--PPrroobbaabbiilliittyy SSaammppllee::
– UUnniittss ooff tthhee ssaammppllee aarree cchhoosseenn oonn tthhee
bbaassiiss ooff ppeerrssoonnaall jjuuddggmmeenntt oorr
ccoonnvveenniieennccee
– TThheerree aarree NNOO ssttaattiissttiiccaall tteecchhnniiqquueess ffoorr
mmeeaassuurriinngg rraannddoomm ssaammpplliinngg eerrrroorr iinn aa
nnoonn--pprroobbaabbiilliittyy ssaammppllee.. TThheerreeffoorree,,
ggeenneerraalliizzaabbiilliittyy iiss nneevveerr ssttaattiissttiiccaallllyy
aapppprroopprriiaattee..

10. Classification of Sampling
Methods
Sampling
Methods
Probability
Samples
Systematic Stratified
Simple
Cluster Random
Non-probability
Convenience Snowball
Judgment Quota

11. Probability Sampling
Methods
 Simple Random Sampling
 the purest form of probability sampling.
 Assures each element in the population
has an equal chance of being included in
the sample
 Random number generators
Probability of Selection =
Sample Size
Population Size

12.  Advantages
minimal knowledge of population needed
 External validity high; internal validity
high; statistical estimation of error
 Easy to analyze data
 Disadvantages
 High cost; low frequency of use
 Requires sampling frame
 Does not use researchers’ expertise
 Larger risk of random error than stratified

13.  Systematic Sampling
 An initial starting point is selected by a
random process, and then every nth
number on the list is selected
 n=sampling interval
The number of population elements
between the units selected for the
sample
Error: periodicity- the original list has a
systematic pattern
?? Is the list of elements randomized??

14.  Advantages
 Moderate cost; moderate usage
 External validity high; internal validity
high; statistical estimation of error
 Simple to draw sample; easy to verify
 Disadvantages
 Periodic ordering
 Requires sampling frame

15.  Stratified Sampling
 Sub-samples are randomly drawn from
samples within different strata that are
more or less equal on some characteristic
 Why?
Can reduce random error
More accurately reflect the
population by more proportional
representation

16.  Advantages
minimal knowledge of population needed
 External validity high; internal validity
high; statistical estimation of error
 Easy to analyze data
 Disadvantages
 High cost; low frequency of use
 Requires sampling frame
 Does not use researchers’ expertise
 Larger risk of random error than stratified

17.  Systematic Sampling
 An initial starting point is selected by a
random process, and then every nth
number on the list is selected
 n=sampling interval
The number of population elements
between the units selected for the
sample
Error: periodicity- the original list has a
systematic pattern
?? Is the list of elements randomized??

18.  Advantages
 Moderate cost; moderate usage
 External validity high; internal validity
high; statistical estimation of error
 Simple to draw sample; easy to verify
 Disadvantages
 Periodic ordering
 Requires sampling frame

19.  Stratified Sampling
 Sub-samples are randomly drawn from
samples within different strata that are
more or less equal on some characteristic
 Why?
Can reduce random error
More accurately reflect the
population by more proportional
representation

20.  How?
1.Identify variable(s) as an efficient
basis for stratification. Must be known
to be related to dependent variable.
Usually a categorical variable
2.Complete list of population elements
must be obtained
3.Use randomization to take a simple
random sample from each stratum

21.  Types of Stratified Samples
Proportional Stratified Sample:
 The number of sampling units drawn
from each stratum is in proportion to
the relative population size of that
stratum
Disproportional Stratified Sample:
 The number of sampling units drawn
from each stratum is allocated
according to analytical considerations
e.g. as variability increases sample
size of stratum should increase

22.  Types of Stratified Samples…
Optimal allocation stratified sample:
 The number of sampling units drawn from
each stratum is determined on the basis of
both size and variation.
 Calculated statistically

23.  Advantages
 Assures representation of all groups in
sample population needed
 Characteristics of each stratum can be
estimated and comparisons made
 Reduces variability from systematic
 Disadvantages
 Requires accurate information on
proportions of each stratum
 Stratified lists costly to prepare

24.  Cluster Sampling
 The primary sampling unit is not the
individual element, but a large cluster of
elements. Either the cluster is randomly
selected or the elements within are
randomly selected
 Why? Frequently used when no list of
population available or because of cost
Ask: is the cluster as heterogeneous as
the population? Can we assume it is
representative?

25.  Cluster Sampling example
 You are asked to create a sample of all
Management students who are working in
Lethbridge during the summer term
 There is no such list available
 Using stratified sampling, compile a list of
businesses in Lethbridge to identify
clusters
 Individual workers within these clusters
are selected to take part in study

26.  Types of Cluster Samples
Area sample:
 Primary sampling unit is a
geographical area
Multistage area sample:
 Involves a combination of two or more
types of probability sampling
techniques. Typically, progressively
smaller geographical areas are
randomly selected in a series of steps

27.  Advantages
 Low cost/high frequency of use
 Requires list of all clusters, but only of
individuals within chosen clusters
 Can estimate characteristics of both cluster and
population
 For multistage, has strengths of used methods
 Disadvantages
 Larger error for comparable size than other
probability methods
 Multistage very expensive and validity depends
on other methods used

28. Classification of Sampling
Methods
Sampling
Methods
Probability
Samples
Systematic Stratified
Simple
Cluster Random
Non-probability
Convenience Snowball
Judgment Quota

29. Non-Probability Sampling
Methods
 Convenience Sample
 The sampling procedure used to obtain
those units or people most conveniently
available
 Why: speed and cost
 External validity?
 Internal validity
 Is it ever justified?

30.  Advantages
 Very low cost
 Extensively used/understood
 No need for list of population elements
 Disadvantages
 Variability and bias cannot be measured
or controlled
 Projecting data beyond sample not
justified.

31.  Judgment or Purposive Sample
 The sampling procedure in which an
experienced research selects the sample
based on some appropriate characteristic
of sample members… to serve a purpose

32.  Advantages
 Moderate cost
 Commonly used/understood
 Sample will meet a specific objective
 Disadvantages
 Bias!
 Projecting data beyond sample not
justified.

33.  Quota Sample
 The sampling procedure that ensure that
a certain characteristic of a population
sample will be represented to the exact
extent that the investigator desires

34.  Advantages
moderate cost
 Very extensively used/understood
 No need for list of population elements
 Introduces some elements of
stratification
 Disadvantages
 Variability and bias cannot be measured
or controlled (classification of subjects0
 Projecting data beyond sample not
justified.

35.  Snowball sampling
 The sampling procedure in which the
initial respondents are chosen by
probability or non-probability methods,
and then additional respondents are
obtained by information provided by the
initial respondents

36.  Advantages
 low cost
 Useful in specific circumstances
 Useful for locating rare populations
 Disadvantages
 Bias because sampling units not
independent
 Projecting data beyond sample not
justified.

37. DDeetteerrmmiinniinngg SSaammppllee
SSiizzee
 WWhhaatt ddaattaa ddoo yyoouu nneeeedd ttoo ccoonnssiiddeerr
– VVaarriiaannccee oorr hheetteerrooggeenneeiittyy ooff ppooppuullaattiioonn
– TThhee ddeeggrreeee ooff aacccceeppttaabbllee eerrrroorr
((ccoonnffiiddeennccee iinntteerrvvaall))
– CCoonnffiiddeennccee lleevveell
– GGeenneerraallllyy,, wwee nneeeedd ttoo mmaakkee jjuuddggmmeennttss
oonn aallll tthheessee vvaarriiaabblleess

38. DDeetteerrmmiinniinngg SSaammppllee
SSiizzee
 VVaarriiaannccee oorr hheetteerrooggeenneeiittyy ooff
ppooppuullaattiioonn
– PPrreevviioouuss ssttuuddiieess?? IInndduussttrryy eexxppeeccttaattiioonnss??
PPiilloott ssttuuddyy??
– SSeeqquueennttiiaall ssaammpplliinngg
– RRuullee ooff tthhuummbb:: tthhee vvaalluuee ooff ssttaannddaarrdd
ddeevviiaattiioonn iiss eexxppeecctteedd ttoo bbee 11//66 ooff tthhee
rraannggee..

39. DDeetteerrmmiinniinngg SSaammppllee
SSiizzee
FFoorrmmuullaass::
MMeeaannss nn == ((ZZSS//EE)) 22
PPrrooppoorrttiioonnss nn == ZZ22 ppqq// EE22
PPeerrcceennttiilleess nn == ppcc ((110000 –– ppcc)) ZZ22// EE22
ZZ aatt 9955%% ccoonnffiiddeennccee == 11..9966
ZZ aatt 9999%% ccoonnffiiddeennccee == 22..5588

40. SSaammppllee SSiizzee ((MMeeaann))
EExxeerrcciissee 11
 WWee aarree aabboouutt ttoo ggoo oonn aa rreeccrruuiittmmeenntt ddrriivvee ttoo hhiirree
ssoommee aauuddiittoorrss aatt tthhee eennttrryy lleevveell.. WWee nneeeedd ttoo
ddeecciiddee oonn aa ccoommppeettiittiivvee ssaallaarryy ooffffeerr ffoorr tthheessee nneeww
aauuddiittoorrss.. FFrroomm ttaallkkiinngg ttoo ssoommee HHRR pprrooffeessssiioonnaallss,,
II’’vvee mmaaddee aa rroouugghh eessttiimmaattee tthhaatt mmoosstt nneeww hhiirreess aarree
ggeettttiinngg ssttaarrttiinngg ssaallaarriieess iinn tthhee $$3388--4422,,000000 rraannggee
aanndd tthhee aavveerraaggee ((mmeeaann)) iiss aarroouunndd $$3399,,000000.. TThhee
ssttaannddaarrdd ddeevviiaattiioonn sseeeemmss ttoo bbee aarroouunndd $$33000000..
 II wwaanntt ttoo bbee 9955%% ccoonnffiiddeenntt aabboouutt tthhee aavveerraaggee
ssaallaarryy aanndd II’’mm wwiilllliinngg ttoo ttoolleerraattee aann eessttiimmaattee tthhaatt iiss
wwiitthhiinn $$550000 ((pplluuss oorr mmiinnuuss)) ooff tthhee ttrruuee eessttiimmaattee.. IIff
wwee’’rree ooffff,, wwee ccaann aallwwaayyss aaddjjuusstt ssaallaarriieess aatt tthhee eenndd
ooff tthhee pprroobbaattiioonn ppeerriioodd..
 WWhhaatt ssaammppllee ssiizzee sshhoouulldd wwee uussee??

41. SSaammppllee SSiizzee
((PPrrooppoorrttiioonn))
EExxeerrcciissee 22
 WWee’’vvee jjuusstt ssttaarrtteedd aa nneeww eedduuccaattiioonnaall TTVV pprrooggrraamm
tthhaatt tteeaacchheess vviieewweerrss aallll aabboouutt rreesseeaarrcchh mmeetthhooddss!!!!
 WWee kknnooww ffrroomm ppaasstt eedduuccaattiioonnaall TTVV pprrooggrraammss tthhaatt
ssuucchh aa pprrooggrraamm wwoouulldd lliikkeellyy ccaappttuurree 22 oouutt ooff 1100
vviieewweerrss oonn aa ttyyppiiccaall nniigghhtt..
 LLeett’’ss ssaayy wwee wwaanntt ttoo bbee 9999%% ccoonnffiiddeenntt tthhaatt oouurr
oobbttaaiinneedd ssaammppllee pprrooppoorrttiioonn ooff vviieewweerrss wwiillll ddiiffffeerr
ffrroomm tthhee ttrruuee ppooppuullaattiioonn pprrooppoorrttiioonnss bbyy nnoott mmoorree
tthhaann 55%%..
 WWhhaatt ssaammppllee ssiizzee ddoo wwee nneeeedd??

42. SSaammppllee ssiizzee
((PPeerrcceennttaaggee))
EExxeerrcciissee 33
 WWee wwiisshh ttoo ddeetteerrmmiinnee tthhee rreeqquuiirreedd ssaammppllee
ssiizzee wwiitthh 9955%% ccoonnffiiddeennccee aanndd 55%% eerrrroorr
ttoolleerraannccee tthhaatt tthhee ppeerrcceennttaaggee ooff CCaannaaddiiaannss
pprreeffeerrrriinngg tthhee ffeeddeerraall LLiibbeerraall ppaarrttyy..
 AA rreecceenntt ppoollll sshhoowweedd tthhaatt 4400%% ooff CCaannaaddiiaannss
qquueessttiioonneedd pprreeffeerrrreedd tthhee LLiibbeerraallss..
 WWhhaatt iiss tthhee rreeqquuiirreedd ssaammppllee ssiizzee??