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Samp le Size Methodology and OptimizationSam pling is the
foundation of all resea rch. Reliable sam pling he lps you m ak e b
usiness
dec isions with confidenc e.
There a re tw o m a in com ponents in dete rmining w hom you w
ill interview .
The first is dec iding what kind of people to interview . Resea
rche rs often c a ll this group the
target po pulation. If you c ond uct an emp loyee attitude
survey or an a ssoc iation
me mb ership survey, the p op ulation is ob vious. If you a re
trying to d etermine the likely suc c ess
of a prod uct, the target po pulation ma y be less ob vious.
Correc tly de termining the ta rge t
pop ulation is c ritica l. If you d o not inte rview the right
kinds of p eo p le, you will no t suc c essfully
me et your goa ls.
The next step is to dec ide how ma ny peop le you need to
interview . Sta tisticians know tha t a
sma ll, rep resenta tive samp le w ill reflec t op inions and
beha viour of the group from whic h it
wa s d rawn. The la rge r the samp le, the mo re p rec isely it
rep resents the ta rge t g roup .
However, the rate of improvement in the precision decreases as
your sample size increases.For exam p le, to inc rease a samp le
from 250 to 1,000 only do ub les the p rec ision. You m ust
ma ke a d ec ision ab out your sam p le size b ased on fa c tors
such as: time a vailab le, bud ge t
and ne c essa ry de gree o f prec ision.
Sample Size Terminolo gy
There a re three fa c tors tha t d ete rmine the size o f the c
onfidenc e interval for a given
c onfidenc e level. These a re: samp le size, pe rc entag e of
sa mp le tha t picked a p a rticular
answers and population size.
Sample Size
The large r your samp le, the m ore sure you c an b e tha t the
ir answe rs truly reflec t the op inion
of the pop ula tion. This indica tes tha t for a given c
onfidenc e level, the larger your sam p le
size, the sma ller your c on fidenc e inte rva l. How eve r, the
rela tionship is not linea r (i.e., doub ling
the samp le size d oes not ha lve the c onfidenc e interva
l).
Percentage of sam ple that pic ked a pa rticular answer
Your acc urac y also d ep end s on the p ercenta ge of your sam
ple that picks a pa rtic ular
answer. If 99% of your samp le sa id "Yes" and 1% sa id "No" the
c ha nc es of error are rem ote,
irrespec tive of samp le size. How eve r, if the percenta ges a
re 51% and 49% the c ha nc es of
error a re muc h g rea ter. It is ea sier to be sure of e xtrem
e answe rs tha n o f m idd le-of-the-roa dones.
When de termining the samp le size need ed for a given level of
ac c urac y you must use the
wo rst-ca se p erce nta ge (50%). You should also use this perce
nta ge if you w ant to de termine
a ge neral level of ac c urac y for a sam ple you a lrea dy ha
ve. To d etermine the c onfide nce
interval for a spec ific a nswe r your samp le ha s given, you c
an use the pe rc enta ge p ic king
tha t a nswe r and ge t a sma ller interval.
Population Size
How ma ny peop le do es your sa mp le rep resent? This ma y be
the number of pe op le in a c ity
you are studying, the numb er of peo ple who buy new c ars, etc.
Often you ma y not know theexac t p op ulation size. This is not a
p rob lem. The m a thema tics of p rob ab ility proves the size o
f
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the po pulat ion is irrelevant , unless the size o f the samp le
e xc eeds a few perce nt o f the tota l
pop ulation yo u are exam ining . This me ans tha t a samp le of
500 peo p le is eq ua lly useful in
examining the op inions of a sta te of 15,000,000 as it wo uld a
c ity of 100,000. For this reason,
the pop ulation size is igno red when it is "large " or unknow
n. Pop ulation size is on ly likely to be
a fac tor when you w ork with a relatively sma ll and know n
group o f pe op le (e.g., the
me mb ers of a n a ssoc iation).
The c onfidenc e interva l c a lculations assume yo u have a ge
nuine rand om samp le of the
relevant p op ula tion. If your samp le is not truly rand om ,
you c annot rely on the intervals. Non-
random samp les usually result from som e flaw in the samp ling
p roc ed ure. An e xamp le o f
suc h a flaw is to only ca ll peo p le during the day, and miss
a lmo st e veryone w ho w orks. For
mo st purpo ses, the non-working p op ula tion ca nnot b e a
ssume d to ac c urat ely rep resent the
entire (working and non-working) population.
Confidence interval is the p lus-or-minus figure usua lly
reported in newspaper or television
op inion p oll results. For exam ple, if you use a c onfidenc e
interval of 4 and 47% perce nt o f
your sa mp le picks an answe r you c an be "sure" that if you ha
d asked the que stion of the
entire releva nt pop ula tion be twe en 43% (47-4) an d 51%
(47+4) would have p icked tha tanswer.
Confidence level tells you ho w sure yo u c an b e. It is
expressed a s a perce nta ge and
rep resents how often the true p ercenta ge of the po pulation
who w ould pick a n a nswe r lies
within the c onfidenc e interval. The 95% c onfidenc e level me
ans you c an b e 95% c ertain; the
99% c onfidenc e level means you c an be 99% c erta in. Mo st
resea rche rs use the 95%
c onfide nce level.
When you p ut the confidence level and the co nfidence interval
tog ether, you ca n say tha t
you a re 95% sure tha t the true pe rc enta ge of the pop ula
tion is betw een 43% and 51%.
Correlation between sam ple size and confidenc e interval
The w ider the confidenc e interval you a re willing to a cc
ept, the mo re certain you c an be that
the whole p opulation's answers would be within that range . For
examp le, if you asked a
sam ple of 100 pe op le in a c ity which brand of co la they p
referred, and 60% said Brand A,
you c an b e very ce rtain that between 50% and 70% of all the
peo ple in the c ity actua lly do
