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Sample size calculation
Assistant Professor: Ahmed S.Ishtiaque
ULAB
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Why calculating samplesize
• Reduce unnecessary expense(time, labor, money, materials)
• Avoid useless research
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Approaches and decisionsa!out sample size
• Depends on research questions andresearch designs
• Some common situations – Estimating prevalence /mean
– omparing t!o groups•
"ean• #roportion
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Sample size for pre"alencestudy
• $or dichotomous data (only %outcomes& sic'/not sic', male/emale,dead/alive)
• he study describe results inpercentage
• $or example, disease prevalencesurvey
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Sample size: pre"alencesur"ey
2
)]1([2
d
p p Z n −=
• p * estimated prevalence(percentage)
• q * +p•
- * critical value or .0 1*+2.3• d * allo!able error• n * sample si4e
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#rror
• Suppose, the survey !ants toestimate the true prevalence o adisease in population
• he estimate !e get rom the survey!ill be !ithin 5/ d0 o the trueprevalence
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#$ample
• A survey is to estimate prevalence oin6uen4a virus inection in school'ids
• Suppose the available evidencesuggests that approximately %70(#*%7) o the children !ill have
antibodies to the virus• Assume the investigator !ants to
estimate the prevalence !ithin 30 othe true value (30 is called allo!able
error& d)
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Sample size for estimationof mean
• A Survey to 8nd an average o aparameter (birth !eight, antibodytitre, blood pressure)
• he study reports average oparameters
• he parameter must be quantitative
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Sample size for estimation ofmean
• SD * Standard Deviation o variableo interest
• d * Allo!able error
• - * value or the desired con8dencelimit
• n * required sample si4e
2
22
d
SD Z n =
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#$ample
• Suppose an investigator has someevidence suggests that the standarddeviation o rat !eight is about 9 g
• :e !ishes to provide an estimate!ithin ;7 g o the true average (;7 gis the allo!able error& d)
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Example• he required sample si4e is
n * (+2.3) % x (9)% & '()*%
+,%-.-
• hus approximately +
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Sample Size to /omparePercentages
• A study to compare percentages ooutcomes rom di=erent groups(incidence, cure rate, mortality rate,survival rate)
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Sample Size to /omparePercentages
• #c * percentage rom control group
• >c * + #c
•
#e * #ercentage rom theexperimental group
• >e * + #e
22
)(
)()(2
+++
=d d
Q P Q P C n eecc
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Sample Size to ComparePercentages
• d = Difference between the twogroups (must be positive)
• C = Constant (See table nextpage)
22
)(
)()(2
+++
=d d
Q P Q P C n eecc
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/ : /onstant
• ?hen po!er is ;70
•#o!er * Ability to 8nd signi8cance!hen the t!o groups are reallydi=erent (the ormula is or t!o sideddi=erence)
alpha 727 727+
@2; ++23;
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#$ample ,
• he research question is !hethersmo'ers have a greater incidence os'in cancer than nonsmo'ers
•
A revie! o previous literaturesuggests that the incidence o s'incancer is about 72% in nonsmo'ers
•
At alpha*727, and po!er*;70, ho!many smo'ers and nonsmo'ers !illneed to be studied to determine!hether s'in cancer incidence is atleast 72< in smo'ers
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#$ample %
• Bull :ypothesis C he incidence os'in cancer does not di=er insmo'ers and nonsmo'ers
• Alternative :ypothesis C heincidence o s'in cancer is di=erentbet!een smo'ers than nonsmo'ers
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#$ample
• #e * 72
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Sample Size to /ompare0eans
• :ypothesisC ompare means odi=erent groups
• he parameters are quantitative(birth !eight, blood pressure)
• Select % groups that you thin' they!ill be most di=erent (such as& a
control and a treatment group)
• $or ttest, ABA
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Sample Size to /ompare0eans
• S * Standard Deviation o thevariable
• d * Di=erence bet!een the % groups• * onstant (rom previous table)
2
21
+=d
sC n
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#$ample
• he research question is to compare theeFcacy o DRGH A and DRGH I in thetreatment o asthma
• he outcome variable is $E+ (orcedexpiratory in + second) + hour ater treatment
• A previous study has reported that the mean$E+ in persons !ith treated asthma !as %27
litres, !ith a standard deviation o +27 litre• he investigator !ould li'e to be able to
detect a di=erence o +70 or more in mean$E+ bet!een the t!o treatment groups
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#$ample
• Bull :ypothesis C "ean $E+ is thesame in asthmatics treated !ithDRGH A as in those treated !ith
DRGH I
• Alternative :ypothesis C "ean$E+ is di=erent bet!een asthmatic
patients treated !ith DRGH A andthose treated !ith DRGH I
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Example
• S * +
• d * +70 o % litre * 72% litre
2
2.0
185.721
×+=n
2
21
+=d
sC n
*
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