How to determine sample size

How to determine sample size

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  Greetings to youall
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  Determination of SampleSize
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  What is SampleSize ?  This is the Sub population to be studied in order to make an inference to a reference population ( A broader population to which the findings from a study are to be generalized ).  In census , the sample size is equal to the population size . However , in research , because of time constraint and budget , a representative sample are normally used .  The larger the sample size the more accurate the findings from a study .
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  What is SampleSize Determination ? • Sample size determination is the mathematical estimation of the number of subjects/units to be included in a study . • When a representative sample is taken from a population , the findings are generalized to the population • Optimum sample size determination is required for the following reasons :  To provide the desired level of accuracy  To allow for appropriate analysis  To allow validity of significance test
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  How Large SampleDo I Need ? • If a sample size is too small :  Even a well conducted study may fail to answer its research question  It may fail to detect important effect or association  It may associate the effect imprecisely • Conevrsely if the sample size is too large :  The study will be difficult and costly  Time constraint  Loss of accuracy
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  Ways to CalculateSample Size There are four procedures that could be used for calculating sample size : 1. Use of formulae 2. Ready made table 3. Nomograms 4. Computer software
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  Use of FormulaeFor Sample Size Calculation • There are many formulae for calculating sample size in different situations for different study designs. • The appropriate sample size for population based study is determined by 3 factors –  The estimated prevalence of the variable of interest  The desired level of confidence  The acceptable margin of error
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  • To calculatethe minimum sample size required for accuracy , in estimating promotions , following decisions must be taken : • Decide on a reasonable estimate of key proportions (P) to be measured in the study • Decide on the degree of accuracy(D) that is desired in the study , 1%- 5% or .01-.05 . • Decide on the confidence level(Z) you want to use . Usually 95% • Determine the size(N) of the population that the sample is supposed to represent • Decide on the minimum differences you would expect to find statistical significance .
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  • For population>10,000. n=Z2pq/d2 n= desired sample size(when the population>10,000) Z=standard normal deviate; usually set at 1.96(or a~2), which correspond to 95% confidence level. p=proportion in the target population estimated to have a particular characteristics. If there is no reasonable estimate, use 50%(i.e 0.5) q=1-p(proportion in the target population not having the particular characteristics) d= degree of accuracy required, usually set at 0.05 level( occasionally at 2.0)28
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  • If studypopulation is < 10,000 nf=n/1+(n)/(N) nf= desired sample size, when study population <10,000 n= desired sample size, when the study population > 10,000 N= estimate of the population size Example, if n were found to be 400 and if the population size were estimated at 1000, then nf will be calculated as follows nf= 400/1+400/1000 nf= 400/1.4 nf=28630
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  Sample Size FormulaFor Comparison Of Groups • If we wish to test difference(d) between two sub-samples regarding a proportion & can assume an equal number of cases(n1=n2=n’) in two sub- samples, the formula for n’ is n’=2z2pq/d2 E.g suppose we want to compare an experimental group against a control group with regards to women using contraception. If we expect p to be 40 & wish to conclude that an observed difference of 0.10 or more is significant at the 0.05 level, the sample size will be: n’= 2(1.96)2(0.4)(0.6)/0.12 =184 Thus, 184 experimental subject & another 184 control subjects are required.
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  Use Of ReadymadeTable For Sample Size Calculation • How large a sample of patients should be followed up if an investigator wishes to estimate the incidence rate of a disease to within 10% of it’s true value with 95% confidence? • The table show that for e=0.10 & confidence level of 95%, a sample size of 385 would be needed. • This table can be used to calculate the sample size making the desired changes in the relative precision & confidence level .e.g if the level of confidence is reduce to 90%, then the sample size would be 271. • Such table that give ready made sample sizes are available for different designs & situation
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  Use Of NomogramFor Sample Size Calculation • For use of nomogram to calculate the sample size, one needs to specify the study(group 1) & the control group(group 2). It could be arbitrary or based on study design; the nomogram will work either way. • The researcher should then decide the effect size that is clinically important to detect. This should be expressed in terms of % change in the response rate compared with that of the control group
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  USE OF COMPUTERSOFTWARE FOR SAMPLE SIZE CALCULATION & POWER ANALYSIS The following software can be used for calculating sample size & power : • Epi-info • nQuerry • Power & precision • Sample • STATA • SPSS
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  Finally - Sample sizedetermination is one of the most essential component of every research/study. • The larger the sample size, the higher the degree accuracy, but this is limit by the availability of resources. • It can be determined using formulae, readymade table, nomogram or computer software