## Sample Size Calculation

Most people who plan for a study or a survey are often faced with one challenge. What should be the sample size. There are many different lines of thoughts, many different opinions. Some people think that simply taking 10% of the population as sample should be good enough. This may work well in some cases, but if the population is too large, even that 10% would be very large a size to manage.

Some people are smarter. They straight go for online tools that some websites offer. One can enter a few input parameters and get a sample size as result. This also, may work is some cases. But the fact is that, you will probably not know which formula the site uses to calculate the sample size, and whether that formula is applicable for your kind of study design or not.

We need to understand that there are many different formulas for the calculation of sample size. All formulas are valid, but within its particular scope. For any given study/survey design, only one of these many formulae is applicable and valid. All other formulae are useless for that particular study. If you pick just any of the different formulae, you might just be wrong. Totally wrong.

Have a look at the formulae in the sub-pages and take note of what each formula is to be used for. And you will know which one fits your requirement. First, note the various symbols and their conventional use (representation) in various formulae for sample size calculation.

Some people are smarter. They straight go for online tools that some websites offer. One can enter a few input parameters and get a sample size as result. This also, may work is some cases. But the fact is that, you will probably not know which formula the site uses to calculate the sample size, and whether that formula is applicable for your kind of study design or not.

We need to understand that there are many different formulas for the calculation of sample size. All formulas are valid, but within its particular scope. For any given study/survey design, only one of these many formulae is applicable and valid. All other formulae are useless for that particular study. If you pick just any of the different formulae, you might just be wrong. Totally wrong.

Have a look at the formulae in the sub-pages and take note of what each formula is to be used for. And you will know which one fits your requirement. First, note the various symbols and their conventional use (representation) in various formulae for sample size calculation.

α = Set limit of type 1 error
β = Set limit for type 2 error
σ = Standard deviation in the population/sample
x ̅ = Expected sample mean
μ = Hypothesized mean (null value)
p

_{0}= Population proportion p = Expected sample proportion d = Absolute precision (margin of error) ɛ = Relative precision λ = Expected sample incidence rate λ_{0}= Population incidence rate p_{1}= proportion of exposed individual developing the outcome of interest p_{2}= proportion of unexposed individual developing the outcome of interest f = error factor R = Relative risk n = sample size required for one arm δ = Difference in proportions or means (non null value) λ_{2}= event rate in control arm λ_{1}= event rate in treatment arm y=required person-years of observation in each group f(α, β) = (Z_{(1-α/2)}+ Z_{(1-β)})^{2}Sample Size Calculation for:

Measuring Means

Measuring Proportions

Measuring Rates

Sample Size Adjustments