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Sample size

How to Calculate Sample Size in a Research

This is a very important question that what should be your sample size? In any study there are various factors that affect your sample size.  You have to know these factors and determine your sample. You can keep your sample size large if the study requires greater accuracy. You can keep the sample size small if you are short of time and money to conduct the study. You should know yourself how much confidence you want to put in your study, in short, at what confidence level you want to test your hypothesis. Another very important consideration is the variability in the study population. When the population or the variable to be studied in the population has greater variation the researcher has no option but to take a large sample. This will ensure that the findings are more accurate and reliable. Ensuring the correct sample size is crucial to your study. To make it simple a formula has been designed to get sample size for any study type.

You need to know the following before calculating sample size.

Confidence level

At what confidence level you want to test your hypothesis. Suppose you want to test the hypothesis at 95 % confidence level, it means that you are 95 % confident about your findings. The chances of error in your study are 0.5 %.

Population size

The population size needs to be known and it is known in majority of the studies if the population is small. In case the population is large the size is unknown. Sample size can be calculated even if the accurate population size is unknown. An approximation of the population can be made in case you do not know the exact number of the people in your study population.

Standard deviation

You need to know how much variation there might exist among the values or responses  that you will get for your questions.Since the study is still not done you do not know the variation or standard deviation. You can take a standard deviation of 0.5 or 0.1 for example. This is only a probabilistic deviation and not the actual one. A 0.5 deviation means that there will be great variation in the responses and data will be spread over a large range. A 0.1 deviation means that there will be less deviation in the responses and you will get a range of data that is closer to the mean.

Formula to calculate sample size

Sample mean  =     X

Population mean = mu

Sample size  = n

Standard Error  = E

Standard Deviation  = s

Critical Value  =   za/2


The formula for standard error is

Sample size calculation
standard error






By rearranging this equation and adding the value of critical value we can get the formula for sample size.




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