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Sample size calculation - Math Problem Example

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Sample size calculation

Sampling is important in that we involve fewer respondents than using the entire population, the sample saves time and money and an appropriate sample will represent the population in that the results derived from the sample will explain the population with less error. A large sample will waste time and money while a small sample will give inaccurate results.
In any given study if we were to determine the mean of the population and the mean of the sample there means are not the same, the difference between the two is termed as an error, therefore when determining the sample size we need to consider the expected error that will result to these differences. The other factor to consider is the margin of this error, this represents the maximum possible difference between the sample mean and the population mean. We consider also consider the standard deviation of the population, the reason why we consider the standard deviation is because we assume that the population assumes a normal distribution which is depicted by the central limit theorem that states that as the number of variables increase indefinitely then the variables assumes a normal distribution.
For a clustered study there is need to consider the sampling design when calculating the sample size, we consider the number of clusters after calculating the sample size, after determining the sample size as shown above we multiply the results by the number of clusters, the results of this are then mu...
n = [(1.96/2 . 6.9) /(0.4)] 2
n = 285.779
In this case therefore we will use a sample size n =286 derived from rounding off the figure into the nearest whole number.
Cluster sampling:
For a clustered study there is need to consider the sampling design when calculating the sample size, we consider the number of clusters after calculating the sample size, after determining the sample size as shown above we multiply the results by the number of clusters, the results of this are then multiplied by the an expected non response or error, example use 5%. After multiplying we then divide the results by the number of clusters to determine the number of n in each cluster.
Example assumes that we have 10 clusters and we assume the level of error is 5% from our above results; the following will be the results:
285.779 X 10 = 2857.79
2857.79 X 1.05 = 3000.68
We will consider a 3,000 sample size and for each cluster we will have n = 300
Formula 2:
The other formula that can be used is where we have the prevalence of the variable being studies, in this case for example we have a prevalence rate of 40% of a disease and we use the following formula:
n = [Z2. x (1-x)]/ E2
Where Z is the confidence interval where if we choose 95% the area under the normal curve will be 1.96
E is the expected margin error and x is the expected prevalence of the variable being studied.
Formula 3:
Cochran (1963) formulated a formula that could be used in the calculation of the sample size in a study, the formula is as follows:
n = (Z2 PQ)/ e2
Where n is the sample size, Z is the confidence interval, P is the estimated proportion of the attribute under study, q is derived from 1 - p and finally e is the precision level.
He further stated that the above sample would further be ...Show more


Sampling is an important issue when undertaking research, there are various methods of sampling that can be used and the sampling method must be specifies in any study, the reason for specifying the sampling method is because this helps validate the sample used…
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