Biostatistics

1. Md. Shahjahan, PhD
e-mail: mdshahjahan@agnionline.com
Sample size Estimation

2. Determination of minimum sample size
The minimum sample size (n) depends on the:
 Objective
 Design of the study
 Plan for statistical analysis
 Accuracy of the measurements to be made (d);
 Degree of precision required for generalization;
 Degree of confidence with which to conclude.
With simple random sampling, for a given magnitude of confidence interval, the
precision (z) can be measured by z = d/SE.
If we want a 95% confidence interval, z must be 1.96. Since the SE depends on
n, we can calculate the value of n required to achieve the chosen level of
confidence.
If s is the sample estimate of the population standard deviation, then the
standard error (SE) of the mean, for a sample of size n, is s/n.

3. For estimating a population mean, with SE = s/n, the minimum required sample
size, in general, is:
s2 = z2s2
SE2 d2
For a population of size n, involving a binomial distribution with probability p , let a
individuals be observed with the relevant characteristics. Then the standard error of
the estimate of p (pq/n) where q = 1 – p.
Scinece SE2 = (pq/n),
n = pq/SE2 = z2pq/d2
if n0, is the sample from an infinite population, the finite population sample size is:
n = n0/(1+n0/N).

4. Representativeness
If researchers want to draw conclusions that are valid
for the whole study population, they should take care
to draw a sample in such a way that it is representative
of that population.
A representative sample has all the important
characteristics of the population from which it is drawn.

5. Criteria for Choosing test statistics
Situation 1: Compare a single Mean with an
assigned Mean
A.Population Normally Distributed
Sample size  Known  Not known
Large (n 30) z z
Small (n <30 z t

6. Situation 2: Comparing two independent
sample means
Populations Normally distributed
Sample size Equal var assumed Equal var not assumed
Large z (or t) t
(beyond the scope of
syllabus)Small t

7. Thank you so much!