Research Methodology:Sample Size Determination

1. Sample size Determination
Pritish Biswal
Utsho Chowdhary
Anurag Guha
Gopal Kumar

2. General Idea
Sample size is usually determined by the
primary objective of trial.
Sample size calculation should be explicitly
mentioned in the protocol.

3. Determining sample size
The estimate of the population standard
deviation
The acceptable level of sampling error
The desired confidence level

4. Methods
Unaided Judgment
All You can Afford
Average Size for samples for similar studies
Required Size per cell
Use of a Traditional Statistical Model
Use of a Bayesian Model

5. Sampling Distribution
 To help understand the concept of a sampling
distribution of the mean by drawing samples from a
population of 1250 sales invoices.
 We use simple random sample of size n=50 from this
population for the illustration.
 A sampling distribution of the mean is the relative
frequency distribution of the means of all possible
samples of size n taken from a population of size N
should be taken, and the mean of each sample be
calculated and plotted in a relative frequency
distribution.

6. sampling distribution of the mean
Frequency of Sample
Means
Relative frequency of
sample means
38-39.99 1 1/500=.002
40-41.99 2 2/500=.004
42-43.99 17 17/500=.034
44-45.99 39 39/500=.078
46-47.99 52 52/500=.104
48-49.99 85 85/500=.170
50-51.99 110 110/500=.220
52-53.99 77 77/500=.154
54-55.99 64 64/500=.128
56-57.99 37 37/500=.074
58-59.99 10 10/500=.020
60-61.99 4 4/500=.008
62-63.99 2 2/500=.004
Total 500 1.000

7. Facts

8. Statistical Estimation & the sampling
distribution of the Mean
We want to estimate a population mean that we do not
know from a sample mean. Two kinds of estimates of a
population mean
 Point-An estimate involving only a single value. If a
random sample is taken, the sample mean is the best
estimate that can be made from the sample data.
 Interval-An estimate concerning an interval, or range of
values. A statement of probability that the interval will
enclose the true value of the mean is also given. It is
called confidence coefficient and the interval is called a
confidence interval.

9. Sampling distribution of the proportion

10. Traditional statistical methods of
determining sample size
What information is needed before a
calculation of the sample size can be made?
Specification of error that can be allowed-how
close must the estimate be?
Specification of confidence coefficient-what
level of confidence is required that the actual
sampling error does not exceed that specified?
Estimate of the population standard deviation-
what is the s.d of the population?

11. Estimating variances for rating scales
used in marketing research
On a 5 point scale responses can't be <1 or >5.
This constraint leads to a relationship between
mean & variance.
If a sample mean is 4.6 on a 5 point scale,then
there must be a large proportion of responses of 5.
If the mean is near 3,the variance can be
potentially much greater.
The nature of the relationship between the mean
and the variance depends on the number of scale
points and on the shape of the distribution of
responses.

12. Specification required for estimation
problems involving proportions
The specification must be made to determine the
sample size for an estimation problem involving a
proportion are very similar to those for the mean
Specification of error that can be allowed-how
close must the estimate be?
Specification of confidence coefficient-what level
of confidence is required that the actual sampling
error does not exceed that specified?
Estimate of population proportion using prior
information-what is the approximate or estimated
population proportion?

13. Sample size, Incidence & Nonresponse
Incidence-is the percentage of individuals who
have the traits necessary to be included in a
survey.
Nonresponse-refers to the percentage of
respondents who refuse to participate in a survey
or can’t be contacted.
Initial sample size=required
response (incidence response rate)

14. Thank You