by Dr Abu Zar Taizai Sat Jan 02, 2010 5:50 am
Key Concepts in Determing Sample Size
From a sampling point of view, the key concern is having a
large enough number of cases to minimize the variable
sampling (standard) error in the estimates
Sampling error can be reduced by increasing the sample size
(denominator) or minimizing the random errors in the data
collection process
What Difference Do You Expect?
In experimental designs, there is a particular interest in
determining the effect (or difference) between experimental
and control groups
The effect size, which essentially reflects the hypothesized
difference between groups, provides a basis for calculating
the sample size for these types of designs
Type I and Type II Errors
A Type I error results from falsely rejecting the null hypothesis
when the hypothesis is actually true (alpha)
A Type II error refers to the reverse error—failing to reject the
null hypothesis when it is actually false
The probability of Type I and Type II errors decreases as the
sample size increases, primarily because the estimates
obtained from larger samples are more reliable (have less
random sampling variation)
Criteria for Estimating Sample Size Based on The Study Design
Objective—to test a hypothesis
Framework—power analysis
Steps
1.
Identify the major study hypotheses
2.
Determine the statistical tests for the study hypotheses,
such as a t-test, F-test, or chi-square
Steps
3.
Select the population or subgroups of interest (based on
study hypotheses and design)
4.
Step 4
a.
Indicate what you expect the hypothesized
difference to be
b.
Estimate the standard deviation of the difference
Steps
4.
Step 4
c.
Compute the effect size
5.
Decide on a tolerable level of error in rejecting the null
hypothesis when it is true (alpha) (this is usually set at
.05.)
Steps
6.
Decide on a desired level of power for rejecting the null
hypothesis when it is false (power) (this is usually set at
.80.)
7. Compute sample size, based on study assumption
Examples of Major Study Hypothesis
Proportion of patients (improving in health [by a global
health index measure] and who received the treatment) will
not differ from the proportion who improve and did not
receive the treatment (null hypothesis)
-
Ho P1 -
P2 = 0
Alternative hypothesis
-
Ha P1 -
ne 0
Determing the Statistical Test
Calculation of sample size depends on the study design and
what statistical test you will be using to test the hypotheses
It is possible that you will have several outcomes, each of
which will be determined using a different statistical test
Different sample sizes will be required, depending on the
outcome
Weighting the sample Data to Reflect The Population
You may want to sample some sub groups in the population
at different rates to ensure that there will be enough of these
individuals without having to increase the overall size of the
sample
The sample can be weighted so that it resembles the
population from which it was drawn
Weighting literally involves a process of statistically assigning
more, or less, weight to some groups than others so that their
distribution in the sample corresponds more closely to their
actual distributions in the population as a whole
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