Transcript sample design: who will be in the sample?

SAMPLE DESIGN: HOW
MANY WILL BE IN THE
SAMPLE—DESCRIPTIVE
STUDIES ?
Lu Ann Aday, Ph.D.
The University of Texas
School of Public Health
TYPES OF OBJECTIVES
DESCRIPTIVE
Describes
Is more exploratory
Profiles characteristics
of group(s)
Focuses on what?
Assumes no hypothesis
Does not require
comparisons (between
groups or over time)
Try to maximize
precision of estimates
ANALYTICAL
Explains
Is more explanatory
Analyzes why group(s)
have characteristics
Focuses on why?
Assumes an hypothesis
Requires comparisons
(between groups or
over time)
Try to maximize
power to detect
differences, if they exist
RELATING SAMPLE SIZE ESTIMATION
TO STUDY OBJECTIVES
Select the sample size estimation procedure that
best matches the study design underlying the
respective study objectives
Compute the sample size required to address each
objective
Based on the sample sizes required to address each
of the objectives, appropriate sample size
adjustments, as well as time and resource
constraints, recommend an overall sample size
Discuss possible limitations in terms of statistical
precision or power in addressing any specific study
objective(s), given the recommended sample size
CRITERIA:
Descriptive Studies
Objective:
to estimate a parameter, i.e.,
provide a precise estimate for
selected variable(s)
Framework:
normal sampling distribution
NORMAL SAMPLING
DISTRIBUTION
Sampling Distribution: distribution of
estimates, e.g., mean, for all possible
simple random samples of a certain size
that could be hypothetically drawn from
the target population
Population Mean: grand mean of all
possible simple random samples of a
certain size that could be hypothetically
drawn from the target population
STANDARD ERROR
Definition: average variation of all
possible simple random samples of a
certain size that could be hypothetically
drawn from the target population
Formula:
SE = s/n, where,
SE
= standard error
s
= sample standard deviation
n
= sample size

= square root (sqrt)
CONFIDENCE INTERVAL
Definition: range of values in which the
population mean is likely to be contained,
with a given level of probability, defined
by the standard errors of the sampling
distribution
Confidence Interval
Standard Errors (Z)
68 %
90 %
95 %
99 %
1.00
1.645
1.96
2.58
EXAMPLE: Mean Estimate
Population Mean: 5 visits
Standard Error: .50 visits
Confidence Interval:
68 % = 1.00 * .50 = +/- .50 visits
90 % = 1.645 * .50 = +/- .82 visits
95 % = 1.96 * .50 = +/- .98 visits
99 % = 2.58 * .50 = +/- 1.29 visits
EXAMPLE: Proportion Estimate
Population Proportion: .50, i.e., 50%
Standard Error: .025, i.e., 2.5%
Confidence Interval:
68 % = 1.00 * 2.5
90 % = 1.645 * 2.5
95 % = 1.96 * 2.5
99 % = 2.58 * 2.5
= +/= +/= +/= +/-
2.5%
4.1%
4.9%
6.4%
SAMPLE SIZE ESTIMATION: CrossSectional (One Group)—Proportion
Formula:
n = Z21-α/2 P(1-P)/d2, where,
n
= sample size
Z21-α/2
= confidence interval
P
= estimated proportion
d
= desired precision
SAMPLE SIZE ESTIMATION: CrossSectional (One Group)—Proportion
Example:
n =
n =
n =
Z21-α/2 P (1-P)/d2
1.962 * .50(1-.50)/.052
384
Note: See Table 7.1B, Aday & Cornelius,
2006, for sample size estimates based on
different estimated proportions (P) and levels
of desired precision (d).
SAMPLE SIZE ESTIMATION: CrossSectional (One Group)—Mean
Formula:
n = Z21-α/2 σ2/d2, where,
n
= sample size
Z21-α/2
= confidence interval
σ
= estimated standard deviation
d
= desired precision
SAMPLE SIZE ESTIMATION: CrossSectional (One Group)—Mean
Example:
n = Z21-α/2 σ2/d2
n = 1.962 * (2.5 2) /1 2
n = 24
Note: To estimate σ when not known, estimate
the inter-quartile range by dividing the possible
range of values by 4, e.g., if range is 0-10, then
10/4 = 2.5.
SAMPLE SIZE ESTIMATION: GroupComparison (Two Groups)—Proportion
Formula:
n = Z21-α/2[P1(1-P1) + P2(1-P2)]/d2, where,
n
= sample size
Z21-α/2
= confidence interval
P1
= estimated proportion (larger)
P2
= estimated proportion (smaller)
d
= desired precision
SAMPLE SIZE ESTIMATION: GroupComparison (Two Groups)—Proportion
Example:
n = Z21-α/2 [P1(1-P1)
+ P2(1-P2)]/d2
n = 1.962 [(.70)(.30) + (.50)(.50)]/.052
n = 707 (in each group)
SAMPLE SIZE ESTIMATION: Group
Comparison (Two Groups)—Mean
Formula:
n = Z21-α/2 [2σ2]/d2, where,
n
= sample size
Z21-α/2
= confidence interval
σ
= estimated standard deviation
d
= desired precision
SAMPLE SIZE ESTIMATION: Group
Comparison (Two Groups)—Mean
Example:
n =
n =
n =
Z21-α/2 [2σ2]/d2
1.962 * [2 * (2.5 2)] /1 2
48 (in each group)
Note: To estimate σ when not known, estimate
the inter-quartile range by dividing the possible
range of values by 4, e.g., if range is 0-10, then
10/4 = 2.5.
SUMMARY:
Steps in Estimating
Sample Size – Descriptive Studies
1. Identify the major study variables.
2. Determine the types of estimates of
study variables, such as means or
proportions.
3. Select the population or subgroups
of interest (based on study objectives
and design).
4a. Indicate what you expect the
population value to be.
4b. Estimate the standard deviation of
the estimate.
SUMMARY:
Steps in Estimating
Sample Size – Descriptive Studies
5. Decide on a desired level of
confidence in the estimate
(confidence interval).
6. Decide on a tolerable range of
error in the estimate (desired
precision).
7. Compute sample size, based on
study assumptions.
SAMPLE SIZE ESTIMATION:
EXCEL SPREADSHEET
See EXCEL file with spreadsheet
for computing sample sizes.