Transcript Stratification - BYU Marriott School

Stratified Sampling
Lecturer: Chad Jensen
Sampling Methods
SRS (simple random sample)
 Systematic
 Convenience
 Judgment
 Quota
 Snowball
 Stratified Sampling

What is Stratified Sampling?
Stratification is the process of grouping
members of the population into relatively
homogeneous subgroups before sampling.
Advantages
Provides greater precision than a SRS
(simple random sample) of the same size
 Often requires a smaller sample, which
saves money
 Can guard against an "unrepresentative"
sample
 Focuses on important subpopulations but
ignores irrelevant ones

Disadvantages
Can be difficult to select relevant
stratification variables
 Often requires more administrative work
than an SRS
 Not useful when there are no
homogeneous subgroups
 Can be expensive

Proportionate Stratification

Each Stratum has the same sampling
fraction.
– Can provide better precision than a SRS of the
same size.
– Gains in precision are greatest when values
within strata are homogeneous.
– Gains in precision accrue to all survey
measures.
Proportionate Stratum
n h = ( Nh / N ) * n
nh = is the sample size for stratum h.
 Nh = is the population size of stratum h.
 N = the total population size
 n = the total sample size

Disproportionate Stratification

The sampling fraction may vary from one
stratum to the next.
– If variances differ across strata, disproportionate
stratification can provide better precision than
proportionate stratification, when sample points are
correctly allocated to strata.
– The researcher can maximize precision for a single
important survey measure.
– Gains in precision may not accrue to other survey
measures.
Disproportionate Stratum
nh = n * ( Nh * Sh ) / [ Σ ( Ni * Si ) ]
nh = sample size for stratum h.
 n = total sample size
 Nh = population size of stratum h.
 Sh = Standard deviation of stratum h

Proportionate vs. Disproportionate
Disproportionate can be a better choice
(e.g., less cost, more precision) if sample
elements are assigned correctly to strata.
– Example: Given a fixed budget or fixed
sample size, how should sample be allocated
to get the most precision from a stratified
sample?
Proportionate vs. Disproportionate
Recommendation:
If costs and variances are about equal
across strata, choose proportionate
stratification.
 If they differ, consider disproportionate
stratification.

Example
Stratum
Mean Score
Standard Deviation
Boys
Girls
70
80
10.27
6.66
The state administers a reading test to a
sample of 36 third graders.
 The school system has 20,000 third
graders
 10,000 boys and 10,000 girls.

Proportionate Stratum
n h = ( Nh / N ) * n
18 boys = (10,000/20,000) *36
 18 girls = (10,000/20,000) *36

Disproportionate Stratum
Stratum
Mean Score
Standard Deviation
Boys
Girls
70
80
10.27
6.66
nh = n * ( Nh * Sh ) / [ Σ ( Ni * Si ) ]
21.83 boys = 36 * ( 10,000 * 10.27 ) / [ (
10,000 * 10.27 ) + ( 10,000 * 6.67 ) ]
 14 girls = (36 – 22 boys)

Conclusion

How can you use stratified sampling in
your project?
Questions? Comments? Concerns?
Emotional Outburst?