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Survey Sampling Techniques course is one of important courses in Statisitics. Major poiuts of this course are: probability sampling, confidence intervals, Two-stage cluster sampling, Two-stage cluster sampling, estimation for mean, choosing strata, allocation across strata, ratio estimation, domain estimation, Two-stage cluster sampling. Keywords in these slides are: Cluster Sampling, Probabilities, Cluster, Isu Employees, Data Collection, Population, Cluster and Stratified Sampling, Single-Sta
Typology: Slides
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-^ DEFN:
Population
Elements
Cluster
U.S. residents
person
household
Ames households
household
city block, orpostal route
ISU employees
employee
department
Maple trees inVermont
tree^
1 km
^ 1 km plot
Frame
SU^
Element
List of phone numbers
phone number
person
List of blocks
block
household
List of ISU departments
department
faculty member
List of plots
plot^
tree
We will no longer assume SU = element
(for cluster sampling)
Take anSRS of clusters; observe all elements within the clusters in thesample:
A blockof cellsis astratum
A blockof cellsis aclusterSU is aclusterDon’tsamplefromeverycluster
SU is anelementSamplefromeverystratum
Sample of 40 elements
-^ Cluster
-^ Divide
K^ elements
into
N^ clusters
-^ Cluster
or^ PSU
i^ has
M^ elements i^
sample
of^ n
clusters
-^ Stratified
elements
divided
into
H^ strata
-^ An
element
belongs
to^1 and^
only^
1 stratum
-^ Take
a^ sample
of^ n
elements,
consisting
of^ n
elements h^
from
stratum
h^ for
each
of^ the
H^ strata
Mi K^
1
-^ May
when
cost
of^ data
collection
increases
with
distance
between
elements
-^ Household
surveys
using
in‐person
interviews
(household
=^ cluster
of^ people)
-^ Field
data
collection
(plot
=^ cluster
of^ plants
or^ animals)
-^ Elements
-^ Members
of^ a
household
-^ Employees
in^ a
business
-^ Plants
or^ soil
within
a^ field
plot
-^ Define
-^ Make
each
cluster
as^ heterogeneous
as^ possible
-^ Like
making
each
cluster
a^ mini
‐population
that
reflects
variation
in^ population
-^ Part
of^ the
gain
comes
from
improving
the
representativeness
of^ the
sample
-^ Part
of^ the
gain
comes
from
reducing
the
amount
of
correlation
among
elements
in^ the
cluster
-^ Note:
-^ Large
variation
among
strata,
homogeneous
within
strata
-^ Define
-^ Extreme
-^ The
of^ n
dorm
rooms
-^ Data
on^ each
cluster
(all^
students
in^ dorm
room)
-^ t^ i^ =^ total
number
of^ dining
hall^
dinners
for^ dorm
room
i
-^ t^2
=^14
dining
hall^
dinners
for^4
students
in^ dorm
room
2
20 + 12 + … + 9 + 16
150 SSUs
M= 20 SSUs^1
M= 12 SSUs^2
M= 16 SSUs^12 M=^11 9 SSUs
SSUi = 9j = 1^
SSUi = 9j = 7
-^ y^ ij –^ e.g.,
-^ e.g.,
-^ Cluster
-^ Within
^
M^ i j
iU ij i i
y y
M S^
1
2
2
iU i M j
ij i iU
i
^
7 5 6
4 3 7 5 11
3 5 3 1 6
9 7 4 3 0
7 3
(^83). 3
46
(^88). 6 S 2 boxes 12 Cluster
2
2
2 2
2
U
U
y
M t
(^33). 3
30
(^00). 9 S (^69) Cluster
6
6
26
6
U
U
y
M t
1 elements^209995.^400. 7
(^75). 7
39
(^33). 4 S 11 9 Cluster
11
11
(^211)
11
U
U
y
M t
