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2 Stage Cluster Sampling - Survey Sampling Techniques - Lecture Slides, Slides of Survey Sampling Techniques

Cochin University of Science and TechnologySurvey Sampling Techniques

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: 2 Stage Cluster Sampling, Primary Sampling Unit, Secondary Sampling Unit, 1-Stage Cluster, Notation, Cluster-Level, Complete Enume

Typology: Slides

2012/2013

Uploaded on 08/30/2013

faroq
faroq 🇮🇳

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2-stage cluster sampling with equal
selection probs
•Overview
–Process
•Stage 1: select clusters
•Stage 2: select elements within each sampled cluster
–First stage sampling unit is a …
•PSU = primary sampling unit = cluster
–Second stage sampling unit is a …
•SSU = secondary sampling unit = element
–Only collect data on the SSUs that were sampled from the
cluster
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Download 2 Stage Cluster Sampling - Survey Sampling Techniques - Lecture Slides and more Slides Survey Sampling Techniques in PDF only on Docsity!

2-stage cluster sampling with equal

selection probs

  • Overview
    • Process
      • Stage 1: select clusters
      • Stage 2: select elements within each sampled cluster
    • First stage sampling unit is a …
      • PSU = primary sampling unit = cluster
    • Second stage sampling unit is a …
      • SSU = secondary sampling unit = element
    • Only collect data on the SSUs that were sampled from the cluster

1-stage vs. 2-stage cluster sampling

Sample all SSUs in sampled PSUs: Take an SRS ofmi SSUs in sampled PSUi :

1-stage cluster sample (stop here)

Stage 1 of 2-stage cluster sample (select PSUs)

Stage 2 of 2-stage cluster sample (select SSUs w/in PSUs)

Now we have to estimate cluster-level

pop. parameters

  • For 1-stage cluster samples
    • Have a complete enumeration of the cluster elements
    • Cluster population parameters are known
      • Directly observe , tiU , piU
  • For 2-stage cluster samples
    • Observe data on a sample of elements in a cluster
    • Estimate cluster population parameters
      • Calculate estimates of , tiU , piU

yiU

yiU

Motivation for 2-stage cluster samples

  • Recall most common motivations for cluster

sampling

  • Only have access to a frame that lists clusters
  • Reduce data collection costs by going to groups of

nearby elements (cluster defined by proximity)

CSE2 unbiased estimation for

population total t

  • Have a sample of elements from a cluster
    • We no longer know the value of cluster

parameter, tiU

  • Estimate tiU using data observed for mi

elements

 

 

m i

j

ij i

i i i i^ y m

M t M y 1

ˆ

CSE2 unbiased estimation for

population total

  • Approach is to plug estimated cluster totals

into CSE1 formula

  • CSE
  • CSE

   

n

i

i i

n

j

unb i n M^ y

N t n

N t 1 1

   

n

i

i iU

n

j

unb iU n M^ y

N t n

N t 1 1

CSE2 unbiased estimation for

population total

  • In CSE1, we observe all elements in a cluster
    • We know ti
    • Have variance component 1, but no component 2
  • In CSE2, we sample a subset of elements in a cluster
    • We estimate ti with
    • Component 2 is a function of estimates variance for

tˆi

tˆi

i

i i

i i m

s M

m M

2 (^2 ) 

 

 

 

 

CSE2 unbiased estimation for

population total

  • Estimated variance among cluster totals
  • Estimated variance among elements within a

single cluster i

  

 

 

 

  

n

i

t i unb N

t t n

s 1

2 (^2) ˆ ˆ 1

1

^  

m i

j

ij i i

s (^) i m y y 1

2 2 1

Dorm example

  • Stage 2: select 2 students in each room

Stu-

dent

Rm

Rm

Rm

Rm

Rm

Total?????

Dorm example

  • Stage 1
    • Cluster =
    • N =
    • n =
    • SRSWOR
  • Stage 2
    • Element =
    • Mi =
    • mi =
    • SRSWOR

tˆi

Dorm example

tˆi

Stu- dent (j)

Rm 6 (i=1)

Rm 21 (i=2)

Rm 28 (i=3)

Rm 54 (i=4)

Rm 89 (i=5)

5.5 2.5 4.5 4.5 3. 22 10 18 18 12 si^2 0.5 0.5 0.5 0.5 2.

yi Mi y i 

 ^ i ^  ^ 

m m (^) i j 1 yij^ yi

2 1

1

Dorm example

 (^)   

n

j

unb n^ ti

N t 1

  

 

 

  

 (^)  

n

i

unb t i N

t t n

s 1

2 (^2) ˆ ˆ 1

1

CSE2 unbiased estimation for

population mean

 

  2

ˆ ˆ ˆ^ ˆ

K

V t

V y

K

t

y

unb unb

unb unb

yU

Dorm example

2

K

V t V y

K

t y

unb unb

unb unb