Exercise 9.1

Load the file BURKINA_94 and initialize its sampling design (SD). Do this first only by specifying the variable WEIGHT
as sampling weight.
 

  1. Compute the mean of total expenditure per adult equivalent (EXEPQ) with the size variable equal to SIZE. Why does STD1 differ from STD2? What is a sufficient condition so that both standard deviations be equal?

  2. Now use both variables WEIGHT and STRATA to reinitialize the SD of this file. Compute, again, the mean of total expenditure per adult equivalent when the size variable is SIZE, and compare between the STD's of question a. What can be said about the impact of stratification on STD1?

  3. Now use variables WEIGHT, STRATA and PSU to reinitialize the SD of this file. Compute, again, the mean of total expenditure per adult equivalent when the size variable is SIZE, and compare between the STD's of questions a and b. What can you say about the impact of PSU's on STD1?

  4. By using the GSE variable to specify the social professional group, compute the mean of total expenditure per adult equivalent when the size variable is SIZE and for groups 1,2, and 6. How does the sampling variability differ across these estimates?

Answer
STEP 1: Initialising  the sampling weight: EDIT|Set Sample Design

 

  • After choosing the appropriate variable(s), click on  the button OK.

 

STEP 2: Use the DAD Application: DISTRIBUTION|STATISTICS

  • After choosing the appropriate variable(s) and parameters, click on the COMPUTE button.

 

RESULTS
 

Statistics (Distribution)

Session Date Mon Sep 13 14:09:05 EDT 2004
Execution Time 0.172 sec
FileName BURKINA_94.daf
OBS 8639
Sampling Weight WEIGHT
Variable of interest EXPEQ
Size variable SIZE
Group variable No Selection

Statistic

STRATA PSU WEIGHT

Estimate

STD1

STD2

DEFF

Mean

    X
86596.25901382
1224.76502091
1125.43571620
1.18430663

Mean

X   X
86596.25901382
1134.80855925
1125.43571620
1.01672574
Mean X X X 86596.25901382 2177.80495686 1125.43571620 3.74452364
Remarks :
  1. STD1 is the square root of V1, where V1 is the design-based estimate of the sampling variance of the parameter estimate.
  2. STD2 is the square root of V2, where V2 is the estimate of sampling variance of the parameter estimate under the hypothesis of simple random sampling without replacement.
  3. DEFF is the ratio of V1 over V2.

 

  1. STD1=STD2 if the sample is not weighted.

  2. Stratification helps to increase the precision of the estimated value and to decrease consequently the standard error.

  3. PSU's increase the concentration of local sampling and decrease the precision of estimates.

  4.  

Statistics (Distribution)

GSE

STRATA PSU WEIGHT

Estimate

STD1

STD2

DEFF

1 X X X 306622.55 14111.86 10704.52 1.73793814
2 X X X 227152.12 16149.16 14574.01 1.22784015

 

 

 
 

Complete Sampling Design Information

 

Number of observations 8639
Sum of weights 1210997.4992027283
Number of strata 7 strata in the Sampling Design

 

 

CODE

STRATA

PSU

LSU

OBS

P(strata)

FPC (f_h)

1

1

42

839

839

0.179867

0.0

2

2

37

737

737

0.135772

0.0

3

3

98

1960

1960

0.197662

0.0

4

4

55

1099

1099

0.231076

0.0

5

5

66

1288

1288

0.062156

0.0

6

6

39

778

778

0.049667

0.0

7

7

97

1938

1938

0.143801

0.0

Total

7

434

8639

8639

1.0

--

Remarks : P(strata_i): represents the share of the population that lives in strata_i.

 

Code of PSU
Strata #1   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
    17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
    33 34 35 36 37 38 39 40 41 42
Strata #2   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
    17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
    33 34 35 36 37
Strata #3   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
    17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
    33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
    49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
    65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
    81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
    97 98
Strata #4   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
    17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
    33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
    49 50 51 52 53 54 55
Strata #5   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
    17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
    33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
    49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
    65 66
Strata #6   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
    17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
    33 34 35 36 37 38 39
Strata #7   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
    17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
    33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
    49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
    65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
    81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
    97