Session 2B: Exercices with stratified and two stage sampling

Transcription

1 Session 2B: Exercices with stratified and two stage sampling Please join this room s channel National Council of Applied Economic Research Sistemas Integrales Delhi, March 19, 2013

2 We will now address some issues related to multi stage sampling and cluster effects You will find the answers using in your computer the simulator Juan showed in the previous session Open the Excel book Lesson4, enable macros and wait for the questions If you don t have a computer, sit next to a colleague and observe attentively Please join this room s channel 2

3 Warming up Let us reproduce Juan s experiment Open the Lesson4 workbook with the following initial parameters: Selected city blocks: 5 Persons selected per city block: 12 (Sample size: 60) What is the standard error? (Remember that the standard error is the limit value of the root mean square error) 3

4 5 city blocks 12 persons per city block (n=60) What is the standard error? 1. About 6% 2. About 13 % 3. About 2 4. About 4 5. None of the above

5 5 city blocks 12 persons per city block (n=60) What would be the standard error of a SRS of the same size? 1. About 6% 2. About 13 % 3. About 2 4. About 4 5. None of the above

6 5 city blocks 12 persons per city block (n=60) What is the design factor (deft)? 1. About 6% 2. About 13 % 3. About 2 4. About 4 5. None of the above

7 5 city blocks 12 persons per city block (n=60) What is the design effect (deff)? 1. About 6% 2. About 13 % 3. About 2 4. About 4 5. None of the above

8 6 city blocks 10 persons per city block (n=60) What is the design effect (deff)? 1. About About 2 3. About 3 4. About 4 5. None of the above

9 12 city blocks 5persons per city block (n=60) What is the design effect (deff)? 1. About About 2 3. About 3 4. About 4 5. None of the above

10 Summary Sample size (n) Number of PSUs (k) Electors per PSU (m) Standard error (2 stage) Standard error of a SRS of the same size Design factor Deft Design effect Deff

11 How can we reduce the design effect for a given sample size? 1. Increasing the number of city blocks 2. Increasing the population size 3. Increasing the prevalence 4. Increasing the number of persons per city block 5. None of the above

12 Which of the following statements is false? 1. The design factor (deft) is the ratio between the standard error of our sample and the standard error of a SRS of the same size 2. The design effect (deff) is the ratio between our sample size and the size of a SRS with the same standard error 3. If the population is big, the design effect can be ignored 4. The design effect is the square of the design factor 5. The design effect of a SRS is 1 6. The design factor of a SRS is 1 0% 6

13 Switching to organic cotton farming

14 Switching to organic cotton farming The ACFI (Association of Cotton Farmers of India) is active in nine states The association conducted a telephone survey to estimate how many of its members would be willing to switch to organic farming The sample was a SRS of the in each state

15 Switching to organic cotton farming The table shows the chosen stratification and the survey results Some numbers are missing because of a printing error, but there is enough information in the rest of the table to reconstruct it You have 10 minutes to find the missing numbers. You can do it by hand on the printout, or use the Excel book Session 2B State Total number of Number of interviewed Of which, willing to switch to organic farming Estimated willingness to switch Andhra Pradesh 10, % Gujarat 1, % Haryana 18,700 1, % Karnataka 8, Madhya Pradesh 10, % Maharashtra 28,000 1, Punjab 26,500 1, % Rajasthan 31, % Tamil Nadu % All India 163,000 7,000 1,900

16 What is the value of A? State Total number of Number of interviewed Of which, willing to switch to organic farming Estimated willingness to switch Andhra Pradesh 10, % Gujarat A 1, % Haryana 18,700 1, % Karnataka 8, C Madhya Pradesh 10, % Maharashtra 28,000 1, D Punjab 26,500 1, % Rajasthan 31,300 B % Tamil Nadu % All India 163,000 7,000 1,900 E 1. 22, , , , ,000

17 What is the value of B? State Total number of Number of interviewed Of which, willing to switch to organic farming Estimated willingness to switch Andhra Pradesh 10, % Gujarat A 1, % Haryana 18,700 1, % Karnataka 8, C Madhya Pradesh 10, % Maharashtra 28,000 1, D Punjab 26,500 1, % Rajasthan 31,300 B % Tamil Nadu % All India 163,000 7,000 1,900 E 1. 1, , ,500

18 What is the value of C? State Total number of Number of interviewed Of which, willing to switch to organic farming Estimated willingness to switch Andhra Pradesh 10, % Gujarat A 1, % Haryana 18,700 1, % Karnataka 8, C Madhya Pradesh 10, % Maharashtra 28,000 1, D Punjab 26,500 1, % Rajasthan 31,300 B % Tamil Nadu % All India 163,000 7,000 1,900 E % % % % %

19 What is the value of D? State Total number of Number of interviewed Of which, willing to switch to organic farming Estimated willingness to switch Andhra Pradesh 10, % Gujarat A 1, % Haryana 18,700 1, % Karnataka 8, C Madhya Pradesh 10, % Maharashtra 28,000 1, D Punjab 26,500 1, % Rajasthan 31,300 B % Tamil Nadu % All India 163,000 7,000 1,900 E % % % % %

20 What is the value of E? State Total number of Number of interviewed Of which, willing to switch to organic farming Estimated willingness to switch Andhra Pradesh 10, % Gujarat A 1, % Haryana 18,700 1, % Karnataka 8, C Madhya Pradesh 10, % Maharashtra 28,000 1, D Punjab 26,500 1, % Rajasthan 31,300 B % Tamil Nadu % All India 163,000 7,000 1,900 E % % % % %

21 The correct calculation State Total number of Number of interviewed Of which, willing to switch to organic farming Weight of each respondent Estimated number of willing to switch Estimated willingness to switch Andhra Pradesh 10, , % Gujarat 28,200 1, , % Haryana 18,700 1, , % Karnataka 8, , % Madhya Pradesh 10, , % Maharashtra 28,000 1, , % Punjab 26,500 1, , % Rajasthan 31,300 1, , % Tamil Nadu % All India 163,000 7,000 1,900 38, % The estimation 1,900/7,000=27.14% is incorrect because the sample is not an equal probability sample We need to weight each respondent by the inverse of his/her selection probability The correct estimation is 38,653/163,000 =23.71% If you gave the wrong answer, don t worry. Everybody makes this mistake once! 21