1. Estimation of Sampling Errors, CV, Confidence Intervals
Arun Srivastava

2. Properties of a good Estimator
Unbiasedness
Efficiency
Variance measures precision of an estimator
Mean square error measures it’s accuracy
Consistency
Concept of Bias
Why estimation of sampling error is so important?

3. Simple random sampling (SRS):
Sample mean is an unbiased estimator of population mean.
; SRSWR
SRSWOR

4. Systematic Sampling An approximate estimator of variance is
If population is assumed to be in random order

5. PPSWR Sampling

6. Varying probability sampling (without replacement):
Horvitz –Thompson estimator
For IPPS

7. Stratified sampling
Estimator of total and estimated variance are

8. Cluster sampling
Estimator of mean and variances are

9. Cluster Sampling (Contd.)
Estimator of variance
Variance formula is also given by

10. Cluster Sampling (Contd.)
Intra-class correlation
Intra-class correlation is the correlation coefficient between pair of units that are in the same cluster. It measures intra-cluster variability.

11. Multi-stage Sampling
Estimator of total
Variance

12. Multi-stage Sampling (Contd.)
Estimator of variance
In case of equal clusters

13. Multi-stage Sampling (Contd.)
Estimator of variance

14. Sample weights Base weights Non response adjustments
Post-stratification adjustments
Base weights are inverse of selection probabilities
Weights provided to ultimate sampling units

15. Sample weights (Contd.)
For unequal probability wor sampling
For two-stage sampling with pps systematic selection at the first stage and equal probability selection at the second stage weights are (define notations)

16. THANKS