Estimation of Sampling Errors, CV, Confidence Intervals Arun Srivastava

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?

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

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

PPSWR Sampling

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

Stratified sampling Estimator of total and estimated variance are

Cluster sampling Estimator of mean and variances are

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

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.

Multi-stage Sampling Estimator of total Variance

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

Multi-stage Sampling (Contd.) Estimator of variance

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

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)

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