Estimation of Sampling Errors CV Confidence Intervals Arun

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 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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