Standard errors and confidence intervals in within-subject ...
Estimation of Sampling Errors, CV, Confidence Intervals
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Transcript of Estimation of Sampling Errors, CV, Confidence Intervals
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Arun Srivastava
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Properties of a good EstimatorUnbiasednessEfficiency
Variance measures precision of an estimator Mean square error measures it’s accuracy
ConsistencyConcept of BiasWhy estimation of sampling error is so
important?
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Simple random sampling (SRS): Sample mean is an unbiased estimator of
population mean.
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Systematic SamplingAn approximate estimator of variance is
If population is assumed to be in random order
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PPSWR Sampling
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Varying probability sampling (without replacement):Horvitz –Thompson estimator
For IPPS
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Stratified samplingEstimator of total and estimated variance are
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Cluster sampling
Estimator of mean and variances are
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Cluster Sampling (Contd.)Estimator of variance
Variance formula is also given by
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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.
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Multi-stage SamplingEstimator of total
Variancei
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Multi-stage Sampling (Contd.)Estimator of variance
In case of equal clusters
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Multi-stage Sampling (Contd.)Estimator of
variance
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Sample weights Base weights Non response adjustments Post-stratification adjustments Base weights are inverse of selection
probabilities Weights provided to ultimate sampling
units
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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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