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Stratified Random Sampling. Stratified Random Sampling. A stratified random sample is obtained by separating the population elements into non-overlapping groups, called strata Select a simple random sample from each stratum. Stratified Random Sampling….

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## Stratified Random Sampling

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**Stratified Random Sampling**• A stratified random sample is obtained by separating the population elements into non-overlapping groups, called strata • Select a simple random sample from each stratum**Stratified Random Sampling…**• Eg: sampling fish from a stream with the goal being to estimate the average length of trout • Want to know the size of fish (length) • Stream is made up of riffles, runs and pools • larger (longer) fish live in the pools • smaller fish in the riffles. • Strata = stream habitat type**Why Choose Stratification?**• Minimize uncertainty • equivalent to minimizing the variability associated with our response variable • Example • If fish in riffles are similar in length (thus small within habitat variability) then taking averages on a stratum by stratum basis will mean low variation for each average**Note with the**stratified random sample that the sampling distribution of the sample mean is characterized by less variation/uncertainty than in the simple random sample protocol.**Why Choose Stratification…**• Estimates of population parameters may be desired for subgroups of the population Eg: By stratifying on stream habitat type • You can easily provide estimates of the mean fish length for each habitat type (riffle, run, and pool) • Separate confidence intervals for each of the strata**Why Choose Stratification…**• The cost per observation in the sample may be reduced • Eg. Gear changes when habitat changes • Simple random sampling of stream sections means more gear changes**Example Data**Obtain a 95% bootstrap CI on the mean length of fish across the three habitats

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