Stratified and Cluster Sampling

Robb T. Koether Stratified and Cluster Sampling Introduction Stratified Lecture 8 Random Samples Sections 2.6, 2.8 Example

Estimating Parameters

Cluster Robb T. Koether Samples Example Hampden-Sydney College Stratified vs. Cluster Assignment Tue, Jan 27, 2008 Outline

Stratified and Cluster Sampling 1 Introduction Robb T. Koether 2 Stratified Random Samples Introduction

Stratified Example Random Samples Example 3 Estimating Parameters Estimating Parameters 4 Cluster Samples Cluster Samples Example Example

Stratified vs. Cluster 5 Stratified vs. Cluster Assignment 6 Assignment Introduction

Stratified and Cluster Sampling Suppose we know that our population is 60% male and Robb T. Koether 40% female.

Introduction Wouldn’t it make sense to ensure that our sample is Stratified also 60% male and 40% female. Random Samples Example After all, our goal is representativeness, not

Estimating randomness, right? Parameters If our sample size were n = 100, we could Cluster Samples Select a simple random sample of 60 males. Example Select a simple random sample of 40 females. Stratified vs. Cluster Is this a good idea? Assignment If we left it to chance, we might end up with 50 males and 50 females. Introduction

Stratified and Cluster Sampling Suppose we know that our population is 60% male and Robb T. Koether 40% female.

Introduction Wouldn’t it make sense to ensure that our sample is Stratified also 60% male and 40% female. Random Samples Example After all, our goal is representativeness, not

Estimating randomness, right? Parameters If our sample size were n = 100, we could Cluster Samples Select a simple random sample of 60 males. Example Select a simple random sample of 40 females. Stratified vs. Cluster Is this a good idea? Assignment If we left it to chance, we might end up with 50 males and 50 females. Introduction

Stratified and Cluster Sampling Suppose we know that our population is 60% male and Robb T. Koether 40% female.

Introduction Wouldn’t it make sense to ensure that our sample is Stratified also 60% male and 40% female. Random Samples Example After all, our goal is representativeness, not

Estimating randomness, right? Parameters If our sample size were n = 100, we could Cluster Samples Select a simple random sample of 60 males. Example Select a simple random sample of 40 females. Stratified vs. Cluster Is this a good idea? Assignment If we left it to chance, we might end up with 50 males and 50 females. Introduction

Stratified and Cluster Sampling Suppose we know that our population is 60% male and Robb T. Koether 40% female.

Introduction Wouldn’t it make sense to ensure that our sample is Stratified also 60% male and 40% female. Random Samples Example After all, our goal is representativeness, not

Estimating randomness, right? Parameters If our sample size were n = 100, we could Cluster Samples Select a simple random sample of 60 males. Example Select a simple random sample of 40 females. Stratified vs. Cluster Is this a good idea? Assignment If we left it to chance, we might end up with 50 males and 50 females. Introduction

Stratified and Cluster Sampling Suppose we know that our population is 60% male and Robb T. Koether 40% female.

Introduction Wouldn’t it make sense to ensure that our sample is Stratified also 60% male and 40% female. Random Samples Example After all, our goal is representativeness, not

Estimating randomness, right? Parameters If our sample size were n = 100, we could Cluster Samples Select a simple random sample of 60 males. Example Select a simple random sample of 40 females. Stratified vs. Cluster Is this a good idea? Assignment If we left it to chance, we might end up with 50 males and 50 females. Introduction

Stratified and Cluster Sampling Suppose we know that our population is 60% male and Robb T. Koether 40% female.

Introduction Wouldn’t it make sense to ensure that our sample is Stratified also 60% male and 40% female. Random Samples Example After all, our goal is representativeness, not

Estimating randomness, right? Parameters If our sample size were n = 100, we could Cluster Samples Select a simple random sample of 60 males. Example Select a simple random sample of 40 females. Stratified vs. Cluster Is this a good idea? Assignment If we left it to chance, we might end up with 50 males and 50 females. Introduction

Stratified and Cluster Sampling Suppose we know that our population is 60% male and Robb T. Koether 40% female.

Introduction Wouldn’t it make sense to ensure that our sample is Stratified also 60% male and 40% female. Random Samples Example After all, our goal is representativeness, not

Estimating randomness, right? Parameters If our sample size were n = 100, we could Cluster Samples Select a simple random sample of 60 males. Example Select a simple random sample of 40 females. Stratified vs. Cluster Is this a good idea? Assignment If we left it to chance, we might end up with 50 males and 50 females. Introduction

Stratified and Cluster Sampling Suppose we know that our population is 60% male and Robb T. Koether 40% female.

Introduction Wouldn’t it make sense to ensure that our sample is Stratified also 60% male and 40% female. Random Samples Example After all, our goal is representativeness, not

Estimating randomness, right? Parameters If our sample size were n = 100, we could Cluster Samples Select a simple random sample of 60 males. Example Select a simple random sample of 40 females. Stratified vs. Cluster Is this a good idea? Assignment If we left it to chance, we might end up with 50 males and 50 females. Introduction

Stratified and Cluster Sampling

Robb T. Koether

Introduction On the other hand, is this necessary? Stratified What is we did end up with 50 males and 50 females? Random Samples Example Suppose male opinion in our sample was divided 20

Estimating yes, 30 no and female opinion was divided 10 yes, 40 Parameters no. Cluster Samples How would we come up with an overall estimate for the Example

Stratified vs. proportion of yeses in the population? Cluster

Assignment Introduction

Stratified and Cluster Sampling

Robb T. Koether

Introduction On the other hand, is this necessary? Stratified What is we did end up with 50 males and 50 females? Random Samples Example Suppose male opinion in our sample was divided 20

Estimating yes, 30 no and female opinion was divided 10 yes, 40 Parameters no. Cluster Samples How would we come up with an overall estimate for the Example

Stratified vs. proportion of yeses in the population? Cluster

Assignment Introduction

Stratified and Cluster Sampling

Robb T. Koether

Introduction On the other hand, is this necessary? Stratified What is we did end up with 50 males and 50 females? Random Samples Example Suppose male opinion in our sample was divided 20

Estimating yes, 30 no and female opinion was divided 10 yes, 40 Parameters no. Cluster Samples How would we come up with an overall estimate for the Example

Stratified vs. proportion of yeses in the population? Cluster

Assignment Introduction

Stratified and Cluster Sampling

Robb T. Koether

Introduction On the other hand, is this necessary? Stratified What is we did end up with 50 males and 50 females? Random Samples Example Suppose male opinion in our sample was divided 20

Estimating yes, 30 no and female opinion was divided 10 yes, 40 Parameters no. Cluster Samples How would we come up with an overall estimate for the Example

Stratified vs. proportion of yeses in the population? Cluster

Assignment Stratified Random Sample

Stratified and Cluster Sampling Definition (Homogeneous) Robb T. Koether A group is homogeneous if its member all have similar

Introduction characteristics with regard to the variables of interest.

Stratified Random Samples Definition (Stratum) Example

Estimating A stratum is a homogeneous subset of the population. Parameters

Cluster Samples Definition (Stratified random sampling) Example

Stratified vs. Stratified random sampling is a sampling method in which Cluster the population is first divided into strata. Then a simple Assignment random sample is taken from each stratum. The results constitute the sample. Examples

Stratified and Cluster Sampling

Robb T. Koether

Introduction Stratified Possible strata: Random Samples Male and female strata. Example Resident and non-resident strata. Estimating Parameters White, black, Hispanic, and Asian strata.

Cluster Protestant, Catholic, Jewish, Muslim, etc., strata. Samples Example

Stratified vs. Cluster

Assignment Stratified Random Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified Random Samples Example

Estimating Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The population Stratified Random Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified Random Samples Example

Estimating The population Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The strata Stratified Random Sampling

Stratified and Cluster Sampling

Robb T. Random sample from this stratum Koether

Introduction

Stratified Random Samples Example

Estimating The population Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The strata Stratified Random Sampling

Stratified and Cluster Sampling

Robb T. Random sample from this stratum Koether

Introduction

Stratified Random Samples Example

Estimating The population Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The strata Stratified Random Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified Random Samples Example

Estimating The population Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment Random samples from all strata Stratified Random Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified Random Samples Example

Estimating Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The stratified sample Example

Stratified and Cluster Sampling

Robb T. Koether Example (Stratified random sample) Introduction

Stratified Let the population consist of males Anthony, Benjamin, Random Christopher, Daniel, Ethan, Francisco, Gabriel, and Samples Example Hunter and females Isabella, Jasmine, Kayla, Lily, Estimating Parameters Madison, Natalie, Olivia, and Paige. Cluster Choose a stratified sample of size n = 8, where the Samples Example strata are the two sexes. Stratified vs. Cluster Is the sample representative with regard to sex?

Assignment Estimating Parameters

Stratified and Cluster Sampling

Robb T. Koether

Introduction Suppose that Stratified The population is 60% male and 40% female. Random Samples Our sample is 50% male and 50% female. Example Our variable has an average value of 10 for the males Estimating Parameters and 15 for the females. Cluster What is our best estimate for the variable’s average for Samples Example the population? Stratified vs. Cluster

Assignment Estimating Parameters

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified We need to compute a weighted average. Random Samples Example average = (0.60)(10) + (0.40)(15) Estimating Parameters = 6 + 6 Cluster = 12 Samples Example

Stratified vs. Cluster

Assignment Cluster Sampling

Stratified and Cluster Sampling Definition (Heterogeneous) Robb T. Koether A group is heterogeneous if is members vary in regard to the variables of interest in the same way that the population Introduction varies. Stratified Random Samples Example Definition (Cluster) Estimating Parameters A cluster is a heterogeneous subset of the population.

Cluster Samples Example Definition (Cluster random sampling) Stratified vs. Cluster Cluster random sampling is a sampling method in which the Assignment population is first divided into clusters. Then a simple random sample of clusters is taken. All the members of the selected clusters together constitute the sample. Cluster Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified Random Note that it is the clusters that are selected at random, Samples Example not the individuals. Estimating It is hoped that each cluster by itself is representative of Parameters the population, i.e., each cluster is heterogeneous. Cluster Samples Example

Stratified vs. Cluster

Assignment Cluster Random Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified Random Samples Example

Estimating Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The population Cluster Random Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified Random Samples Example

Estimating The population Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The clusters Cluster Random Sampling

Stratified and Cluster Sampling Robb T. Randomly select some clusters Koether

Introduction

Stratified Random Samples Example

Estimating The population Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The clusters Cluster Random Sampling

Stratified and Cluster Sampling Robb T. Selected all member in the clusters Koether

Introduction

Stratified Random Samples Example

Estimating The population Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The clusters Cluster Random Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction

Stratified Random Samples Example

Estimating Parameters

Cluster Samples Example

Stratified vs. Cluster

Assignment The cluster sample Example

Stratified and Cluster Sampling

Robb T. Koether

Introduction Example (Cluster sample) Stratified Now suppose that Random Samples Anthony, Benjamin, Isabella, and Jasmine live in Example Fredericksburg. Estimating Parameters Christopher, Daniel, Kayla, and Lily live in Richmond.

Cluster Ethan, Francisco, Madison, and Natalie live in Samples Charlottesville. Example

Stratified vs. Gabriel, Hunter, Olivia, and Paige live in Roanoke. Cluster

Assignment Example

Stratified and Cluster Sampling

Robb T. Koether

Introduction Stratified Example (Cluster sample) Random Samples Example Use cluster sampling to choose a sample of size n = 8, Estimating where the clusters are the cities. Parameters

Cluster Is the sample representative with regard to sex? Samples Example

Stratified vs. Cluster

Assignment Stratified Sampling vs. Cluster Sampling

Stratified and Cluster Sampling

Robb T. Koether

Introduction In stratified sampling Stratified Random From all of the strata we take randomly selected Samples Example individuals. Estimating In cluster sampling Parameters

Cluster From randomly selected clusters we take all of the Samples individuals. Example

Stratified vs. Cluster

Assignment Assignment

Stratified and Cluster Sampling

Robb T. Koether

Introduction Homework Stratified Random Samples Read Sections 2.6, 2.8, pages 108 - 115, 122 - 126. Example Let’s Do It! 2.6, 2.8. Estimating Parameters Page 115, exercises 19 - 23, 25. Cluster Samples Page 126, exercises 35 - 38. Example

Stratified vs. Cluster

Assignment