Section 4.2 Random Sampling

Quiz 4.1 – 4.2 -- no notes

Is bias in our sampling method good or bad? Explain.

If sample selection bias is present in a sampling method, samples tend to result in estimates of population parameters that systematically are too high or too low.

Protecting Against Bias Selecting your sample by chance is the only method guaranteed to be unbiased.

Protecting Against Bias Probability sample: each unit in population has fixed probability of being in the sample

Types of Probability Samples

Types of Probability Samples Simple Random Sample (SRS)

Types of Probability Samples Simple Random Sample (SRS) Stratified Random Sample

Types of Probability Samples Simple Random Sample (SRS) Stratified Random Sample Cluster Sample

Types of Probability Samples Simple Random Sample (SRS) Stratified Random Sample Cluster Sample Two-Stage Cluster Sample

Types of Probability Samples Simple Random Sample (SRS) Stratified Random Sample Cluster Sample Two-Stage Cluster Sample Systematic Sampling with Random Start

Simple Random Sample Simple random sampling: all possible samples of a given fixed size are equally likely.

Simple Random Sample Simple random sampling: all possible samples of a given fixed size are equally likely. all units have the same chance of belonging to the sample

Simple Random Sample Simple random sampling: all possible samples of a given fixed size are equally likely. all units have the same chance of belonging to the sample all possible pairs of units have the same chance of belonging to the sample

Simple Random Sample Simple random sampling: all possible samples of a given fixed size are equally likely. all units have the same chance of belonging to the sample all possible pairs of units have the same chance of belonging to the sample all possible triples of units have the same chance, and so on

Choosing a Simple Random Sample Steps: 1.  Start with a list of all the units in the population (list is known as a sampling frame).

Choosing a Simple Random Sample Steps: 1.  Start with a list of all the units in the population (list is known as a frame). 2.  Number the units in the list.

Choosing a Simple Random Sample Steps: 1.  Start with a list of all the units in the population (list is known as a frame). 2.  Number the units in the list. 3.  Use a random number table or generator to choose units from the numbered list, one at a time, until you have as many as you need

Choosing a Simple Random Sample random number table: see page 828

Choosing a Simple Random Sample random number generator (calculator): To generate random integers between 0 and 99: Press MATH Arrow right to select PRB Arrow down to select 5: randInt( Enter expression randInt( 0, 99) Press ENTER to generate as many integers as needed

Choosing a Simple Random Sample Display 4.8, page 240

Stratified Random Sampling Steps:  Divide the units of the entire sampling frame into non-overlapping subgroups. -- Make strata as different as possible

Stratified Random Sampling Steps:  Divide the units of the entire sampling frame into non-overlapping subgroups. -- Make strata as different as possible Take a simple random sample from each subgroup -- Allocate units in sample proportionally to number of units in the strata

Stratified Random Sampling

Stratified Random Sampling 32 Females 16 Males

Why Stratify? Easier to sample in smaller, compact groups than in one large population

Why Stratify? Easier to sample in smaller, compact groups than in one large population Coverage of each stratum is ensured

Why Stratify? Easier to sample in smaller, compact groups than in one large population Coverage of each stratum is ensured Precision of results may be improved. Fundamental statistical reason for stratification

Problems?? May encounter problems using simple random samples and stratified random samples. Sampling individual units from population one at a time is often: too costly too time consuming simply not possible if a good frame is not available

Solution Form larger sampling units out of groups of population units

Cluster Sampling Steps: Create a numbered list of all the clusters in your population.

Cluster Sampling Steps: Create a numbered list of all the clusters in your population. Take a simple random sample of clusters.

Cluster Sampling Steps: Create a numbered list of all the clusters in your population. Take a simple random sample of clusters. Obtain data on each individual in each cluster in your SRS

Cluster Sampling

Two-Stage Cluster Sampling Steps: Create a numbered list of all the clusters in your population, and then take a simple random sample of clusters.

Two-Stage Cluster Sampling Steps: Create a numbered list of all the clusters in your population, and then take a simple random sample of clusters. Create a numbered list of all the individuals in each cluster already selected, and then take an SRS from each cluster

Two-Stage Cluster Sampling

Cluster vs Two-Stage Cluster Uses SRS once Uses SRS twice

Systematic Sampling with Random Start Steps:  By a method such as counting off, divide your population into groups of the size you want for your sample.

Systematic Sampling with Random Start Steps:  By a method such as counting off, divide your population into groups of the size you want for your sample. Use a chance method to choose one of the groups for your sample

Systematic Sampling with Random Start

To select students to explain homework problems, a teacher has students count off by 5’s. She then randomly selects an integer from 1 through 5. Every student who counted off that integer is asked to explain a problem. What type of sampling plan is this? A. cluster B. two-stage cluster C. simple random D. stratified random E. systematic with random start

To select students to explain homework problems, a teacher has students count off by 5’s. She then randomly selects an integer from 1 through 5. Every student who counted off that integer is asked to explain a problem. What type of sampling plan is this? A. cluster B. two-stage cluster C. simple random D. stratified random E. systematic with random start

Questions? Selecting your sample by chance is the only method guaranteed to be unbiased

Fathom Activity 4.2a Complete steps 1 and 2 before you come to class tomorrow.