Other Probability Sampling Methods

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Class Objective

After this class, you will be able to- Apply different Probability Sampling Methods

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Other Sampling MethodsNot always practical to take a simple random sample, can be difficult to get a numbered list of all units.Example: College administration would like to survey a sample of students living in dormitories.

Shaded squares show a simple random sample of 30 rooms.

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Stratified Random SamplingDivide population of units into groups (called strata) and take a simple random sample from each of the strata.

College survey: Two strata = undergrad and graduate dorms.

Take a simple random sample of 15 rooms from each of the strata for a total of 30 rooms.

Ideal: stratify so little variability in responses within each of the strata.

Advantages of Stratified Sampling • By taking a separate SRS in each stratum, we can set

sample sizes to allow separate conclusions about each stratum.

• A stratified sample usually has a smaller margin of error than an SRS of the same size because the individuals in each stratum are more alike than the population as a whole. Therefore working stratum-by stratum eliminate some variability in the sample.

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Problem of Stratified Sampling • Violate the most appealing properties of the SRS –

Stratified samples need not give all individuals in the population the same chance to be chosen. The data collected could be _b_________

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Cluster SamplingDivide population of units into groups (called clusters), take a random sample of clusters and measure only those items in these clusters.

College survey: Each floor of each dorm is a cluster.

Take a random sample of 5 floors and all rooms on those floors are surveyed.

Advantage: need only a list of the clusters instead of a list of all individuals.

Cluster Sampling

• Divide the demographic area into sections/clusters

• Randomly select sections or clusters• Include every member of the cluster in the sample• Example: divide the schools in a large city into

different sections. Randomly select a section and include all the children of the schools in the elected section as sample

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Systematic SamplingOrder the population of units in some way, select one of first k units at random and then every kth unit thereafter. College survey: Order list of rooms starting at top floor of 1st undergrad dorm. Pick one of the first 11 rooms at random room 3, then pick every 11th room after that.

Note: often a good alternative to random sampling but can lead to a biased sample.

Systematic Sampling

• Assumed the elements of the population are arranged in a “natural” sequential order

• Select a (random) starting point• Select every kth element for the sample • Example: People lining up to buy rock concert

tickets are “in order” - > include every 5th person in the line in the sample

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Systematic Sampling Example• Use systematic sampling method to select 10

representative from 280 students at TRMC• Determine the kth element for the sample

– 280 / 10 - that is every 28 students, we pick one representative

• Determine the entry point (based on the random number table)– If the entry point is 114th, then 142th will be the next

one

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Now you try it

• Use systematic sampling method to choose 4 rooms out of the 100 rooms in an apartment complex.

• Enter the Random number table at line 21• Which are the 4 rooms selected?

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Multistage SamplingUsing a combination of the sampling methods, at various stages.

Example:• Stratify the population by region of the country.

• For each region, stratify by urban, suburban, and rural and take a random sample of communities within those strata.

• Divide the selected communities into city blocks as clusters, and sample some blocks.

• Everyone on the block or within the fixed area may then be sampled.

Homework

• Assignment: –Chapter 5 Exercise 5.52 and 5.53

• Reading:–Chapter 5 – p. 159 - 165