Section 1.2

Random Samples

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Section 1.2 Objectives

• Explain the importance of random samples• Construct a simple random sample using random

numbers• Simulate a random process• Describe stratified sampling, cluster sampling,

systematic sampling, multi-stage and convenience sampling

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Sampling TechniquesSimple Random Sample• Every possible sample of the same size has the same chance of being selected.• Every individual of the population has an equal chance of being selected.

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Simple Random Sample

• Random numbers can be generated by a random number table, a software program or a calculator.

• Assign a number to each member of the population.

• Members of the population that correspond to these numbers become members of the sample.

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Example: Simple Random Sample

There are 731 students currently enrolled in statistics at your school. You wish to form a sample of eight students to answer some survey questions. Select the students who will belong to the simple random sample.

• Assign numbers 1 to 731 to each student taking statistics.

• On the table of random numbers, choose a starting place at random (suppose you start in the third row, second column.)

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Solution: Simple Random Sample

• Read the digits in groups of three• Ignore numbers greater than 731

The students assigned numbers 719, 662, 650, 4, 53, 589, 403, and 129 would make up the sample.

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Other Sampling Techniques

Stratified Sample• Divide a population into groups (strata) and select a

random sample from each group.

• To collect a stratified sample of the number of people who live in West Ridge County households, you could divide the households into socioeconomic levels and then randomly select households from each level.

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Other Sampling Techniques

Cluster Sample• Divide the population into groups (clusters) and

select all of the members in one or more, but not all, of the clusters.

• In the West Ridge County example you could divide the households into clusters according to zip codes, then select all the households in one or more, but not all, zip codes.

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Other Sampling Techniques

Systematic Sample• Choose a starting value at random. Then choose

every kth member of the population.

• In the West Ridge County example you could assign a different number to each household, randomly choose a starting number, then select every 100th household.

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Example: Identifying Sampling Techniques

You are doing a study to determine the opinion of students at your school regarding stem cell research. Identify the sampling technique used.

1. You divide the student population with respect to majors and randomly select and question some students in each major.

Solution:Stratified sampling (the students are divided into strata (majors) and a sample is selected from each major)

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Sampling Terminology

Sampling Frame: • a list of individuals from which a sample is actually

selected• ideally, should match the population

Example: When doing a phone survey, the sampling frame might be the phone book

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Sampling Undercoverage

Undercoverage: the condition resulting from omitting population members from the sample frame

Example: The phone book might not be representative of all residents of a community

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  Population  

   

       

  Sampling Frame

       

       

Sampling Terminology

Sampling Error is the mismatch between • measurements taken from samples• corresponding measurements taken from the

respective population• sampling errors do not represent mistakes!

Nonsampling Error results from- poor sample design- sloppy data collection techniques- bias in questions- nonsampling errors are inadvertent errors

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Multi-Stage Sampling

• Multi-stage sampling involves selecting a sample in at least two stages.

• Successively smaller groups are created at each stage

• Final sample consists of clusters

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Example: Three-Stage Sampling

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The following is an example of the stages of selection that may be used in a three-stage household survey.

STAGE 1: Electoral SubdivisionsElectoral subdivisions (clusters) are sampled from a city or state

STAGE 2: BlocksBlocks of houses are selected from within the electoral subdivisions.

STAGE 3: HousesHouses are selected from within the selected blocks.

Convenience Sampling

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Create a sample by using data from population members that are readily available

Example 1: Survey people in a shopping mall• Select the mall entrance closest to where you parked

your car• Stand in a location next to the coffee bar and

interview people as they are waiting on line

Example 2: Survey people attending an opera concert• Gather data regarding their musical preferences

Potential Drawback:• Your results might be severely biased!

Section 1.2 Summary

• Describe simple random samples• Construct a simple random sample using random

numbers• Simulate a random process• Describe stratified sampling, cluster sampling,

systematic sampling, multi-stage and convenience sampling

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