5.1: Simple Random Samples

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5.1 Simple Random Samples

• Simple Random Sample (SRS) n individuals from
  the population chosen such that every set of n
  individuals has an equal chance to be the sample
  actually selected.
• Note not only does each individual have an equal
  chance of being selected, but each group has an
  equal chance. Something that would violate this
  would be randomly picking two people from each
  row

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Table of Random Numbers

• A table can be given that represents a list of
  completely random numbers it is essentially
  like picking from a hat
• Each entry is equally likely to be any digit
• The entries are independent on each other one
  does not influence the other

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Using Table B

• Assign a number to everyone in your population.
  Make sure each number is equally likely to come
  up.
• For 25 subjects assign them each a number 00
  24 OR 01 25
• For 225 subjects assign them each a number 000
  224 or 001 225
• What is more effective, assigning numbers
  alphabetically or by rows of desks?

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Using Table B ctd

• Pick a line on the table to start with
• Note that the lines are numbered 101 and up, but
  do NOT use those numbers
• It does not matter what row you choose to start
  with
• Start underlining numbers of however many digits
  are appropriate one at a time
• Circle the first number you get to that is also
  one of your subjects.
• Continue along the line until you have filled all
  the spots that you need.

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• Use Table B to come up with a SRS of 5 students
  from a group of 50.

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Other Sampling Designs

• Probability Sample sample chosen by chance
  does not have to be equal chances for each sample
• Essential piece is that chance is used to select
  the sample
• Ex. Roll a die for each subject, if they get a
  1, they are chosen to be in the study

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• Stratified Random Sample (used only in surveys
  or studies)
• 1. Divide the population into groups or strata
• 2. Choose a separate SRS from each strata
• Ex. I want to know the voting habits of all
  teachers in the U.S. What are some possible ways
  to divide this population?
• Cluster Sampling the population is divided into
  groups(clusters) and some clusters are randomly
  selected with everyone in the cluster being in
  the sample.
• Ex. You want to know the of students who think
  they have enough time to finish the SAT math.
  You cluster students by high school, then
  randomly select high schools and survey every
  student that took the SAT in that school.

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• Given the following list, explain in detail how
  you will randomly select 5 people
• Ames
• Anderson
• Smith
• Johnson
• Jackson
• Yates
• Kruczek
• Shay
• Santoro
• Perillo
• Tokarska
• Zipoli
• Strzpek
• Unger
• Pudlinski
• Wustrow
• Evans