lesson objectives at the end of the lesson, students can: recognize and define different sampling...
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Lesson Objectives
At the end of the lesson, students can:
• Recognize and define different sampling strategies
• Design sampling strategies
• Use the Random Digits Table and calculator to select random samples
How do we gather data?
• Surveys
• Opinion polls
• Interviews
• Studies
─ Observational
─ Retrospective (past)
─ Prospective (future)
• Experiments
How do we gather data?
Observational study - observe outcomes without imposing any treatment
Experiment - actively impose some treatment in order to observe the response
How do we gather data?
Population:
the entire group of individuals that we want information about
How do we gather data?
Census:
a complete count of the population
How do we gather data?
Census:
a complete count of the population
Why do we census? How good is a census?
Activity
Should We Census?
Why would we not census all the time?
1) Not accurate2) Very expensive3) Perhaps impossible4) If using destructive sampling, you would
destroy population • Breaking strength of soda bottles• Lifetime of flashlight batteries• Safety ratings for cars
How do we gather data?
Sample:
• A part of the population that we actually examine in order to gather information
• Use sample to generalize to population
How do we gather data?
Sampling Design:
• refers to the method used to choose the sample from the population
How do we gather data?
Sampling Frame:
• a list of every individual in the population
How do we gather data?Example:Mrs. Hood wants to find out what the Wake County high school students think about the effectiveness of their math teachers.
a) Mrs. Hood sends out a survey to 1500 high school students randomly selected from the Wake County Public Schools records. 941 surveys are returned, indicating that 80% of the respondents believe their math teacher is effective.
What is the population?What is the sampling frame?
Types of Sampling Design
Simple Random Sample (SRS):
consist of n individuals from the population chosen in such a way that every individual has an equal chance of being selected every set of n individuals has an equal chance of being selected
Types of Sampling Design
Stratified Random Sample:
• population is divided into homogeneous groups called strata
• SRS’s are pulled from each strata
Types of Sampling Design
Systematic Random Sample:• select sample by following a
systematic approach
• randomly select where to begin
Types of Sampling Design
Cluster Sample:
• based upon location
• randomly pick a location & sample all there
Types of Sampling Design
Multistage Sample:
• select successively smaller groups within the population in stages
• SRS used at each stage
The Pros and the Cons
SRS• Advantages
–Unbiased–Easy
• Disadvantages–Large variance–May not be
representative–Must have
sampling frame (list of population)
The Pros and the Cons
Stratified Random Sample• Advantages
– More precise unbiased estimator than SRS
– Less variability
– Cost reduced if strata already exists
• Disadvantages–Difficult to do if
you must divide stratum
–Formulas for SD & confidence intervals are more complicated
–Need sampling frame
The Pros and the Cons
Systematic Random Sample• Advantages
– Unbiased– Ensure that
the sample is distributed across population
– More efficient, cheaper, etc.
• Disadvantages–Large variance–Can be
confounded by trend or cycle
–Formulas are complicated
The Pros and the Cons
Cluster Sample• Advantages
– Unbiased – Cost is
reduced– Sampling
frame may not be available (not needed)
• Disadvantages–Clusters may
not be representative of population
–Formulas are complicated
Identify the Sampling Design
The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, etc.) Then they randomly selected 3 colleges from each group.
Identify the Sampling Design
A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks.
Identify the Sampling Design
A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer, and to every 10th customer after them, to fill it out before they leave.
Random Digits Table
• each entry is equally likely to be any of the 10 digits
• digits are independent of each other
101 19223 95034 05756 28713 96409 12531 42544 82853
102 73676 47150 99400 01927 27754 42648 82425 36290
103 45467 71709 77558 00095 32863 29485 82226 90056
104 52711 38889 93074 60227 40011 85848 48767 52573
Using the Random Digits TableSuppose your population consisted of these 20 people: 1) Aidan 6) Fred 11) Kathy 16) Paul2) Bob 7) Gloria 12) Lori 17) Shawnie3) Chico 8) Hannah 13) Matthew 18) Tracy4) Doug 9) Israel 14) Nan 19) Uncle Sam5) Edward 10) Jung 15) Opus 20) Vernon
Use the Random Digits Table to select a sample of five from these people. Start at line 101.
101 19223 95034 05756 28713 96409 12531 42544 82853
102 73676 47150 99400 01927 27754 42648 82425 36290
103 45467 71709 77558 00095 32863 29485 82226 90056
104 52711 38889 93074 60227 40011 85848 48767 52573
Using the Random Digits TableSuppose your population consisted of these 20 people: 1) Aidan 6) Fred 11) Kathy 16) Paul2) Bob 7) Gloria 12) Lori 17) Shawnie3) Chico 8) Hannah 13) Matthew 18) Tracy4) Doug 9) Israel 14) Nan 19) Uncle Sam5) Edward 10) Jung 15) Opus 20) Vernon
Seed your calculator to 1234. Then select five from these people.
Homework
Read Textbook pages 207-225
Do exercises 4.1—pp. 226-230/#1, 3, 5, 6, 8, 9, 11, 12, 15, 19, 21, 37-42
Check answers to odd problems
Be prepared for a HW quiz!
Lesson Objectives
At the end of the lesson, students can:
• Recognize and define different sampling strategies
• Design sampling strategies
• Use the Random Digits Table and calculator to select random samples