APSTAT Section 3 Experimental Design

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APSTAT Section 3Experimental Design
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Chapter 11Simulation
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• HOW TO SET UP
• Describe the experiment
• Assumptions
• Independence
• Percentages
• Randomization
• Assign Digits (Table)
• Explain TI83 procedure
• Conduct Multiple Simulations
• Conclusion (Estimate Probability)

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Simulated Simulation Problem

• David Gamburd is a 70 Free Throw Shooter. One
  game he made only 4 out of 10 free throws and
  felt very sad. Is this a rare occurrence?

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Describe Simulation

• David, being a 70 shooter would be expected to
  make 7 out of 10 free throws. In order to
  determine the experimental probability of his 4
  for 10 performance, I will conduct a simulation
  with 20 repetitions.

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Assumptions

• Each free throw is independent of the next free
  throw
• David has a 70 chance of making each attempt

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Assign Digits

• Let the digits 0-6 be makes and 7-9 be misses

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Conduct Simulations

• Use Line 104 and group in 10s, tally how many of
  the simulations end up with 4 or fewer makes

104 52711 38889 93074 60227 40011 85848
48767 52573 105 95592 94007 69971 91481
60779 53791 17297 59335 106 68417 35013
15529 72765 85089 57067 50211 47487 107
82739 57890 20807 47511 81676 55300 94383
14893 108 60940 72024 17868 24943 61790
90656 87964 18883
1. BOX OUT EACH SIMULATION
2. IDENTIFY MAKES AND MISSES Makes leave
blank Misses
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Conclusions

• In the simulation, only 2 of the 20 simulations
  resulted in a 4 of 10 performance or lower.
• Based on our simulation, we estimate that David
  would hit 4 or fewer free throws (out of 10)
  about 10 of the time.

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Do same Simulation Using TI83

• EXPLAIN Randomization
• Using my TI83, I will use a random integer
  program to spit out 10 integers between 1 and 10.
  1 through 7 will represent a make and 9
  through 10 will represent a miss
• I will then count the number of makes in each
  group of ten

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Conduct Simulation
Randint(1,10,10)

• Trial makes
• 1 7
• 2 6
• 3 7
• 4 7
• 5 9
• 6 5
• 7 7
• 8 6
• 9 8
• 10 7

Trial makes 11 8 12 5 13
6 14 4 15 7 16 8 17
6 18 5 19 7 20 7
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Chapter 12Surveys/Samples
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Sample Surveys

• Why a Sample?
• Asking everyone in a population may be impossible
  or cost-prohibitive
• ie. Field Day T-Shirts
• 2004 Too many L and XL
• Molly does survey of SR Girls sizes
• I extend(ish) percentages to other classes
• People are happier
• Idea is to get data that is representative of the
  larger group as a whole.

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A Little Vocab

• Population
• Whole group we want info on
• In Field Day example, population is WPS high
  schoolers
• Sample
• Part of the population whom we get the info from
• In Field Day example, sample was 17 senior girls

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Types O Samples

• Voluntary Response
• People decide for themselves whether to
  participate or not
• Radio opinion surveys
• Not a good sampling option
• Convenience Sampling
• Take sample of individuals easiest to reach.
• Field Day T-shirts
• Not a good sampling option

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Are there any good sample designs out there? Yep!

• SIMPLE RANDOM SAMPLE (SRS)
• Selecting individuals at random without
  replacement.
• Every member in the population has an EQUAL
  chance of being selected
• ie. Pick 5 names out of a hat

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SRS HOW TO

• Assign all individuals in population a number
  from 1 to n (nin population)
• Use a random number generator or a table of
  random numbers to choose the desired of
  individuals for your sample

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Lets Do One!!!! (CALC)

• Choose an SRS of 5 Priory APStat Students.

1 List all Students
Ted Whitney Alicia Steph Yoon-Young Lampert Marian
a
1 2 3 4 5 6 7
8 9 10 11 12 13 14
Sharuch Munger Sean Leah Chrissa Alexa Blaine
2 Assign s
3 Use MATHgt PRBgt RndInt(1,14,5)
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Lets Do One!!!! (TABLE)

• Choose an SRS of 5 Priory APStat Students.

1 List all Students
Ted Whitney Alicia Steph Yoon-Young Lampert Marian
a
1 2 3 4 5 6 7
8 9 10 11 12 13 14
Sharuch Munger Sean Leah Chrissa Alexa Blaine
2 Assign s
3 Use Tbl o Rnd Digits. Line 104
104 52711 38889 93074 60227 40011 85848
48767 52573 105 95592 94007 69971 91481
60779 53791 17297 59335
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Stratified Random Sample

• Do not call this an SRS!!!!!!!!!!!!
• Ex. I want a sample of 12 WPS High School
  Students but it may be important to have all 4
  classes represented
• Strata 4 Classes
• Separate entire Pop into strata and then do an
  SRS of 3 from each strata

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More Vocab

• Non-Response Members of Population are chosen,
  but can not be contacted (no phone, _at_ work)
• Response Bias
• Wording agree or disagree, the taking of
  anothers life should never be condoned
• Appearance/Attitude of interviewer
• Honesty of responders

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Chapter 13Designing Experiments
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Experimental Design

• Observational study
• Checking out individuals and measuring variables
  of interest without actually imposing a
  treatment. Surveys are a type.
• Experiment
• DELIBERATELY imposing some form of treatment(s)
  on individuals and observing their responses.

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Factors/Levels/Treatments

• Factor
• Explanatory variable(s) in an experiment
• Can have multiple levels
• Example
• Steroid Use - Cream and Clear

The factor clear has 3 levels
clear
The factor cream has 2 levels
tongue pill inhaler
25mg
50mg
cream
This gives us 6 total treatments
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Comparative Experiment

• Treatment gt Observation
• 4th grade plant experiments
• Observe gt Treatment gt Observe
• Rogaine!!!!!
• Problem 1 PLACEBO EFFECT
• Vitamin C Example
• To Combat Placebo Effect, Use a CONTROL GROUP!

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Completely Randomized Experiment

• Vitamin C Experiment

Group1
Treatment1
Random Allocation
Compare
Group2
Treatment2
IMPORTANT! You may not be dealing with an SRS,
so do not state that you have one. Random
allocation is not an SRS.
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Completely Randomized Experiment

• Cream and Clear

Group1
Treatment1
Group2
Treatment2
Random Allocation
Group3
Treatment3
Compare
Group4
Treatment4
Group5
Treatment5
Group6
Treatment6
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Double Blind

• Subjects dont know which treatment
• People who administer treatment dont know

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Block Design

• Blocks help control lurking variables
• Blocking creates groups that are similar with
  respect to the blocking factor(s)
• Treatments assigned randomly in each block

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Room Temperature vs. Calculus Exam Grade

• Temp Is Explanatory Variable
• 4 sections
• 2 _at_ 75 degrees, 2 _at_ 65 degrees
• If we find higher scores in 65 degree classes can
  we conclude that a lower temperature results in
  higher grades?
• What lurking variables???

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Room Temperature vs. Calculus Exam Grade

• Say we control everything but teacher. Two Calc
  Teachers w/ two sections each.Block for teacher!

75 degree
Compare
Teacher1
65 degree
Subjects
Compare
75 degree
Teacher2
Compare
65 degree
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Matched Pairs

• Type of Blocked design
• Two treatments
• Each block 2 similar units/individuals
• Assigned randomly to treatments
• Example Effect of a cancer fighting drug.
  Researchers are concerned that age may be a
  lurking variable

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Matched Pairs
SUBJECT AGE 1 25 2 27 3 32
4 35 5 36 6 37 7 43 8
46 9 56 10 60
Older people may be more prone to cancer with or
without the treatment and if I did a random
allocation, there is a chance I could have mostly
older people in one group and mostly younger ones
in the other
TREATMENT 1
TREATMENT 2
TREATMENT 2
TREATMENT 1
TREATMENT 2
SoMatch up subjects with similar traits in
terms of the variable I wish to block for. In
this case, age.
TREATMENT 1
TREATMENT 1
TREATMENT 2
Randomly allocate treatments in each pair.
Compare each pair. Compare the pairs!
TREATMENT 2
TREATMENT 1
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Matched Pairs Another Way

• One Individual
• Both Treatments
• One after the other
• Order may matter
• Randomize to determine which goes 1st
• Example
• Hand Squeezing Strength Experiment

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Hand Squeezing Strength Experiment

• Is your strong hand really stronger than your
  weak hand?
• Subject may be a better squeezers the 2nd time

Compare individual differences S-W
Strong
Group1 Strong 1st
Weak
Random allocation
Subjects
Compare
Weak
Compare individual differences S-W
Group2 Strong 2nd
Strong