Transcript APSTAT Section 3 Experimental Design

APSTAT Section 3
Experimental Design
Chapter 11
Simulation
•
HOW TO SET UP
1. Describe the experiment
2. Assumptions
–
–
Independence
Percentages
3. Randomization
–
–
Assign Digits (Table)
Explain TI83 procedure
4. Conduct Multiple Simulations
5. Conclusion (Estimate Probability)
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?
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.
Assumptions
• Each free throw is independent of
the next free throw
• David has a 70% chance of making
each attempt
Assign Digits
• Let the digits 0-6 be makes and 7-9
be misses
Conduct Simulations
• Use Line 104 and group in 10’s, tally
how many of the simulations end up
with 4 or fewer makes
104
105
106
107
108
52711
95592
68417
82739
60940
38889
94007
35013
57890
72024
93074
69971
15529
20807
17868
60227
91481
72765
47511
24943
1. BOX OUT EACH SIMULATION
2. IDENTIFY MAKES AND MISSES:
Makes= leave blank
Misses=
40011
60779
85089
81676
61790
85848
53791
57067
55300
90656
48767
17297
50211
94383
87964
52573
59335
47487
14893
18883
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.
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
Conduct Simulation
Randint(1,10,10)
Trial
1
2
3
4
5
6
7
8
9
10
#makes
7
6
7
7
9
5
7
6
8
7
Trial
11
12
13
14
15
16
17
18
19
20
#makes
8
5
6
4
7
8
6
5
7
7
Chapter 12
Surveys/Samples
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.
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
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
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
SRS HOW TO
• Assign all individuals in population a
number from 1 to n (n=#in
population)
• Use a random number generator or a
table of random numbers to choose
the desired # of individuals for your
sample
Let’s Do One!!!! (CALC)
• Choose an SRS of 5 Priory APStat
Students.
#1 List all
Students
#2 Assign #’s
1 Ted
8
Sharuch
2 Whitney
9
Munger
3 Alicia
10 Sean
4 Steph
11 Leah
5 Yoon-Young 12 Chrissa
#3 Use MATH>
PRB>
RndInt(1,14,5)
6 Lampert
13 Alexa
7 Mariana
14 Blaine
Let’s Do One!!!! (TABLE)
• Choose an SRS of 5 Priory APStat
Students.
#1 List all
Students
#2 Assign #’s
1 Ted
8
Sharuch
2 Whitney
9
Munger
3 Alicia
10 Sean
4 Steph
11 Leah
5 Yoon-Young 12 Chrissa
#3 Use Tbl o’ Rnd
Digits. Line 104
104
105
6 Lampert
13 Alexa
7 Mariana
14 Blaine
52711 38889 93074 60227 40011 85848 48767 52573
95592 94007 69971 91481 60779 53791 17297 59335
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
More Vocab
• Non-Response – Members of Population are
chosen, but can not be contacted (no phone, @
work…)
• Response Bias
– Wording “agree or disagree, the taking of
another’s life should never be condoned”
– Appearance/Attitude of interviewer
– Honesty of responders
Chapter 13
Designing Experiments
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.
Factors/Levels/Treatments
• Factor
– Explanatory variable(s) in an experiment
– Can have multiple levels
• Example:
– Steroid Use - Cream and Clear
clear
cream
The factor
“cream”
has 2
levels
tongue
pill
inhaler
25mg
50mg
This gives us 6 total treatments
The factor
“clear” has
3 levels
Comparative Experiment
• Treatment > Observation
– 4th grade plant experiments
• Observe > Treatment > Observe
– Rogaine!!!!!
• Problem #1 – PLACEBO EFFECT
– Vitamin C Example
– To Combat Placebo Effect, Use a
CONTROL GROUP!
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.
Completely Randomized
Experiment
• Cream and Clear:
Random
Allocation
Group1
Treatment1
Group2
Treatment2
Group3
Treatment3
Group4
Treatment4
Group5
Treatment5
Group6
Treatment6
Compare
Double Blind
• Subjects don’t know which treatment
• People who administer treatment
don’t know
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
Room Temperature vs.
Calculus Exam Grade
• Temp Is Explanatory Variable
• 4 sections
– 2 @ 75 degrees, 2 @ 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???
Room Temperature vs.
Calculus Exam Grade
• Say we control everything but
teacher. Two Calc Teachers w/ two
sections each….Block for teacher!
75 degree
Teacher1
Compare
65 degree
Subjects
Compare
75 degree
Teacher2
Compare
65 degree
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
Matched Pairs
SUBJECT
AGE
1TREATMENT 1 25
2TREATMENT 2 27
3TREATMENT 2 32
4TREATMENT 1 35
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
5 TREATMENT 236
6 TREATMENT 137
7TREATMENT 1 43
8 TREATMENT 246
9 TREATMENT 256
10TREATMENT 160
So……Match up subjects with similar
traits in terms of the variable I wish
to block for. In this case, age.
Randomly allocate treatments in
each pair. Compare each pair.
Compare the pairs!
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
Hand Squeezing Strength
Experiment
• Is your strong hand really stronger than
your weak hand?
• Subject may be a better squeezers the 2nd
time
Compare
Strong
individual
differences
Group1
Strong 1st
Subjects
Weak
S-W
Random
allocation
Compare
Weak
Group2
Strong 2nd
Strong
Compare
individual
differences
S-W