stat 217 – day 6 two-way tables (topic 6) preliminary questions 1-3 calculators!
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Stat 217 – Day 6
Two-way Tables (Topic 6)
Preliminary Questions 1-3
Calculators!
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Last Time (Wrap Up p. 84)
An experiment deliberately imposes the explanatory variable on the subjects, rather than passively observing and recording information
A randomized comparative experiment can establish a cause-and-effect relationship between two variables by guarding against confounding Should be no other systematic differences between
the groups Random assignment vs. random sampling
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Activity 5-5 (p. 80)
(a) An experiment?
This study is experimental because the experimenter actively imposed the explanatory variable (the sequence of letters) on the subjects. Identify what was controlled/imposed (context) Therefore can draw cause-and-effect
(b) EV/RV?EV = which sequence (categorical)
RV = number of letters memorized (quantitative) Don’t confuse with research question
JFK-CIA-FBI-USA-SAT-GPA-GRE-IBM-NBA-CPRJFKC-IAF-BIU-SASA-TGP-AGR-EIB-MN-BAC-PR
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Activity 5-5 (p. 80)
(c) How and Why random assignment?Random assignment was implemented by randomly distributing the sheets without choose who received which number sequence Shuffled and dealt out blindlyIt is important because different people have different memorizing abilities. Random assignment cancels out this factor (and others) Allows us to draw cause and effect conclusions
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Activity 5-4
Def: Placebo Often give fake or empty treatment to equate
psychological effects
Ideally study will be double-blind
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Three main issues in drawing conclusions Issue #1: Do I believe the sample I have is
representative of the population that I am interested in for this issue (generalizable)? Yes, if have a random sample
Issue #2: Can I draw a cause and effect conclusion when comparing groups (causation)? Yes, if have a randomized comparative experiment
Issue #3: Is the result statistically significant? Yes, if p-value is small
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Uses of randomness
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Scope of ConclusionsAllocation of units to groups
By random assignment
No random assignment
Selection of units
Random sampling
A random sample is selected from one population; units are then randomly assigned to different treatment groups
Random samples are selected from existing distinct populations
Inferences to populations
can be drawn
Not random sampling
A groups of study units is found; units are then randomly assigned to treatment groups
Collections of available units from distinct groups are examined
Cause and effect conclusions can be
drawn
In its statement, Merck said that both it and some of its consultants were also concerned that, because patients with acute coronary syndrome in the Vioxx study would also be taking low doses of aspirin to prevent heart attack and stroke, their experiences might not be representative of patients who were not taking aspirin.
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Next Step
Now that we can properly design a study and collect data, what are the best ways to analyze the data, especially to compare groups Topic 6: Categorical variables For example: Do males and females feel
differently about choice of lifetime achievement? Activity 6-3 (p. 100)
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Activity 6-3 (p. 100)
Blackboard Survey: If you could choose one of the following accomplishments for your life, which would you choose: To win an Olympic gold medal To win a Nobel Prize To win an Academy Award
Research question: Do men and women respond differently to this question?
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Activity 6-3 (p. 100)
(a) Classify variables
Gender: categorical
Preferred lifetime achievement: categorical
(b) Explanatory: gender
Response: preferred lifetime achievement
(c) Determine the marginal distribution of preferred lifetime achievement
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Marginal distribution
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Does this answer our research question? Gender
Two-way table
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Descriptive Statistics
Segmented bar graph
57% of women chose Nobel prize; 78% of men chose Olympic gold medal
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“Independence”
There is an association between gender and choice
There is no association between gender and choice
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Caution
Most choosing the Olympic gold medal were men?
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Lab 2: Is Yawning Contagious Anecdotal evidence? Experiment?
Mythbusters Pre-lab on video posted soon!
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To turn in with partner Activity 6-2 (p. 99-100) (a)-(g) skip (e)
For Thursday Remember to meet in computer lab, bring USB Turn in Lab 1 Pre-lab for Lab 2 in Blackboard
No class Monday!
For Tuesday Activity 6-1, 6-5, and (optional) 6-4 Be working on HW 2
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Analyzing Two Categorical Variables Activity 6-1 (p. 94)
Two-way table Explanatory variable as the columns
Marginal distribution = just one variable Too little: 398/646 .616 About right: .307, too much: .077
Tendency to think government spends too little on the environment
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Activity 6-1
Conditional Distribution
Liberal Moderate Conservative
Too Little 127 158 113
About Right 27 80 91
Too Much 1 17 32
Total 155 255 236
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Activity 6-1
Conditional Distribution
Of 155 liberals, 127 or about .819 said “too little” “About right” = 27/155 .174 “Too much” = 1/155 .006
Liberal Moderate Conservative
Too Little 127 158 113
About Right 27 80 91
Too Much 1 17 32
Total 155 255 236
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Activity 6-1 (p. 94)
Marginal distribution Conditional distributionsEnvironmental Spending
00.10.20.30.40.50.60.70.80.9
1
Too Little About Right Too Much
Pro
po
rtio
n
Respondents' Opinions
Government Spending on Environment
Tendency to think government spends too little on the environment
Liberals are more likely to think govt spends too little, conservatives less so
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Activity 6-1
Environmental Spending
Space Spending
The differences between the political parties are smaller when asked about space spending. Opinion is closer to independent of party with space.
35%
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Perfect independence…
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Activity 6-1
Conditional Distribution
127/398 = .319 31.9% of “too little” group classified as liberal 127/155 => 81.9% of liberals think “too little”
Liberal Moderate Conservative
Too Little 127 158 113
About Right 27 80 91
Too Much 1 17 32
Total 155 255 236
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Activity 5-4 (p. 79)
(a) Need something to compare to, maybe most people experience pain relief just over time
(b) comparison group, random assignment
(c) Confounding variable = knowledge that drug receiving should reduce their pain
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Activity 5-4 (p. 79)
(a) Need something to compare to, maybe most people experience pain relief just over time
(b) comparison group, random assignment
(c) Confounding variable = knowledge that drug receiving should reduce their pain
What about? Extent of pain
Cause of painPain tolerance ExerciseOther health issuesBack pain could have subsided on own
Not “confounding” if don’t differ between EV groups (“lurking”)
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Activity 5-4 (p. 79)
(a) Need something to compare to, maybe most people experience pain relief just over time
(b) comparison group, random assignment
(c) Confounding variable = knowledge that drug receiving should reduce their pain
(d) Both groups believe they could be receiving the helpful treatment