Stat 217 – Day 6

Two-way Tables (Topic 6)

Preliminary Questions 1-3

Calculators!

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

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

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

Activity 5-4

Def: Placebo Often give fake or empty treatment to equate

psychological effects

Ideally study will be double-blind

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

Uses of randomness

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.

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)

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?

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

Marginal distribution

Does this answer our research question? Gender

Two-way table

Descriptive Statistics

Segmented bar graph

57% of women chose Nobel prize; 78% of men chose Olympic gold medal

“Independence”

There is an association between gender and choice

There is no association between gender and choice

Caution

Most choosing the Olympic gold medal were men?

Lab 2: Is Yawning Contagious Anecdotal evidence? Experiment?

Mythbusters Pre-lab on video posted soon!

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

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

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

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

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

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%

Perfect independence…

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

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

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”)

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