Welcome to Statistics 111

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Welcome to Statistics 111

• Alex Braunstein

The goal of this course is to develop basic tools
for data analysis, probability and statistical
methods. Key topics covered in the course include
exploratory data analysis, regression,
probability, estimation, and hypothesis testing
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Syllabus notes website

• All handouts will be available on the website
• http//stat.wharton.upenn.edu/braunsf/stat111.htm
  l
• Website also contains my contact information
• Link on website for getting Wharton class account
  if you are not a Wharton student
• Helpful if you want to use Wharton computer labs

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Syllabus notes Homeworks

• Homeworks will be handed out at the beginning of
  every week
• 5 homeworks in all
• Homeworks will be submitted at the beginning of
  class on Mondays
• You are encouraged to work together on homework,
  but homeworks are to be completed separately and
  handed in individually.
• Do not copy from another person.
• No late homeworks will be accepted!!
• Late homeworks will get a score of zero, without
  exception
• Your lowest homework grade is not included in
  final grade

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Syllabus Notes Midterm Exam

• Midterm is held on following date
• Monday, June 15th (in class)
• No makeup midterm examination!
• A missing midterm exam counts as a zero score
• Consider taking this class in the fall or spring
  if you can not attend the midterm!

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Student Questionnaire

• Fill out a questionnaire and hand it in before
  the break
• I will try to incorporate some of the subjects
  that interest you into future lectures

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Course Overview
Collecting Data
1
Exploring Data
2
Probability Intro.
3
Inference
4
Comparing Variables
Relationships between Variables
2
1
1
1
Means
Proportions
Regression
Contingency Tables
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Out in public You do statistics ?!?

• I hated that class in college!
• That was the most boring class ever!
• Lame.

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Big Picture Ideas

• Statistics is all about uncertainty
• Focus as much on what we dont know (or havent
  observed) instead of what we know
• Formulating the question that we want to answer
  is often the most difficult part
• Statistics is part mathematics, part
  roll-up-your-sleeves-and-get-thinking.

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Science and Skepticism

• We always need to be cautious about conclusions
  based on data
• Possible sources of bias and confounding?
• How might things have gone wrong?
• A little bit of skepticism is a good thing!

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Statistical Modeling

• Inference using mathematical models of
  uncertainty to answer questions
• Connect probability concepts to our data
• Can not make claims without using models and
  making assumptions
• Are the assumptions reasonable?

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After the break

• Collecting Data Design of Experiments
• Sections 3.1-3.2 in Moore, McCabe and Craig
• First couple of classes will not involve much
  math at all, but we will get into lots of data
  analysis after that!

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Break!

• Hand in questionnaire
• 5 minutes

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Outline for Second Half of Lecture

• Introduction to Experiments
• Sources of Bias in Experiments
• Techniques for Avoiding Bias
• Matching
• Randomization
• Block Designs
• Blinding and Double-Blinding
• Experiments vs. Observational Studies
• Association vs. Causation

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Experiments

• Used to address a specific question
• Often used to examine causal effects
• Eg. medical trials, education interventions

Treatment Group
Treatment
Result
1
Experimental Units
2
3
4
Population
Control Group
No Treatment
Result

• Can we just look at difference in results to get
  the causal effect of the treatment?
• Depends on whether the experiment was done well
• many possible sources of bias in design of
  experiments

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Sources of Bias

• An experiment or study is biased if it
  systematically favors a particular outcome
• Subjects are not representative of the population
• Treatment and control groups are inherently
  different on some lurking or confounding variable
• Subjects are influenced by knowing they are in
  treatment or control groups
• Evaluator of outcomes is influenced by knowing
  they are in treatment or control groups

Treatment Group
Treatment
Result
1
Experimental Units
2
3
4
Population
Control Group
No Treatment
Result
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Bias 1 Non-representative units

• If your subjects are not representative of the
  population, you wont be able to generalize the
  results even if the experiment is well done
• Here are two examples
• Treatment group High Level NICUs
• Control Group Low Level NICUs
• Problem classification of NICU is different from
  state to state, so a hospital that might qualify
  as a high level NICU in one state might not in
  another
• Observed differences between the groups can not
  be generalized from one state to another

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Bias 2 Confounding/Lurking Variables

• Treatment group and control group are different
  on some variable that also influences the outcome
• A confounding variable means that we cant
  attribute difference in outcomes to just the
  treatment
• Part of the difference may be due to the
  confounding variable not the treatment
• Simple example a breast cancer drug trial where
  only women receive the treatment and only men
  receive the control
• Gender becomes a confounding variable
• Are treatment vs control outcomes different due
  to the treatment or gender differences between
  groups?

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Bias 3 Subject knows treatment assignment

• A subjects outcome is influenced by knowing that
  he/she is in a treatment or control group
• Eg. drug trials patients improve just because
  they think they are receiving the drug
• Solution blinded experiment with placebo
• Placebo appears to be the treatment, so all
  subjects (treatment and control) dont know their
  true treatment assignment
• Controls may improve outcomes slightly this is
  often called the placebo effect

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Bias 4 Evaluator knows treatment assignment

• Person evaluating outcome (eg. doctor in drug
  trial) may also be influenced by knowing who
  receives treatment
• Not a problem if outcome is something
  indisputable, such as death!
• This is a problem for more subjective measures
  like pain reduction or results from social
  programs
• Solution double-blinded experiment where neither
  subjects not evaluators know treatment
  assignments

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Association vs Causation

• In the presence of a confounding variable, we can
  only conclude there is an association between
  treatment and outcome, not causation

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Examples Reporters are stupid

• Children who watch many hours of TV get lower
  grades in school on average than those who watch
  less TV
• Does this mean that TV causes poor grades?
• What are potential confounding variables?
• People who use artificial sweeteners in place of
  sugar tend to be heavier than people who use
  sugar
• Does this mean that sweeteners cause weight gain?
  
• What is probably happening here?

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One solution Matching

• Make sure that treatment and control groups are
  very similar on observed variables like race,
  gender, age etc.
• Block designs divide subjects into blocks with
  similar observed variables before dividing them
  into treatment vs control
• Special case Matched Pairs
• Subjects are matched up into pairs, then one
• member of each pair gets treatment and the
• other gets control
• Example Dandruff experiment
• treatment applied to one side and control
• to other side of head
• No reason to expect difference
• in sides except for treatment

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Another Solution Randomization

• Problem with matching is that you cannot usually
  match on unobserved characteristics (eg.
  Genetics)
• Eg. Cholesterol drug trial - cant match
  treatment and control groups on genetic
  predisposition for high cholesterol
• Randomly assign subjects to treatment or control
• Random assignment should lead to groups that are
  similar or balanced on both observed and
  unobserved confounding variables
• Example student questionnaire earlier in class -
  each form you filled out was randomly assigned
  either a 1 or 2

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Randomization of In-Class Survey

• Check to see if groups are balanced
• There are differences, but are they
  significant?
• Later on in the course, we will be able to answer
  questions like this
• Of course, we cant check the balance for
  unobserved variableswe just have to trust the
  randomization process
• This is why good science needs to be replicable

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Even Better Randomization Matching

• Randomization generally leads to treatment and
  control groups that are evenly balanced but you
  can still get unlucky and get unbalanced groups
• Example randomly placing 20 people (10 males, 10
  females) into treatment and control groups.
• How many males will end up in treatment group?
• Ideally, we would have 5 males in treatment
  group, and 5 males in control group (balanced)
• However, there is a chance to get 9 males in
  treatment and 1 male in control group (unbalanced)

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Even Better Randomization Matching

• Randomized Blocks randomize within blocks of
  observed variables
• Example
• Divide up subjects into males and females first,
  then randomly assign treatment or control to
  subjects in each group separately
• Guarantees that equal number of males end up in
  treatment group and control group (same with
  females)
• Randomized Matched Pairs randomly decide which
  member of each pair gets treatment vs. control
• Example
• For each head in dandruff experiment, randomly
  assign which side of head to get dandruff shampoo
  vs. control

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Experiments vs. Observational Studies

• Often, we want the causal effect of some
  treatment, but our data are from an observational
  study
• Observational studies examine effects of some
  variable but without the advantages of a
  controlled experiment
• No treatment is applied in observational studies
• Example health effects of smoking
• Unethical to randomly impose a treatment
• Could there be some confounding variable that
  explains health differences between smokers and
  non-smokers ?
• Very risky to make causal statements from
  observational data, since we can not avoid bias!

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Health Effects of Chocolate

• Report to European Society of Sexual Medicine
• 153 Italian women filled out sexual function
  questionnaires
• intriguing correlation sexual function/desire
  significantly greater among chocolate-eaters
• Observational study association does not imply
  causation!
• Confounding average age is 35 among frequent
  chocolate-eaters, compared with 40.4 in
  non-chocolate group

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Next Class - Lecture 2

• Collecting Data
• Surveys and Sampling
• Graphical summaries of a single variable
• Moore, McCabe and Craig Sections 3.3 and 1.1