STA291 day 2

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    Spring 2010

Monday, January 25 th

 Consumers Union asked all subscribers whether
 they had used alternative medical treatments. They
 found that 20% of all their subscribers said “yes.” Is
 this number a parameter or statistic?

 A survey was conducted in a city with 500,000
 residents. They contacted 100 people randomly and
 found that 67% of them thought that businesses
 should be required to pay for their employees’ health
 insurance. Is this number a parameter or statistic?
               Scales of Measurement

 Quantitative or Numerical
   Variable with numerical values associated with them

 Qualitative or Categorical
   Variables without numerical values associated with them
                    Qualitative Variables

 Nominal
   Gender, nationality, hair color, state of residence
       Nominal variables have a scale of unordered categories
         It does not make sense to say, for example, that green hair is
          greater/higher/better than orange hair

 Ordinal
   Disease status, company rating, grade in STA 291
       Ordinal variables have a scale of ordered categories, they are often
        treated in a quantitative manner (A = 4.0, B = 3.0, etc.)
          One unit can have more of a certain property than another unit
                   Quantitative Variables

 Quantitative
   Age, income, height
       Quantitative variables are measured numerically, that is, for each
        subject a number is observed
         The scale for quantitative variables is called interval scale

 A study about oral hygiene and periodontal
 conditions among institutionalized elderly measured
 the following
    Nominal (Qualitative): Requires assistance from staff?
      Yes
      No
    Ordinal (Qualitative): Plaque score
      No visible plaque
      Small amounts of plaque
      Moderate amounts of plaque
      Abundant plaque
    Interval (Quantitative): Number of teeth

 A birth registry database collects the following information on
     Birth weight: in grams
     Infant’s Condition:
         Excellent
         Good
         Fair
         Poor
     Number of prenatal visits
     Ethnic background:
         African-American
         Caucasian
         Hispanic
         Native American
         Other
 What are the appropriate scales? Quantitative (Interval) Qualitative
  (Ordinal, Nominal)
      Importance of Different Types of Data

 Statistical methods vary for quantitative and qualitative
 Methods for quantitative data cannot be used to analyze
  qualitative data
 Quantitative variables can be treated in a less quantitative
     Height: measured in cm/in
           Interval (Quantitative)
         Can be treated at Qualitative
           Ordinal:
              • Short
              • Average
              • Tall
             Nominal:
              • Greater than 60in? (Yes/No)
              • Between 60in-72in? (Yes/No)
                        Discrete Variables

 A variable is discrete if it can take on a finite number
 of values
    Gender
    Nationality
    Hair color
    Disease status
    Grade in STA 291
    Favorite MLB team
        All Qualitative variables are discrete
                  Continuous Variables

 Continuous variables can take an infinite continuum
 of possible real number values
    Time spent studying for STA 291 per day
      43 minutes
      2 minutes
      27.487 minutes
      27.48682 minutes
        Can be subdivided into more accurate values

        Therefore continuous
                   Discrete or Continuous

 Quantitative variables can be discrete or continuous
 Age, income, height?
   Depends on the scale
        Age is potentially continuous, but usually measured in years
 The following are examples of quantitative variables.
 Identify them as discrete or continuous:
    Number of children in a family
    Distance a car travels on a tank of gas
    Number of customers in a store
    Weight of a textbook
     Data Collection and Sampling

Methods of Collecting Data
          Methods of Collecting Data I

            Observational Study
• An observational study observes individuals and
  measures variables of interest but does not attempt
  to influence the responses.
• The purpose of an observational study is to describe/
  compare groups or situations.
• Example: Select a sample of men and women and ask
  whether he/she has taken aspirin regularly over the
  past 2 years, and whether he/she had suffered a
  heart attack over the same period.
         Methods of Collecting Data II

• An experiment deliberately imposes some treatment
  on individuals in order to observe their responses.
• The purpose of an experiment is to study whether the
  treatment causes a change in the response.
• Example: Randomly select men and women, divide
  the sample into two groups. You assign one group to
  take aspirin daily and the other group a placebo.
  After 2 years, determine for each group the percent
  of people who had suffered a heart attack.
         Methods of Collecting Data III

     Observational Study/Experiment
• Observational Studies are passive data
  • We observe, record, or measure, but don’t
• Experiments are active data production
  • Experiments actively intervene by imposing
  some treatment in order to see what happens
• Experiments are preferable if they are possible
        Simple Random Sample

• Each possible sample has the same
probability of being selected.
• The sample size is usually denoted
by n.
                   SRS Example

• Population of 4 students: Adam, Bob, Christina,
• Select a simple random sample (SRS) of size n=2 to
  ask them about their smoking habits
• 6 possible samples of size n=2:
      (1) A+B, (2) A+C, (3) A+D
      (4) B+C, (5) B+D, (6) C+D
             How to choose a SRS?

• Old way: use a random number table.

• A little more modern:
How to Choose a Simple Random Sample (SRS)

• Each possible sample has the same probability of
  being selected.
• The sample size is denoted by n.
• Enumerate all possible samples, and then
  randomly choose one of them
• Or, let the computer choose a random sample, for
  example using this tool:
        How not to choose a SRS?

• Ask Adam and Dana because they are in
your office anyway
  – “convenience sample”
• Ask who wants to take part in the survey
and take the first two who volunteer
  – “volunteer sampling”
     Problems with Volunteer Samples

• The sample will poorly represent the
• Misleading conclusions
• Examples: Mall interview, call-in poll,
  internet poll, street corner interview
    Why are call-in polls usually biased?

People are much more likely to call in if
they feel strongly about an issue:

   (Israel-Palestine, Iraq, water company,
   mountaintop removal, pedestrian safety,
            name of the UK mascot)
                 The UK Mascot

• Wildcat named “Blue” is the
  official UK mascot
• The name was selected in
  2002 in an online poll
  where multiple voting
  was possible
• The choices were “Champ”,
  “Blue”, or “Tucky”
• Somebody felt strongly about
  it and voted often
        Sampling: Famous Example

• 1936 presidential election
• Alfred Landon vs. Franklin Roosevelt
• Literary Digest sent over 10 million
  questionnaires in the mail to predict the
  election outcome
• More than 2 million questionnaires returned
• Literary Digest predicted a landslide victory
  by Alfred Landon
    Sampling: Famous Example (cont’d)

• George Gallup used a much smaller
random sample and predicted a clear
victory by Franklin Roosevelt
• Roosevelt won with 62% of the vote
• Why was the Literary Digest prediction so
far off?
                    Other Example

• TV, radio call-in polls
• “should the UN headquarters continue to be located in
  the US?”
• ABC poll with 186,000 callers: 67% no
• Scientific random sample with 500 respondents: 28%
• Explain to someone who knows no statistics why the
  opinions of only 500 randomly chosen respondents are
  a better guide to what all Americans think than the
  opinions of 186,000 callers.

 Please check your online homework.

 Listen for any announcements made in class today
 about the first homework assignment!!!
        Attendance Survey Question 2

• On a 4”x6” index card (or little piece
of paper)
  – Please write down your name and
  section number
  – Today’s Question (please answer with a complete
  What are the 2 main ways to collect data?

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