Where do data come from and Why we dont always trust statisticians'

1
Where do data come from and Why we dont
(always) trust statisticians.
2
Induction vs. Deduction the gist of statistics

• Deduction What is true about the whole, must be
  true about a part.
• Induction What is true about the part might be
  true about the whole.

3
Population vs. Sample

• Population is the entire group of individuals
  about which we want information.
• Sample is a part of population from which we
  actually collect information.
• We use samples to study population because,
  often, populations are impossible or impractical
  to study.

4
Real Life Example of a Bad Sample

• Ann Landers, a famous columnist, collected a
  sample of 10,000 people who wrote in to answer
  this question If you could do it all over
  again, would you have children?
• 70 of the respondents said that they would not
  have children.
• When a sample was selected at random, 91 of the
  people said that they would have children.

5
Potential problems with sample surveys

• Undercoverage occurs when some groups in
  population are left out of the process of
  choosing the sample.
• Nonresponse occurs when an individual chosen for
  the sample cannot be contacted or refuses to
  respond.

6
Another Real life Example of a Bad Sample

• In 1936 Literary Digest mailed out 10,000,000
  ballots asking who the respondents are going to
  vote for A. Landon or F.D. Roosevelt.
• 2,300,000 ballots were returned, predicting a
  strong win (57) for Landon.

7
Another Real life Example of a Bad Sample

• George Gallup surveyed 50,000 people chosen
  randomly.
• Comparison of forecasts
• Gallups Prediction for Roosevelt 56
• Gallups prediction of Digest 44
• Digest prediction for Roosevelt 43
• Actual vote 62
• Literary Digest used their subscription list,
  phone directory, lists of car owners, club
  members.

8
(No Transcript)
9
Right and Wrong Ways to Sample

• A simple random sample is a sample where (1) each
  unit of population has an equal chance of being
  chosen and (2) all units are chosen
  independently.
• The sample is biased if at least one group of
  individuals has greater chances of being selected.

10
Example of a good sample

• You want to study effects of computers on GPA.
  You dont have the resources to study all
  students.
• To select a sample of students for the study you
• Get a list of all students,
• Select at random students on the list,
• Collect information from the students selected,
• Compare those who have computer with those who
  dont.

11
Example of a bad sample

• You want to study effects of computers on GPA.
  You dont have the resources to study all
  students.
• To select a sample of students for the study you
• Use your friends.
• Hang an ad in the computer lab.
• Post an on-line questionnaire on WKU site.

12
Stratified Random Sample

• When we know proportions of each group in the
  population Stratified random sample is better
  than SRS.
• In stratified sample, number of people chosen
  from each group is proportional to the size of
  that group in the population.

13
Confounding

• Two explanatory variables are confounded when
  their effects on the response variable cannot be
  distinguished from each other.
• Confounding is often a problem with a study that
  uses sample surveys to collect data (even if
  sampling is done right).

14
Observation vs. Experiment

• Observational study - observes individuals and
  measures variables but does not attempt to
  influence responses.
• Experiment imposes treatment on individuals to
  observe their responses.

15
How to design an Experiment

• The purpose of an experiment is to find out how
  one variable (response variable) changes in
  response to change in another variable
  (explanatory variable).
• Experiment
• Subject ?Treatment ?Response

16
Placebo Effect

• Placebo effect change in behavior due to
  participation in experiment.
• Placebo effect is a problem when experiment does
  not have a control group (a basis for
  comparison)
• To avoid the problem design a randomized
  comparative experiment.

17
How to design a Randomized Comparative Experiment

• Randomly split the subjects into two groups
• control group receives no treatment
• treatment group receives treatment
• Compare the results.
• Both will be equally affected by Placebo effect,
  so the difference between the groups shows
  whether the treatment works.

18
How to interpret results of an experiment

• Observe outcomes for treatment and control
  groups.
• If outcomes are different enough so that we can
  say that this difference would rarely occur by
  chance, we conclude that the difference is
  statistically significant.

19
Population vs. Sample

• Population is the entire group of individuals
  about which we want information.
• Sample is a part of population from which we
  actually collect information.
• Based on the sample, we make conclusion about the
  whole population.

20
Parameter vs. Statistic

• A Parameter is the number that describes the
  population.
• A Statistic is a number that describes the
  sample.
• We use statistics to estimate parameters.

21
Sampling Distribution

• The result of your study is a statistic, which
  can vary from sample to sample
• Sampling Distribution of a statistic is the
  distribution of values taken by the statistic in
  all possible samples of the same size from the
  same population
• EstimateTrue Parameter Sampling Error

22
Bias and variability

• A statistic is biased if the mean of the sampling
  distribution is not equal to the true value of
  the parameter being estimated.
• Variability of a statistic is the spread of
  sampling distribution.
• Bias does not go away with larger samples.
• Variability goes away with larger samples.