Statistical Reasoning

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Statistical Reasoning
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Real Estate Statistics

• From Scottsdale Real Estate Report

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What is statistics?

• Statistics is the science of collecting,
  organizing, and interpreting data.
• Statistics are the data that describe or
  summarize something.

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Fundamentals of Statistics

• Suppose that you want to know which candidate is
  most popular choice for the upcoming presidential
  election.
• How might you get some find some data?
• CNN/Opinion Research Corporation Poll. Oct.
  12-14, 2007. N485 registered voters nationwide
  who are Democrats or independents who lean to the
  Democratic Party. MoE 4.5.

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PollingReport.com

• "Please tell me which of the following people you
  would be most likely to support for the
  Democratic nomination for president in the year
  2008 . . . ."
• 10/12-14/07
• Hillary Clinton 46
• Barack Obama 17
• Al Gore 14
• John Edwards 12
• Bill Richardson 3
• Joe Biden 1
• Christopher Dodd 1
• Mike Gravel 1
• Dennis Kucinich 1
• Unsure 4

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Definitions

• Population - the complete set of people or things
  being studied.
• What is the population in our political poll?
• Sample - the subset of the population from which
  your data is obtained.
• What is the sample in our political poll?
• Population parameters - the characteristics about
  the population that we want to learn about.
• What parameters are we interested in with our
  political poll?
• Sample statistics - raw data consolidated into a
  set of numbers that characterize the data.
• What sample statistic are given from our poll?

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Statistical Study
start
1. Identify goals
2. Draw from a population
population
sample
3. Collect raw data and summarize
5. Draw conclusions
4. Make inferences about population
Sample statistics
Population parameters
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Choosing a sample

• Want to find a representative sample - one in
  which the sample members match those of the
  population.
• Sampling methods
• Simple random sampling - choose in a way that
  every sample of a given size has an equal chance
  of being chosen.
• Systematic sampling - use a simple system for
  choosing the sample.
• Convenience sampling - choose a sample based on
  convenience
• Stratified sampling - use when we are interested
  in the difference between different subgroups
• How would we find a representative sample for our
  political poll?

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Sampling Methods

• Which type of sampling is used in each of these
  cases?
• You are conducting a survey of students in a
  dormitory. You choose your sample by knocking on
  every 10th door.
• To survey opinions on a possible property tax
  increase, a research firm randomly draws the
  addresses of 150 homeowners from a public list of
  all homeowners.
• Agricultural inspectors for Jefferson County
  check the levels of residue from three common
  pesticides on 25 ears of corn from each of the
  104 corn producing farms in the county.
• Anthropologists determine the average brain size
  of early Neanderthals in Europe by studying
  skulls found at three sites in southern Europe.

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Bias

• Bias refers to any problem in the design or
  conduct of a statistical study that tends to
  favor certain results.
• How might bias be introduced in our political
  poll?

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Types of studies

• Observational study - researchers attempt to
  observe or measure characteristics of the sample,
  but do not try to influence these
  characteristics.
• Experiment - researchers apply a treatment to
  some or all of the sample members, then look to
  see whether the treatment has any effect

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Experimental studies

• Suppose you want to test whether high doses of
  vitamin C can help prevent colds. Researches
  must ask some people in the sample to take the
  high dose of vitamin C - we call this the
  treatment group, and we compare to a control
  group who does not take vitamin C
• Both the treatment group and the control group
  must be chosen randomly and must be alike in all
  respects except for the treatment.

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Placebo effect and Blinding

• What is the Placebo effect?
• A placebo lacks the active ingredients of a
  treatment being tested in a study, but is
  identical in appearance to the treatment.
  Participants dont know if they are getting the
  treatment or not.
• In statistical terms, keeping people in the dark
  about whether they are receiving the treatment is
  called blinding.
• Single blind participants dont know if they
  are receiving the treatment or the placebo.
• Double blind the researchers dont know who is
  getting the treatment and who is getting the
  placebo.

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Case control studies

• Observational studies that look like experiments
  because the sample naturally divides into groups.
• Consider that you want to study how alcohol
  consumed during pregnancy can be harmful to the
  baby. Obviously you couldnt set this up as an
  experiment since you know that alcohol can cause
  harm, instead you might look for participants
  who engage in the behavior under study and they
  form cases. The participants who dont engage in
  the behavior are the control group.

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Margin of error

• Surveys and opinion polls usually include a
  margin of error.
• The margin of error is used to describe the
  confidence interval that is likely to include the
  true population parameter. The confidence
  interval is
• (sample statistic - margin of error) to (sample
  statistic margin of error)

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Should you believe a statistical study?

• 8 guidelines
• Identify goal, population, type of study
• Consider the source
• Look for bias in the sample
• Look for problems in defining or measuring the
  variables of interest
• Watch out for confounding variables
• Consider the setting and the wording in surveys
• Check that results are presented fairly
• Stand back and consider the conclusions

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Should you believe these studies?

• Spend time working on the worksheet

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Statistical Tables and Graphs

• Think about the grade distribution from our last
  exam. How was the data presented?
• Suppose the grades on the exam were
• 57, 63, 94, 68, 88, 86, 73, 91, 83, 84, 79, 59,
  72, 75, 96, 81, 76, 89, 75, 78
• What are some things you could do with this data
  to get a better feel for how your score compares
  to the rest of the class?

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Frequency Table

• A frequency table has two columns
• The first column lists all the categories of data
• The second column lists the frequency of each
  category

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Another way to look at the data
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Quantitative vs. Qualitative data

• Suppose that the tests were given a letter grade
  instead of an score - this is called qualitative
  data because it describes the quality of the data
  (Aexcellent, Bgood, Csatisfactory,)
• The score is quantitative data. It is a measure
  of what percentage of the work was correct.
  Quantitative data is always in the form of a
  number, but data in the form of numbers is not
  always quantitative.
• For example, film reviewers might rate a new
  movie on a scale of 1 to 5 stars. This is a
  number rating, but the numbers represent
  subjective opinions.

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Carbon Dioxide Emissions

• Carbon dioxide is released into the atmosphere
  primarily by the combustion of fossil fuels (oil,
  coal, natural gas). The following table lists
  the 8 countries that emit the carbon dioxide each
  year.

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Bar Graphs
A bar graph with the bars in descending order is
often called a Pareto chart.

• Why might you want to display the bars in
  descending order?

• Why are the countries in a different order in the
  two charts displayed here?

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Pie Chart
-What stands out on the pie chart?
-Why might you choose to represent the data in a
pie chart rather than a bar graph?
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Histogram and Line Charts
Histograms and Line charts are used when the
categories are quantitative.
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Time series diagram
A time series diagram is a line chart where the
horizontal axis is time.
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• The following data shows how a state lottery
  distributed its 2.1 million proceeds in the year
  2000.
• Draw two graphs. One should support the argument
  that too much money from the state lottery went
  toward education. The other should support the
  counter argument, too little money from the state
  lottery went toward education.
• Choose a side to the above argument, either pro
  or con. Write a paragraph defending your
  argument, citing social, political, ethical
  and/or religious facts.

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Graphics in the Media

• Multiple bar graphs
• Stack Plots
• Geographical data
• Contour maps
• 3 dimensional data

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Contour Map of Temperature
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Median Age by State
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Cautions about Graphics

• Perceptual distortion
• Watch the scales