Statistics of Illumination

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Statistics of Illumination

• Beth Chance
• Roxy Peck
• Cal Poly, San Luis Obispo

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STATISTICS SAY

• Increasingly daily life involves statistical
  information
• interpretations of graphical and numerical
  summaries
• comparisons of groups
• poll results from random samples
• conclusions from randomized experiments
• predictions of future outcomes

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Most people use statistics as a drunkard uses a
lamppost-
more for support than for illumination.
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Predicting Variable Behavior
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Predicting Variable Behavior

• (a) Height of students in this class
• (b) Students preference for coca-cola vs.
  pepsi-cola
• (c) Number of siblings of individuals
• (d) Amount paid for last haircut
• (e) Gender breakdown
• (f) Students guesses of my age

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Matching Variables to Graphs
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Matching Variables to Graphs

• Think about context!
• Anticipate patterns and variations
• variable intuition
• graph-sense

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STATISTICS SAY

• Students heights would show more variability
  than guesses of my age
• KDC Pursues High-Return, Low-Risk Strategy

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What is Variability?

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What is Variability?
Class F Class G Class H Class I Class J
range 6 8 8 8 8
IQR 2.75 3 0 8 5
Std. Dev. 1.769 2.041 1.180 4.000 2.657
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Describing Variability

• The bumpiness of a histogram does not determine
  the variability of the observations
• The number of distinct values the variable takes
  does not determine the variability of the
  observations

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STATISTICS SAY

• 5236 drivers age 65 and over were involved in
  fatal accidents, compared to only 2900 drivers
  aged 16 and 17, so young people are safer
  drivers...
• 65 of motorcycle fatalities occurred in states
  with mandatory helmet laws...

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Counts Versus Ratios

• Simple counts are often not a good basis for
  comparison of two or more groups.
• Group size isnt always obvioustwo groups of 25
  U.S. states may have very different sizes even
  though both include the same number of states.
• Deciding on a sensible basis for comparison
  requires thought!

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STATISTICS SAY

• 85 of software developers predicted that
  Microsoft's integration of Internet functions
  into Windows would help their company

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Some Simple Questions

• Question 1
• Lost ticket
• Yes 6
• No 9
• Lost 20
• Yes 8
• No 6

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Some Simple Questions

• People are more likely to say yes when they
  have lost a 20 bill
• People tend to answer not surprising to both
  expressions
• People are more likely to choose program A with
  the save version and program B with the die
  version

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Some Simple Questions

• Be careful when wording survey questions ask to
  see the phrasing!
• Bill Gates It would help me EMENSELY to have a
  survey showing that 90 of developers believe
  putting the browser into the operating system is
  a good idea
• Browser vs. browser technologies

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STATISTICS SAY

• Researchers in Philadelphia investigated whether
  pamphlets containing information for cancer
  patients are written at a level that the cancer
  patients can comprehend
• Median reading levels are equal

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Readability of Cancer Pamphlets
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Readability of Cancer Pamphlets

• Graphs can illuminate
• Look at the data!
• Think about the question

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STATISTICS SAY

• American men were randomly selected for the 1970
  draft
• Draft numbers (1-366) were assigned to birthdates

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Draft Lottery

• Calculate the median draft number for each month
• 31 days 16th value
• 30 days average 15th and 16th values
• 29 days 15th value

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Draft Lottery

• month median
• January 211.0
• February 210.0
• March 256.0
• April 225.0
• May 226.0
• June 207.5

• month median
• July 188.0
• August 145.0
• September 168
• October 201
• November 131.5
• December 100

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Draft Lottery
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Draft Lottery
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Draft Lottery

• Statistics matter
• Summaries can illuminate
• Randomization can be difficult

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STATISTICS SAY

• The average time between eruptions of the Old
  Faithful Geyser is 71 minutes
• August, 1985

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Geyser Eruptions
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Geyser Eruptions

• Looks can be deceiving!
• Use the graph that summarizes without losing
  important details

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STATISTICS SAY

• The average major league baseball salary in the
  United States is about 1.5 million

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Rowers Weights

• 2000 Mens Olympic Rowing Team

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Rowers Weights
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Rowers Weights

• Mean Median
• Full Data Set 197.29 207.5
• Without Coxswain 200.11 210.00
• Without Coxswain or 210.57 210.00 lightweight
  rowers
• With heaviest at 320 215.33 210.00
• Resistance....

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Rowers Weights

• Know what your numerical summary is measuring
• Investigate causes for unusual observations
• Baseball median salary 500,000

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STATISTICS SAY
People live longer in countries with more
televisions
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Televisions and Life Expectancy

• Buy another television?
• Association is not causation

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STATISTICS SAY

• Overall survival rates
• A 80 B 90
• Fair condition
• A 98.3 B 96.7
• Poor condition
• A 52.5 B 30.0

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Hospital Recovery Rates

• Simpsons Paradox
• Hospital A gets most of the poor condition cases
• Patients in poor condition are less likely to
  survive
• Thus hospital A has the lower survival rate
  despite being the better choice for either
  condition
• Beware of lurking variables

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Hospital Recovery Rates (cont.)
100
Fair
survive
Hospital A
Hospital B
0
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Hospital Recovery Rates (cont.)
100
Fair
survive
Poor
Hospital A
Hospital B
0
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Hospital Recovery Rates (cont.)
100
Fair
survive
Poor
Hospital A
Hospital B
0
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STATISTICS SAY

• Taking an aspirin each day reduces the risk of
  heart attack for men, but less so for women

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How Experiments Take Variability Into Account

• Direct control
• Blocking
• Randomization

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Randomization
1 2
3 4
5 6
7 8
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Blocking Scheme A
1 2
3 4
5 6
7 8
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Blocking Scheme B
1 2
3 4
5 6
7 8
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Results from 100 Trials
First Blocking Scheme
Completely Randomized
Second Blocking Scheme
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Controlling for Variability

• Blocking reduces variability in the estimated
  mean difference
• Homogeneous blocks are desirable
• Randomization evens out the effects of extraneous
  variables

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STATISTICS SAY

• A log was selected at random

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Sampling Logs

• Does choosing times at random result in a random
  sample of logs?
• _______________________________ ?

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Estimating Mean String Length

• Does the sampling procedure produce a simple
  random sample?
• How is this related to the log problem??
• Can you suggest a better sampling method?

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Selecting a Sample

• Random Sampling eliminates human selection bias
  so the sample will be fair and unbiased/representa
  tive of the population.
• While increasing the sample size improves
  precision, this does not decrease bias.

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STATISTICS SAY

• 45 /- 1 of people surveyed claim to prefer
  watching soccer to baseball

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Reeses Pieces
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Reeses Pieces

• Take sample of 25 candies
• Sort by color
• Calculate the proportion of orange candies in
  your sample
• Construct a dotplot of the distribution of sample
  proportions

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Reeses Pieces

• Did everyone obtain the same sample result?
• Is there a pattern to the sample results?
• Is it possible to make predictions about the
  population based on only one sample?
• Can you be confident of your prediction?

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Thank You

• bchance_at_calpoly.edu
• rpeck_at_calpoly.edu