Stat 501

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Stat 501

• Experimental Statistics I

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Handouts

• Print off the following
• Syllabus
• Schedule
• As we go along
• Posted lectures
• Homeworks
• Other handouts and review topics

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About SAS

• Read the Introduction to SAS handout if desired.
• intro.sas is the file with the code.
• Copies of SAS to install on your home computer
  available in STEW G65, there phone is 494-5100.
• SAS is available online at www.itap.purdue.edu/lea
  rning/
• ? Software remote
• E-mail me for SAS coding questions
  colvertn_at_stat.purdue.edu
• Include relevant SAS code in the body of the
  email, attachments dont always work.
• Usually the Stat department provides SAS help
  sessions
• Wednesdays 7-9pm in SC289.
• -Subject to change from semester to semester

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Data, Data, Data, all around us !

• We use data to answer research questions
• What evidence does data provide?
• Example 1
• How do I make sense of these numbers without some
  meaningful summary?

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Example 2

• Study to assess the effect of exercise on
  cholesterol levels. One group exercises and other
  does not. Is cholesterol reduced in exercise
  group?
• people have naturally different levels
• respond differently to same amount of exercise
  (e.g. genetics)
• may vary in adherence to exercise regimen
• diet may have an effect
• exercise may affect other factors (e.g. appetite,
  energy, schedule)

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What is statistics?

• Recognize the randomness, the variability in
  data.
• the science of understanding data and making
  decisions in face of variability
• Design the study
• Analyze the collected Data
• Discover what data is telling you

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Section 1.1

• Displaying Distributions with Graphs

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Individuals and Variables

• Individuals objects described by a set of data
• people, animals, things
• Variable characteristic of an individual, takes
  different values for different subjects.
• The three questions to ask
• Why Purpose of study?
• Who Members of the sample, how many?
• What What did we measure (the variables) and in
  what units?

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Types of Variables
Variables
Quantitative
Categorical
Ordinal
Not ordinal
Continuous
Discrete
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Types of variables

• Categorical outcomes fall into categories
• Ordinal or ordered
• How often do you exercise?
• Never, rarely, occasionally, often, every day
• Not ordinal (nominal) or unordered
• gender, race, political party affiliation

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Types of variables

• Quantitative outcome is a number
• Continuous can take any value within an interval
  
• Examples height, weight, distance
• Discrete those which are separated from each
  other
• Integers are most common example
• Examples number of phone calls made every week,
  number of accidents on SR 26, number of students
  getting an A in Stat 501 this Fall
• Arithmetic operations (like taking mean) is
  meaningful

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Some Student Data
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Exploratory data analysis - graphs

• We begin by examining each variable by itself.
• Definition
• Distribution possible values of a variable and
  how often they occur

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Categorical Example
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Graphical tools for categorical data

• Bar graphs
• height of the columns represent the counts in
  each category
• Pie chart
• What part or of the whole falls in each
  category.
• Bar charts more flexible
• For Pie chart you have to know all the categories
  forming the whole.

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Bar Graph
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Pie Chart
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Quantitative Example

• Breaking strength of connections for electronic
  components
• Need to discuss variation
• How to group these items with so many different
  values?

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Tool 1 Stemplot

• Stem all but the the final digit (could be
  multiple digits)
• Leaf the final digit (always single digit)
• Example
• Numbers of home runs that Hank Aaron hit in each
  of his 23 years in the Major Leagues
• 13 27 26 44 30 39 40 34 45 44 24 32 44 39 29 44 38
  47 34 40 20 12 10

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• Step 1 Identify all the stems
• 1 2 3 4
• Step 2 Write the stems in increasing order
  (usually from top to bottom)
• 1
• 2
• 3
• 4

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• Step 3 Draw a line next to the stem and write
  the leaves against the stem
• 1 3 2 0
• 2 7 6 4 9 0
• 3 0 9 4 2 9 8 4
• 4 4 0 5 4 4 4 7 0

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• Step 4 Rewrite the stemplot rearranging the
  leaves in ascending order (this can be done
  simultaneously with step 3)
• 1 0 2 3
• 2 0 4 6 7 9
• 3 0 2 4 4 8 9 9
• 4 0 0 4 4 4 4 5 7

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Back-to-Back stemplot

• Compare the numbers of Hank Aaron to Barry Bonds
• 5 16 19 24 25 25 26 28 33
• 33 34 34 37 37 40 42
• 45 45 46 46 49 73

0 5
3 2 0 1 6 9
9 7 6 4 0 2 4 5 5 6 8
9 9 8 4 4 2 0 3 3 3 4 4 7 7
7 5 4 4 4 4 0 0 4 0 2 5 5 6 6
9 5
6
7 3
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Examining distributions

• Describe the pattern
• Shape
• How many modes (peaks)?
• Symmetric or skewed in one direction?
• Center midpoints?
• Mean/average median
• Spread
• range between the smallest and the largest
  values, standard deviation, 5-number summary,
  quartiles
• Look for outliers individual values that do not
  match the overall pattern.

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Histograms
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Frequency Table
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(No Transcript)
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What do you see?

• Shape Somewhat symmetric, unimodal
• Center about 110 or 115
• Spread values between 80 and 150
• Remember!
• Histograms only meaningful for quantitative data

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Dealing with outliers
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Outliers

• Check for recording errors
• Violation of experimental conditions
• Discard it only if there is a valid practical or
  statistical reason, not blindly!

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Time plots
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Time plots
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Time Series or Time plots

• We care about two important parts
• Trend persistent, long-term rise or fall
• Seasonal variation a pattern that repeats
  itself at known regular intervals of time.
• Mississippi data
• Increasing trend
• Large seasonal variations there is usually a
  large spike every few years

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Example Gasoline Price Data
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Summary

• Categorical and Quantitative variables
• Graphical tools for categorical variables
• Bar Chart
• Pie Chart
• Graphical tools for quantitative variables
• Stem and leaf plot
• Histogram
• Maybe timeplot if appropriate
• Distributions
• Describe Shape, center, spread
• Watch for patterns and/or deviations from
  patterns.