Stor 155, Section 2, Last Time

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Stor 155, Section 2, Last Time

• Course Organization Website
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155-07Home.html
• What is Statistics?
• Data types and structure
• Get going in EXCEL
• Exploratory Data Analysis
• Bar Graphs

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Reading In Textbook

• Approximate Reading for Todays Material
• Pages 14-23
• Approximate Reading for Next Class
• Pages 40-55

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Stat 31, Student Poll Results
As indicated on Student Info form
Big changes from the past More Public More
diversity
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Stat 31, Student Poll Results

• Have you taken an AP Exam?
• Only 10 had grades generally low
• So dont worry if you havent

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Stat 31, Student Poll Results

• Female 48
• Male 53
• Interesting Point
• Different from all of UNC 60 - 40
• Lesson about which courses to take???

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Major Concept Distributions

• Distribution Patterns of data
• Way data is spread
  out
• e.g. Bar Graph is visual display of categorical
  distribution

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Exploratory Data Analysis 2

• Visual Display of Quantitative Distributions
• Stem and Leaf Plots
• (From last time) Not Recommended
• (Main motivation was pencil and paper statistical
  analysis, but now have better graphical methods
  readily accessible)
• A limited special case of.

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Visual Disp Quantitative Distns

• 2. Histograms
• Idea Apply bar graph idea,
• By creating categories,
• Called class intervals or classes or bins

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Histograms

• Idea put numbers into bins,
• bar heights are counts, or frequencies
• 1.3
• 3.6
• 1.9
• 3.1
• 1.5

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Histograms

• Idea put numbers into bins,
• bar heights Class Intervals
• 1.3 (0,1, (1,2,
  (2,3, (3,4
• 3.6
• 1.9
• 3.1
• 1.5 0 1 2 3
  4

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Histograms

• Idea put numbers into bins,
• bar heights are counts, or frequencies
• 1.3
• 3.6
• 1.9
• 3.1
• 1.5 0 1 2 3
  4

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Histograms

• Idea put numbers into bins,
• bar heights are counts, or frequencies
• 1.3
• 3.6
• 1.9
• 3.1
• 1.5 0 1 2 3
  4

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Buffalo Snowfall Data

• Buffalo, N. Y. (Annual) Snowfall Data
• Raw Data
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg2Raw.xls
• 63 years, ranging from 30 - 120
  (inches)
• Histogram Analysis (pre-done)
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg2Done.xls

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Buffalo Snowfall Data, I

• A. EXCEL default (of bin edges)
• Unround numbers for bin edges
• Harder to interpret
• Data centered around 90
• Most data between 50 and 130
• Assymetric Distribution

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Buffalo Snowfall Data, II

• B. Smaller bins
• Chosen by me
• Binwidth 5, ltlt 13 from EXCEL default
• Nicer edge numbers
• Data centered around 84 (now more precise)
• Bar graph rougher (fewer points in each bin)
• Suggests 3 main groups
• (called modes or clusters)
• (cant see this above bin width is important)

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Buffalo Snowfall Data, III

• C. Larger bins
• Chosen by me
• Binwidth 30, gtgt 13 from EXCEL default
• Bar graph is smooth
• (since many points in each bin)
• Only one mode (cluster)???
• Quite symmetric?
• (different from above bin width is important)

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Buffalo Snowfall Data, IV

• Whats under the hood (how to do this)
• Tools ? Data Analysis ? Histogram ( Chart Out)
• (may need Data Analysis Add-in)
• Massage pic (especially bar width)
• Sigma ? min, max
• Bin range create first two drag
• Histogram, using input bin edges

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Histogram HW

• HW 1.33
• Use Excel and histograms
• Get data from CDrom
• Do both
• Excel Default bins
• Bins set to 0,10,20,,240
• Which gives answers closer to answers in back of
  book?
• Turn in only one page

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And now for something completely different

• Is this class too monotone?
• Easier to understand?
• Calm environment enhances learning?
• Or does it induce somnolence?
• What is somnolence?
• Google definition
• Sleepiness, a condition of
• semiconsciousness approaching coma.

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And now for something completely different

• Recall last classs Student Questionnaire
• I asked you for
• Name
• Major
• Contact Info
• Background

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And now for something completely different

• One response

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And now for something completely different

• OK, will try to send your mind in a different
• direction
• Hopefully, a mental break
• (not on the Homework Assignment!)

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And now for something completely different

• An experiment
• Pull out any coins you have with you
• How many of you have
• gt 1 penny?
• gt 1 nickel?
• gt 1 dime?
• gt 1 quarter?
• Choose most frequent denomination

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And now for something completely different

• Collect data (into Spreadsheet)
• Years stamped on coins
• (chosen denomination)
• Many as person has
• Enter into spreadsheet
• Look at distribution using histogram

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And now for something completely different

• Predicted Answer
• From Text Book, Problem 1.32
• Distribution is Left Skewed
• Works out as predicted?
• Why?
• Note most skewed distns seem to be
• Right Skewed

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Histogram Binwidths

• Nice Example from the Webster West, U.S.C.
• http//www.stat.sc.edu/west/applets/histogram.htm
  l
• Control Binwidth with slider
• Undersmoothing?
• About right?
• Oversmoothing?
• (critical to visual impression)

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Histogram Binwidth Example

• Hidalgo Stamp Data
• From Mexico in 1800s
• How many sources of paper?
• How many modes
• 1, 2, 5, 7, 10?

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Histogram Binwidth Example

• How many modes (i.e. clusters)?
• Caution Answer depends on binwidth
• (a serious and current
• statistical research problem)
• Have seen all of 2,3,5,7,10 in the literature!

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Stamps Data Histogram

• How many modes?
• 2nd Caution Answer also depends on bin location
• (i.e. shift of bins)

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Histogram Bins

• For this course
• Try several binwidths, to get the idea
• Weakness of EXCEL (we will see several)
• This process is inconvenient

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Comparison of Histograms

• Class Example Study Habits Data
• Idea Compare Study Habits of Males vs. Females
  (measured by some survey score, perhaps of
  questionable value?)
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg4Done.xls

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Study Habits Data

• EXCEL default histograms
• Populations look similar???
• Careful Binwidth very big
• Careful Different bin ranges
• Need smaller binwidths, and common scales

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Study Habits Data

• Better Choice Binwidths 10, same bins for
  both
• Clear difference, easy to see
• Females higher on average
• Males are more spread
• 1 exceptional value, really true???

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Things to look for (in histos)

• Population Center Point (Study Habits Data)
• Population Spread (Study Habits Data)
• Shape - Symmetric vs. Skewed
• Right Skewed
• Left Skewed
• Modes - Unexpected clusters
• Outliers - unusual data points

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Histogram Data Examples

• Textbook Applets from Publishers Website
• One Variable Statistical Calculator
• Data Set Service Times at a Call Center
• Histogram
• (hold mouse button, and slide left-right)
• Results
• Broad range of binwdiths (12 25 is best?)
• Single bin is useless
• Distribution is Right Skewed
• Clear Outlier

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Comparison of Histograms HW

• HW 1.35b, 1.34, 1.17
• Work in this order
• Get data from CDrom
• Use EXCEL and histograms
• Odd answers in back
• You choose the bins
• (if you miss something in answers, change this)
• Turn in at most one page for each
• 1.31, 1.32

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Exploratory Data Analysis 3

• Time Plots, i.e. Time Series
• Idea when time structure is important,
• plot variable as a function of time
• variable
• time
• Often useful to connect the dots

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Class Time Series Example

• Monthly Airline Passenger Numbers
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg5Done.xls
• Increasing Trend
• (long term growth, over years)
• Increasing Variation
• (appears proportional to trend)
• Seasonal Effect - 12 Month Cycle
• (Peak in summer, less in winter)

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Airline Passengers Example

• Interesting variation log transformation
• Stabilizes variation
• Since log of product is sum
• Shows changing variation propl to trend
• Log10 is most interpretable
• (log10(1000) 3, )
• Generally useful trick (there are others)

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Airline Passengers Example

• A look under the hood
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg5Raw.xls
• Use Chart Wizard
• Chart Type Line (or could do XY)
• Use subtype for points lines
• Use menu for first log10
• Although could just type it in
• Drag down to repeat for whole column

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Time Series HW

• HW 1.36, 1.37
• Use EXCEL