Stor 155, Section 2, Last Time
• Course Organization & Websitehttp://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
Reading In Textbook
Approximate Reading for Today’s Material:
Pages 14-23
Approximate Reading for Next Class:
Pages 40-55
Stat 31, Student Poll ResultsAs indicated on “Student Info” form:
Big changes from the past:
More Public …
More diversity
Stat 155, Section 2, Majors
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Busine
ss /
Man
.
Biolog
y
Public
Poli
cy /
Health
Pharm
/ Nur
sing
Jour
nalis
m /
Comm
.
Env. S
ci.
Other
Undec
ided
Fre
qu
ency
Stat 31, Student Poll Results
“Have you taken an AP Exam?”
Only ~10% had & grades generally low
So don’t worry if you haven’t…
Stat 31, Student Poll Results
Female: 48
Male: 53
Interesting Point:
Different from all of UNC: ~60 - 40
Lesson about which courses to take???
Major Concept: Distributions
“Distribution” = “Patterns of data”
= “Way data is spread out”
e.g. Bar Graph is visual display of categorical “distribution”
Exploratory Data Analysis 2
Visual Display of Quantitative Distributions:
1. 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….
Visual Disp: Quantitative Dist’ns
2. Histograms
Idea: Apply bar graph idea,
By creating categories,
Called “class intervals” or “classes” or “bins”
Histograms
Idea: put numbers into “bins”,
bar heights are counts, or “frequencies”
1.3
3.6
1.9
3.1
1.5
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
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
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
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
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
Buffalo Snowfall Data, II
B. Smaller bins
• Chosen by me
• Binwidth = 5, << ~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”)
(can’t see this above: bin width is important)
Buffalo Snowfall Data, III
C. Larger bins
• Chosen by me
• Binwidth = 30, >> ~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)
Buffalo Snowfall Data, IV
D. What’s under the hood (how to do this):
i. Tools Data Analysis Histogram (& Chart Out)
(may need Data Analysis “Add-in”)
ii. Massage pic (especially bar width)
iii. Sigma min, max
iv. Bin range: create first two & drag
v. Histogram, using input bin edges
Histogram HWHW: 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
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.
And now for something completely different
Recall last class’s Student Questionnaire…
I asked you for:
• Name
• Major
• Contact Info
• Background…
And now for something completely different
One response:
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!)
And now for something completely different
An experiment:
• Pull out any coins you have with you
• How many of you have:
– >= 1 penny?
– >= 1 nickel?
– >= 1 dime?
– >= 1 quarter?
• Choose most frequent denomination
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
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 dist’ns seem to be:
Right Skewed
Histogram Binwidths
Nice Example from the Webster West, U.S.C.:
http://www.stat.sc.edu/~west/applets/histogram.html
Control Binwidth with slider:
• Undersmoothing?
• About right?
• Oversmoothing?
(critical to visual impression)
Histogram Binwidth Example
Hidalgo Stamp Data
From Mexico in 1800s
How many sources of paper?
How many modes:
1, 2, 5, 7, 10?
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!
Stamps Data Histogram
How many modes?
2nd Caution: Answer also depends on bin location
(i.e. “shift” of bins)
Histogram Bins
For this course:
Try several binwidths, to “get the idea”
Weakness of EXCEL (we will see several):
This process is inconvenient
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
Study Habits Data
EXCEL default histograms:
• Populations look similar???
• Careful: Binwidth very big…
• Careful: Different bin ranges…
• Need smaller binwidths, and common scales
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???
Things to look for (in histo’s)
1. Population Center Point (Study Habits Data)
2. Population Spread (Study Habits Data)
3. Shape - Symmetric vs. Skewed
Right Skewed:
Left Skewed:
1. Modes - Unexpected clusters
2. Outliers - “unusual data points”
Histogram Data ExamplesTextbook Applets: from Publisher’s 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
Comparison of Histograms HWHW: 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
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”
Class Time Series Example
Monthly Airline Passenger Numbershttp://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)
Airline Passengers Example
Interesting variation: log transformation
• Stabilizes variation
• Since log of product is sum
• Shows changing variation prop’l to trend
• Log10 is “most interpretable”
(log10(1000) = 3, …)
• Generally useful trick (there are others)
Airline Passengers Example
A look under the hoodhttp://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
Time Series HW
HW: 1.36, 1.37
• Use EXCEL
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