Stat 31, Section 1, Last Time Course Organization & Website What is Statistics? Data types and structure Get going in EXCEL Exploratory Data Analysis Bar Graphs

Stat 31, Student Poll Results As indicated on “Student Info” form: Big changes from the past: More biology More diversity

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…

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 3 Visual Display of Quantitative Distributions: 1.Stem and Leaf Plots 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”

Class Histogram Example Buffalo, N. Y. (Annual) Snowfall Data Raw Data: 63 years, ranging from ~30 - ~120 (inches)

Buffalo Snowfall Data Buffalo, N. Y. (Annual) Snowfall Data Raw Data: 63 years, ranging from ~30 - ~120 (inches) Histogram Analysis (pre-done):

Buffalo Snowfall Data, I A.EXCEL default (of bin edges) Unround numbers for bin edges 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”) (can’t see this above: bin width counts)

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??? Quite symmetric? (different from above: bin width counts)

Buffalo Snowfall Data, IV C.What’s under the hood (how to do this): i.Tools  Data Analysis  Histogram (& Chart Out) (may need Data Analysis “Add-in”) i.Massage pic (especially bar width) ii.Sigma  min, max iii.Bin range: create first two & drag iv.Histogram, using input bin edges

Buffalo Snowfall Data, IV C.What’s under the hood (how to do this): i.Tools  Data Analysis  Histogram (& Chart Out) (may need Data Analysis “Add-in”) i.Massage pic (especially bar width) ii.Sigma  min, max iii.Bin range: create first two & drag iv.Histogram, using input bin edges

Histogram HW HW:1.21 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

Histogram Binwidths Nice Example from the Webster West, U.S.C.: 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? Caution: Answer depends on binwidth (a serious and current statistical research problem)

Stamps Data Histogram How many modes? 2 nd 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 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?)

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”

Comparison of Histograms HW HW: 1.25b, 1.27, 1.29, 1.22 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

Plotting Bivariate Data Toy Example: (1,2) (3,1) (-1,0) (2,-1)

Plotting Bivariate Data Sometimes: Can see more insightful patterns by connecting points

Plotting Bivariate Data Sometimes: Useful to switch off points, and only look at lines/curves

Plotting Bivariate Data Common Name: “Scatterplot” A look under the hood: EXCEL: Chart Wizard (colored bar icon) Chart Type: XY (scatter) Subtype conrols points only, or lines Later steps similar to above (can massage the pic!)