Visualization and descriptive statistics. D.A. Forsyth
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1 Visualization and descriptive statistics D.A. Forsyth
2 What s going on here? Most important, most creative scientific question Getting answers Make helpful pictures and look at them Compute numbers in support of making pictures Data has types Continuous Discrete Ordinal (can be ordered) Categorical (no natural order, cat vs hat ) Different plots apply
3 Histograms Categorical data Ick!
4 Bar Charts Categorical data - counts in category
5 Histograms Ick! Continuous data
6 Histograms
7 Conditional Histograms
8 Data example Clicks, impressions and ages for NYT website Question: Look at data - what s going on? Example R code on webpage
9 Why R? It s free It s easy to get pictures up and going from weirdly formatted datasets Many, many tools most of the code I ll work with is downloaded/copied that s the right strategy work with tools *without* implementing them
10 Some R setwd('/users/daf/current/courses/bigdata/examples') data1<-read.csv('/users/daf/current/courses/bigdata/doing_data_science-master/dds_datasets/dds_ch2_nyt/nyt1.csv') data1$agecat<-cut(data1$age, c(-inf, 0, 18, 24, 34, 44, 54, 64, 74, 84, Inf)) # This breaks the Age column into categories data1$impcat<-cut(data1$impressions, c(-inf, 0, 1, 2, 3, 4, 5, Inf)) # This breaks the impression column into categories summary(data1)
11 Age Gender Impressions Clicks Signed_In agecat impcat Min. : 0.00 Min. :0.000 Min. : Min. : Min. : (-Inf,0]: (-Inf,0]: st Qu.: st Qu.: st Qu.: st Qu.: st Qu.: (34,44] : (0,1] : Median : Median :0.000 Median : Median : Median : (44,54] : (1,2] : Mean : Mean :0.367 Mean : Mean : Mean : (24,34] : (2,3] : rd Qu.: rd Qu.: rd Qu.: rd Qu.: rd Qu.: (54,64] : (3,4] : Max. : Max. :1.000 Max. : Max. : Max. : (18,24] : (4,5] : (Other) : (5, Inf]:176558
12 Users by age
13 Impression histogram, faceted by age
14 Click histogram, faceted by age
15 Click/Impression histogram, faceted by age
16 2D Data
17 Categorical data Pie charts are deprecated - it s hard to judge area by eye accurately
18 Mosaic Plots
19 The UFO data set UFO sighting data date of sighting; date of report; location; description; some free text rather messy data about 15 years of sightings ( with some others) broke into 1000 day blocks looked at most common shape descriptors (' disk', ' light', ' circle', ' triangle', ' sphere', ' oval', ' other', ' unknown') great example of categorical data R-code on website not great code, but informative building a map, merging datasets, reading datasets, mosaic plots you should look at this
20 Conclusion: UFO shapes haven t changed over time
21 Ordinal data
22 Ordinal data
23 Series
24 Scatter plots Plot a marker at a location where there is a datapoint Simplest case - geographic
25
26
27 Arsenic in well water
28 UFO sightings by state
29 UFO s by interval
30 UFO s by interval
31 UFO s by interval
32 UFO s by interval
33 UFO s by interval
34 UFO s by interval
35 Interesting analogy Blackett s reasoning about submarine sightings in WWII can estimate probability of sightings lead to significantly improved sighting rates, aircraft painting and lighting strategies (see Korner, The pleasures of counting or good histories)
36 NYT data - remarks Many data points lying on top of each other scatter plot can be deceptive jitter the points (move by a small random amount)
37
38 Age Gender Impressions Clicks Signed_In agecat impcat Min. : 0.00 Min. :0.000 Min. : Min. : Min. : (-Inf,0]: (-Inf,0]: st Qu.: st Qu.: st Qu.: st Qu.: st Qu.: (34,44] : (0,1] : Median : Median :0.000 Median : Median : Median : (44,54] : (1,2] : Mean : Mean :0.367 Mean : Mean : Mean : (24,34] : (2,3] : rd Qu.: rd Qu.: rd Qu.: rd Qu.: rd Qu.: (54,64] : (3,4] : Max. : Max. :1.000 Max. : Max. : Max. : (18,24] : (4,5] : (Other) : (5, Inf]:176558
39
40
41 NYT scatters
42 Scale is an issue
43 Outliers can set scale
44 But scale is really a problem
45 Lynx pelts
46 Data example Housing sales in NYC boroughs Question: Look at real estate sales - what s going on?
47 Summary Statistics - mean The average The best estimate of the value of a new datapoint in the absence of any other information about it
48 Summary statistics - Standard deviation Think of this as a scale Average distance from mean Important math properties in notes
49 Standard deviation = there are not many points many standard deviations away from the mean = there is at least one point at least one standard deviation away from the mean
50 Standard coordinates
51 Suppressing scale effects Do scatter plots in standard coordinates for x, y
52
53 Lynx, normalized
54 x, y don t really matter
55
56 Positive Correlation
57 Zero Correlation
58 Negative correlation
59 The Correlation Coefficient
60
61 Correlation isn t causality and foot size is positively correlated with reading ability, etc.
62 but can be used to predict
63 What s going wrong here? NYT normalized
64
65 A Mosaic Plot
66
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