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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