Depicting Quantitative Data PDF

Depicting Quantitative Data  Dimensionality: data about running clubs Univariate: only one variable describes the data – number of members in each club Bivariate: two variables/attributes – numbers of male and female members in each club Tri-variate: three vari...

Depicting Quantitative Data  Dimensionality: data about running clubs Univariate: only one variable describes the data – number of members in each club Bivariate: two variables/attributes – numbers of male and female members in each club Tri-variate: three variables/attributes – number of men, women, average race finishing position for the club Multivariate: more than three variables/attributes – number of men, women, membership fees, colour, founding year, average race finishing position  The data Club name: categorical although note that an alphabetic ordering may be imposed, making the data ordinal Number of members: quantitative Number of women: quantitative Number of men: quantitative Membership fees: quantitative Colour: categorical Founding year: quantitative Average race finishing position: quantitative  Univariate (number of members in a club) AberdeenC 188 Perth Orienteers 200 Achille Ratti 162 Hunters Bog Trotters 197 Aireborough Tri C 136 New Town Hash 197 Alnwick H 59 Inverness H 196 Ambleside 100 Lothian & Borders 196 Annan & Dist 100 Penicuik YMCA 196 Argyll & S 46 Boundary H 191 Ayr & Seaforth 34 Carnethy 191 Bellahouston 96 Riyadh HH Harriers 191 Black Isle 147 Univeristy of Sunder 191 Border Harriers 166 AberdeenC 188 Boundary H 191 Edinburgh Univ 187 Brit Orienteering Squad 86 Peeblesshire 187 Calderglen Harriers 89 N Shields Poly 184 Camuslang Harriers 157 Deeside Runners 183 Carnegie Harriers 113 Skelmersdale 181 Carnethy 191 Macclesfield H 175 Castlemilk 134 Lochaber 173 Central Region 115 Spenborough 172 Claremont 133 Gala Harriers 170 …. 100 clubs …. 100 clubs  Univariate (number of members in a club) mean 116.2 std-dev 51.18 median 113 Q1 72 Q3 158.25 histogram box plot  Bar charts d e c a b number of clubs associated with each colour Pie charts are not good d a b c e number of clubs associated with each colour  3D effects: don’t use them! x y AberdeenC Achille Ratti 133 141 55 21 Bivariate (male and female members) Aireborough Tri C 73 63 Alnwick H 21 38 Ambleside 51 49 Annan & Dist 58 42 Argyll & S 11 35 Ayr & Seaforth 8 26 Bellahouston 69 27 Black Isle 74 73 Border Harriers 148 18 Boundary H 138 53 Brit Orienteering Squad 45 41 Calderglen Harriers 53 36 Camuslang Harriers 113 44 Carnegie Harriers 75 38 Carnethy 136 55 Castlemilk 95 39 Central Region 85 30 Claremont 76 57 … 100 clubs clustered bar chart (alphabetic) Overview of all clubs (top) Detail of some clubs (bottom)  clustered bar chart (ordered by female) stacked bar chart (ordered by total) 100% stacked bar chart (ordered by total) scatterplot  male female mean 80.9 35.3 std-dev 52.6 13.8 median 75.5 36.5 Q1 41.3 26.0 Q3 133.3 43.0 Bar charts vs Line charts number of new clubs opened each year number of clubs associated with each colour  average Tri-variate finishing male female position AberdeenC 133 55 21 Achille Ratti 141 21 32 Aireborough Tri C 73 63 10 Alnwick H 21 38 3 Ambleside 51 49 25 Annan & Dist 58 42 8 Argyll & S 11 35 86 Ayr & Seaforth 8 26 45 Bellahouston 69 27 27 Black Isle 74 73 23 Border Harriers 148 18 19 Boundary H 138 53 14 Brit Orienteering Squad 45 41 4 Calderglen Harriers 53 36 11 Camuslang Harriers 113 44 10 … 100 clubs  scatterplot matrix (SPLOM): one scatterplot for each pair of variables bubble plot One bar chart per variable: relationships between them best shown via interaction methods  Tri-variate: Heat maps Typically, two (independent) categorical variables, and a quantitative variable The categories are on the two axes The quantitative value is represented by change in colour value – typically: ‘darker’ = ‘more’… but be careful! – Often best to show the value encoding in a chart legend The order of the categories on each axis can be changed (and may be important for identification of patterns) Each cell has only one value  trivial easy medium hard guelling Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Record finishing time for races over the same distance, with different difficulty, at different times of year  Jenny Hannah Chen Thembi Farah A B C D E F G H I J K L Proportion of baby girls given particular names, with respect to different countries  Jenny Hannah Chen Thembi Farah F L G C B A J E I H D K Proportion of baby girls given particular names, with respect to different countries, reordered Measles cases over time, per US state Wall Street Journal, Feb 11, 2015 https://onlygrowth.com/blogs/posts/how-to-use-heat-maps-and-eye-tracking-software-to-improve-ux-and-lift-conversion-rates (accessed 25/05/21) https://www.infragistics.com/community/blogs/b/mobileman/posts/geographical-heat-maps-and-how-to-use-them-with-reportplus (accessed 25/05/21)  Multivariate members male female fees colour year average finishing position Carnegie Harriers 113 75 38 15 dark blue 1970 5 Deeside Runners 183 167 16 60 yellow 1970 13 Macclesfield H 175 135 40 40 light green 1970 6 Leeds Uni 56 13 43 20 dark green 1971 16 Brit Orienteering Squad 86 45 41 25 light green 1972 4 Perth Orienteers 200 150 50 50 light green 1972 16 Alnwick H 59 21 38 40 light green 1973 3 Sheffield University 48 16 32 25 white 1974 13 Whitbread 107 52 55 55 yellow 1974 91 Ayr & Seaforth 34 8 26 45 yellow 1975 45 East Lothian Orienteers 155 122 33 20 yellow 1975 76 Glasgow UOC 92 70 22 15 purple 1975 22 St Andrews CCC 156 125 31 10 yellow 1975 49 Doncaster 157 130 27 50 red 1976 39 Edinburgh Triathlete 57 16 41 40 dark blue 1976 18 Forth Valley Orienteers 113 61 52 15 purple 1976 9 Scots Vets Harriers 57 11 46 30 light green 1976 17 Keswick 137 101 36 40 light green 1977 19 Lasswade 99 49 50 35 light green 1977 20 Calderglen Harriers 89 53 36 30 pink 1978 11  Multivariate: Parallel coordinates Each vertical axis is a dimension, with its values equally spaced along it The dimensions are arranged, equally spaced, horizontally A single data point is a line that joins its values on each dimension Robert Kosara, “Parallel Coordinates (eagereyes)”, https://eagereyes.org/techniques/parallel-coordinates, 2010 (accessed 18/04/21) men women fees colour year AFP  MPG Cylinders Horsepower Weight Year 15 8 170 3563 1970 14 8 160 3609 1970 15 8 150 3761 1970 Car models: 14 8 225 3086 1970 released from 1970 to 1982 24 4 95 2372 1970 mileage (MPG) 22 6 95 2833 1970 number of cylinders 18 6 97 2774 1970 horsepower 21 6 85 2587 1970 weight 27 4 88 2130 1970 year 26 4 46 1835 1970 25 4 87 2672 1970 (plus other features not used here) 24 4 90 2430 1970 25 4 95 2375 1970 …and many more data items Robert Kosara, “Parallel Coordinates (eagereyes)”, https://eagereyes.org/techniques/parallel-coordinates, 2010 (accessed 18/04/21) Each line from left to right represents one car Looking at each pair of axes in turn: the cylinder axis has only a few values – all lines pass through a small number of points 8-cylinder cars tend to have lower mileage than cars with 6 or 4 cylinders (inverse correlation) more cylinders means more horsepower (almost direct correlation) more horsepower means more weight (almost direct correlation) older cars are heavier (roughly, an inverse correlation) Robert Kosara, “Parallel Coordinates (eagereyes)”, https://eagereyes.org/techniques/parallel-coordinates, 2010 (accessed 18/04/21) Parallel coordinate transformations 4.8, 3.0, 1.4, 0.3, Iris-setosa The iris data set 5.1, 3.8, 1.6, 0.2, Iris-setosa 4 dimensions 5.3, 3.7, 1.5, 0.2, Iris-setosa 5.0, 3.3, 1.4, 0.2, Iris-setosa – petal width 7.0, 3.2, 4.7, 1.4, Iris-versicolor – petal length 6.4, 3.2, 4.5, 1.5, Iris-versicolor – sepal width 6.9, 3.1, 4.9, 1.5, Iris-versicolor 5.1, 2.5, 3.0, 1.1, Iris-versicolor – sepal length 5.7, 2.8, 4.1, 1.3, Iris-versicolor 6.3, 3.3, 6.0, 2.5, Iris-virginica 5.8, 2.7, 5.1, 1.9, Iris-virginica 7.1, 3.0, 5.9, 2.1, Iris-virginica 6.3, 2.9, 5.6, 1.8, Iris-virginica ……. https://www.data-to-viz.com/graph/parallel.html#code (accessed 18/04/21) https://www.data-to-viz.com/graph/parallel.html#code (accessed 18/04/21) Arrange the order of the dimensions on the x- axis to find and/or highlight clear relationships (direct or inverse) of interest See: Siirtola, H. (2000) Direct manipulation of parallel coordinates https://www.data-to-viz.com/graph/parallel.html#code (accessed 18/04/21)  Multivariate: Scatterplot matrix & Parallel coordinates Munzner (2015), p163, 2015  x axis: life expectancy Multivariate: y axis: infant mortality Bubble Plots size: population colour: continent Robertson et al. (2008) Effectiveness of Animation in Trend Visualisation  Multivariate: Star/Radar plots n=7 n=21 https://www.data-to-viz.com/caveat/spider.html (accessed 26/05/32)  Univariate: Tri-variate – bar charts – scatter plot matrix – histogram – heat map – box plot – mosaic plot – … – … Bivariate Multivariate – clustered bar chart – parallel co-ordinates – stacked bar chart – SPLOM – 100% stacked bar chart – … and other techniques – scatter plot from a later lecture – … Depicting Quantitative Data