In the following subsections, two applications of £3 are examined to illustrate how the framework may be applied to practical situations. In the first example, the presentation of a spatial information system, the London Underground Map, is considered using two different presentation techniques (Figures 3.7 and 3.6a), simple windowing and the Bifocal Display (Spence & Apperley, 1982; Leung, 1989). In this case, the original data is in graphical form. For the simple windowed display (Figure 3.7), only a rectangular sub-section of the map is seen. However, with the Bifocal Display (Figure 3.6a), the entire map is shown, albeit with some areas distorted. In the second example (Figure 5.3), the presentation of data from a spreadsheet using two
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representation methods, one based on position and the other on length, is investigated. The spreadsheet, which consists of sales data of four products over a ten year period, is taken from experimental work on the appropriateness of alternative forms of graphical data presentation (Sparrow, 1989). The original data is in numeric form (Figure 5.3a), and is represented as either a stacked bar chart (Figure 5.3b) or a multiple line graph (Figure 5.3c). In either case, the graphical form is not large, and may be readily displayed on the screen in its entirety.
5 . 4 . 1 Expressiveness
As defined in £3 (Figure 5.2), expressiveness is (E l ) a measure based on the nature of the data and its representation. Because of the graphical nature of the data inherent in the spatial information system, direct representation is involved and no additional data encoding takes place in the simple windowing presentation;
expressiveness for the simple windowing presentation is therefore maximum ( 1). However, as station names are suppressed in the out of focus regions of the Bifocal Display, expressiveness (El) for the Bifocal Display can only be close to this maximum value.
Sales figures
Year Product ! Product 2 Product 3 Product 4 Total
Year 1977 75 130 10 120 335 Year 1978 75 120 20 1 10 325 Year 1979 80 1 10 120 Year 1980 90 105 125 360 Year 1981 105 97 1 15 367 Year 1982 l lO 95 60 120 385 Year 1983 100 90 70 l lO 370 Year 1984 90 80 80 l l 5 365 Year 1985 80 70 90 1 15 355 Year 1986 70 60 100 120 350 Total 875 957 550 1 170 3552 (5.3a)
CHAPTER 5: TilE £3 FRAMEWORK 400 350 300 250 200 150 100 50 0 140 120 100 80 60 40 20 0
Year Year Year Year Year Year Year Year Year Year 1977 1 978 1979 1980 198 1 1982 1983 1984 1985 1986
(5.3b)
Year Year Year Year Year Year Year Year Year Year 1977 1978 1 979 1980 198 1 1982 1983 1984 1985 1986 (5.3c) 103 0 Product 4 l3 Product 3 B Product 2 • Product 1 + Product 1 <> Product 2 • Product 3 a. Product 4
Figure 5.3 Example diagrams as used by Sparrow ( 1987). (a) The spreadsheet of the original sales data used in Sparrow's illustrations; (b) representation of the data set based on length in a stacked bar chart; and (c) representation of the same data set based on position in a multi-line graph.
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In the spreadsheet example (Figure 5.3), the expressiveness of the two representation techniques may be compared according to the accuracy of the encoding methods used, based on human visio-perceptual capabilities. According to Cleveland & McGill's relative ratings (Cleveland & McGill, 1984), the position representation (line graph) of this quantitative data set is one rank higher than the length representation (bar encoding chart) in terms of expressiveness. It is interesting to note that the superiority of position encoding is more prominent in ordinal and nominal data according to Mackinlay
( 1987).
5 . 4 . 2 Efficiency
Efficiency (E2) is defined as the proportion of the represented data set which may be presented on the display screen at one time. In the spatial data example, the
efficiency of the Bifocal Display for the London Underground map is close to 100% as the entire representation (although distorted and with the suppression of station names in the out-of-focus regions) is displayed; S2 is close to St (Figure 5.2). With the simple window presentation technique for the same map, however, the efficiency is calculated as follows:
Efficiency <El)windowing = 0.4 (width) x 0.5 (height) x 100% = 20%
In the spreadsheet example (Figure 5.3) all of the data is displayed, and because
S t is the same as S2, the efficiency is 100%.
5 . 4 . 3 Effectiveness
As mentioned previously, in £3 expressiveness is data dependent while effectiveness is task dependent. Assessment of the relative effectiveness should therefore be based on the underlying tasks performed by the user. In an experimental investigation of report forill,iltS and the decision maker's task conducted by Davis (1989), subjects were asked to make various decisions based on financial information presented in four forms: line graph, bat chart, pie chart, and table. Davis concluded that the most appropriate method of presenting fmancial information is dependent on the decision maker's question and that graphical presentations result in better performance only when they provide specific visual cues with aid in the answering of a question.
In the context of the London Underground map, the user may wish to search for a station and plan a route using station-related information as search keys; the search keys may be in the form of station name, general position in the map, proximity to a landmark station, the colour of the
rail
way line or the intersection of two lines. A criticalCHAPTER 5: THE E3 FRAMEWORK 105
evaluation of these tasks (Leung, 1992) suggests that the Bifocal Display is superior to simple windowing for a search key with station name and proximity information, while the reverse is true for a search key with infonnation about the intersection of two lines.
Six types of information have been identified by Sparrow ( 1989) as most commonly required by users of spreadsheets. They are infonnation about specifics, limits, conjunction, accumulation, trends and proportion. Two of the tasks investigated
in Sparrow's experiment are considered here. One is concerned with identifying the year when a product's sales was the highest or lowest (information about limits), and the other involves determining the year when one product sold less than another (information about conjunction). In the spreadsheet example, Sparrow found that overall, the stacked bar chart was more effective for assessing limits (about twice as good based on error rate). However, the multiple line graph was superior for conjunction and trends assessments.