A COMPARISON OF THREE VISUAL REPRESENTATIONS OFCOMPLEX MULTIDIMENSIONAL ACCOUNTING INFORMATION

Richard B. DullAssistant Professor of Accounting

Indiana UniversityKelley School of Business

801 West Michigan Street, BS 4026Indianapolis, IN 46202-5151

(317) 274-0867rdull@iupui.edu

David P. TegardenAssistant Professor of Accounting Information Systems

Virginia Polytechnic Institute and State UniversityPamplin College of Business

Department of Accounting and Information Systems (0101)3007 Pamplin Hall

Blacksburg, VA 24061(540) 231-6099

dtegarde@vt.edu

Acknowledgements: We appreciate everyone that contributed to the completion of this projectand paper, including Traci Hess, Jason Lockhart, the three anonymous reviewers and the journaleditors.

A COMPARISON OF THREE VISUAL REPRESENTATIONS OFCOMPLEX MULTIDIMENSIONAL ACCOUNTING INFORMATION

ABSTRACT

This study investigates the relationship between three visual representations (two-

dimensional, three-dimensional fixed, and three-dimensional rotatable) of multidimensional data,

and the subjects’ ability to make predictions based on the data. Output of a momentum

accounting system was simulated and graphics were rendered based on that information. An

interactive computer program was developed and used to administer the laboratory experiment

and collect results.

Subjects made prediction decisions based on the graphics produced for four companies.

Each subject made predictions for one type of graphics representation for each of the four

companies. Subjects using three-dimensional data that could be rotated provided the most

accurate predictions. This finding is significant in a systems environment where visualizations and

graphics are steadily increasing. The results should be considered when developing systems to

provide accounting system users with information for making decisions, especially when the

information to be presented is multidimensional in nature.

Key Words: Accounting information systems, information visualization, cognitive fit, proximitycompatibility principle, momentum accounting.

Data Availability: Please contact the authors.

Information, once rare and cherished like caviar,is now plentiful and taken for granted like potatoes.

The First Law of Data Smog, David Shenk, 1997

I. INTRODUCTION

Today's powerful accounting information systems provide decision-makers with an

abundance of accounting information that previously has not been cost-effective to produce.

However, despite significant technological advances in the accumulation of accounting data, the

formats used for presentation of the information produced by accounting information systems

have not kept pace with the information technology available. As such, advanced accounting

information systems, with their increasing volume of information and increasing complexity, can

simply overwhelm the decision-maker. This increase in the quantity of information is

compounded by the generally accepted trend towards enterprise-wide information systems that

integrate all aspects of the business.

There is an increasing trend towards supporting decision-making with multidimensional

data, e.g., on-line analytical processing (OLAP), knowledge discovery, and data mining (Adriaans

and Zantinge, 1996; Fayyad, et al., 1996; Thomsen, 1997). Additionally, there is a trend of using

multidimensional visual representations to support the decision-maker using multidimensional data

(Adriaans and Zantinge, 1996; Card et al., 1999; Parsaye and Chignell, 1993; Thomsen, 1997).

One area of accounting research that provides complex multidimensional accounting information

is momentum accounting.1 One of the main criticisms of momentum accounting is its higher level

of complexity, due chiefly to its multidimensionality, when compared to traditional double-entry

accounting (Fraser 1993).

Recent advances in visualization technologies provide one possible solution to this

information "glut." Specifically, data/information visualization may allow both novice and expert

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decision-makers to use their visual/spatial abilities in the process of making complex decisions

using accounting information. Data/information visualization is the use of visualization technology

to transform non-spatial, business, or behavioral data into multidimensional visual images that

represent an analogy or metaphor of the problem space (Schroeder, et al. 1998).

Visualization technologies have been successfully deployed in finance, litigation, marketing,

manufacturing, training, and organizational modeling (Brown, et al. 1995; Choras and Steinmann

1995; Grantham 1993; Markham 1998; Schroeder, et al. 1998; Thierauf 1995).2 Although these

technologies have been deployed, there are few scientific studies within business and accounting

to analyze the usefulness of this technology. The existing studies are generally limited to the

traditional “graph versus table” literature and do not address multidimensional data/information

visualization. The research reported on in this paper addresses the following general question:

Can accounting-based decision making performance be improved by usingdata/information visualization technologies?

Specifically, we investigate whether multidimensional visualization technology can increase the

usefulness of momentum accounting information when compared to using more traditional two-

dimensional graphics.

The remainder of the paper is organized as follows. The next section provides the literature

background. Section III provides the theoretical basis and states the hypothesis. The research

method is described in the section IV. Section V presents the data analysis and results, and the

final section contains the conclusions and limitations of the study.

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II. PRIOR LITERATURE

Momentum Accounting

Ijiri (1982, 1986, 1990) proposed an extension of double-entry accounting that considers a

third dimension of accounting data -- the time effect of accounting entries. This extension,

referred to as momentum accounting, would include information relating to the wealth of an

organization and the corresponding rates of change in the wealth of an organization3. Momentum

accounting increases the complexity of an accounting system by expanding on the single-

dimension stock (assets and liabilities) and two-dimensional flow (revenues and expenses)

concepts, by adding a third dimension (time) and, therefore, a corresponding third component of

each entry.

This study centers on making decisions using momentum accounting information rather than

on the specifics of a momentum accounting system. As such, we focus on the output of a

momentum accounting system rather than the details of journal entries and the recording of

transactions. Momentum accounting systems should provide a decision-maker with not only

current period information such as income, but also with the rate of change of income –

information useful when making decisions regarding future periods. If accounting information

associated with momentum accounting is presented suitably, the efficiency and effectiveness of

decision-making using momentum accounting information should be improved. The most suitable

presentation of momentum accounting information involves the use of multidimensional

visualization technology to match the dimensionality of the momentum accounting information,

thereby enhancing the understanding of that information (Cooper, 1990; Vessey, 1991).

Blommaert and Olders (1995) used financial statements4 based on momentum accounting

concepts to investigate managers’ use of the additional information provided in their decision

4

making process when predicting earnings for a future year. Their findings indicate that subjects

using momentum accounting based financial statements were capable of making more accurate

predictions of earnings than subjects using traditional financial statements. It may be possible to

reduce the complexity of using momentum accounting information via information visualization

technologies, hence, addressing one of the major criticisms of momentum accounting. In the

current study, we use momentum accounting information to test the viability of using visualization

technologies in accounting.

Visualization Research

From a cognitive science perspective, visualizations can enlarge problem-solving

capabilities. Miller (1956) describes a set of results that imply that a human’s input channel

capacity can be increased by using visual abilities. The results suggest that different parameters in

the visual channel can be exploited to increase the amount of data that decision-makers process

without suffering information overload. Furthermore, visual imagery research suggests that visual

recall is better than verbal recall, i.e., a picture really is worth a thousand words (Kosslyn 1980;

Shepard and Cooper 1982). However, imagery-based recall is highly associated with how the

objects were learned (visual images on visual perception, auditory images on auditory

perceptions, etc.).

Schkade and Kleinmuntz (1994) found that information format had a significant effect on

the decision process when used during information acquisition. Larkin and Simon (1987) found

that diagrams were superior representations to written ones and suggested three reasons for these

results. First, diagrams group related information together. Second, diagrams use location to aid

in information search. Finally, diagrams aid in many perceptual inferences. They concluded that if

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the user is capable of using diagrams to acquire information, diagrams seem to support more

efficient computational processes than their written counterparts.

Jones and Schkade (1995) found that if the information representation did not match

problem representation, decision-makers sometimes “translate” an information format into one

with which they are more familiar and base their decision on the new format. Cooper (1990)

suggests that when confronted with two-dimensional representations of structural objects,

subjects mentally create a three-dimensional representation of the object. Providing a two-

dimensional representation of a three-dimensional object may slow the decision-making

performance of a subject.

Wickens, Merwin and Lin (1994) indicate that for questions requiring an integrative

knowledge of information, extraction and retention of data is superior for 3D images over 2D

images. In addition, although statistical differences in responses were not reported, they

concluded that rotation was used more by subjects when answering questions that were relatively

more integrative. Furthermore, Pani (1993) reports that the angle of rotation affects the

comprehension of an object that is presented within a 3D representation.

The above studies suggest that multidimensional visualizations can be useful in decision-

making. They also suggest that rotation of the multidimensional visualizations facilitates

comprehension. Therefore, if the visualization fits the problem and the decision making process,

the speed and accuracy of problem solving should benefit.

Accounting-Based Visualization Research

The majority of research in accounting visualization relates to report format and

presentation. The formats for most research projects differ significantly, although one theme

continues throughout the literature; the presentation format of information affects the decisions

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that are made (MacKay and Villarreal 1987; Moriarity 1979; Stock and Watson 1984).

Additionally, visual representations have been investigated from several accounting perspectives

including cash flow predictions, financial forecasting, and time series analysis (Bouwman, et al.

1995; Carbone and Gorr 1985; DeSanctis and Jarvenpaa 1989; Goldwater and Fogarty 1995;

Moriarity 1979). However, most of the past research addresses only two-dimensional graphs.

Generally, most of the multidimensional visualization research was performed using

Chernoff Faces.5 Although most results indicate that using Chernoff Faces improves decisions

(Moriarity 1979; Stock and Watson 1984), MacKay and Villarreal (1987) indicate that using faces

may reduce the content validity of a visualization and, as such, limit its usefulness as a decision

aid. Additionally, Amer (1991) reports that using Chernoff Faces and radar charts (Harris, 1996)

in an integrative decision-making task provided no differences when compared with bar charts and

tables. As such, much of the multidimensional visualization research in accounting provides only

mixed results.

With today’s technological advances, most desktop computers can represent

multidimensional data by generating complex multidimensional graphics rather than limited

formats such as the faces and radar charts. The current study moves beyond the use of two-

dimensional graphics, Chernoff Faces, and radar charts to using a multidimensional information

visualization to fit an integrative accounting problem-solving task.

Novice Decision-Making and Visualization Technology

Using multidimensional visualizations to aid novices in decision-making is not a new

concept. Visual technologies are frequently used to help medical students understand how the

human body functions, by using three-dimensional graphics to represent areas that are difficult to

understand (Hallgren and Gorbis, 1999). Multidimensional visualizations have also been used to

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help novices understand abstract accounting concepts such as absorption costing. Park (1989)

suggests a three-dimensional graphic representation to aid in teaching accounting students the

impact of inventory changes on absorption and direct costing incomes. Duffy (1990) suggests

that using graphical analysis can increase student conceptual understanding of interest

capitalization. Schadewald and Limberg (1992) found that students using pictorial and textual

representations outperformed students using only textual representations of routine problem

solving tasks. However, they found that there were no significant differences between the two

groups when tackling novel problems.

Within the realm of accounting decisions, Moriarity’s (1979) investigation of

multidimensional representations found that experienced practitioners and persons of limited

accounting knowledge were able to more accurately make predictions using his representations.

Holland, Lorek and Bathke (1992) found no significant differences among majors, for students

(including MBA students with experience) when using graphics for extrapolative forecasting.

Research has shown that while making decisions, novices and experts may benefit from the

use of graphics within accounting and other disciplines. Additionally, in many instances

multidimensional graphics help novices understand complex concepts. As a first step in

visualization research in accounting, it is important to investigate whether novices are aided by

multidimensional graphics.

III. THEORETICAL DEVELOPMENT

The Cognitive Fit Model and Proximity Compatibility Principle are described in this section,

as is their relationship to the current study. Using these concepts in conjunction with the prior

literature discussion, the hypothesis and research question are developed.

8

Cognitive Fit Model

The Cognitive Fit Model (CFM) suggests that the effectiveness of the problem-solving

process is a function of the relationship between the problem-solving task and the problem

representation (Umanath and Vessey 1995; Vessey 1991, 1994; Vessey and Galletta 1991).

Using the CFM, Vessey (1991) provides an explanation for the mixed results in the "tables versus

graphs" literature. When the problem representation "fits" the problem-solving task, a preferable

mental representation of the problem will be realized and the solving speed and accuracy of the

problem solving process will be improved. Vessey (1991, p. 223) concluded that “matching the

problem representation to the type of task to be solved results in improved decision-making

performance.” Therefore, it should be emphasized that when mismatches do occur between the

problem solving task and the problem representation, decision-making performance suffers in

terms of speed, accuracy, or both.

Proximity Compatibility Principle

The Proximity Compatibility Principle (PCP) suggests a set of guidelines on which to base a

visual display design (Wickens and Carswell 1995; Wickens, et al. 1994). In a similar manner to

the CFM, PCP ties together both the problem solving task and the problem representation. In

PCP, the task is described as the processing, or task, proximity and the representation is described

as the perceptual, or display, proximity. Task proximity has three levels of processing: integrative

processing (high task proximity), non-integrative processing of similar tasks (lower proximity),

and non-integrative processing of dissimilar sources (independent processing). In this study, we

address integrative processing.6 Integrative processing requires combining multiple pieces of

information through some form of mathematical manipulation. There are several different ways in

which display proximity can be manipulated: spatial proximity, connections, source similarity,

9

code homogeneity, object integration, and configuration. In this study, we address spatial

integration and object integration.7 Spatial integration requires that related variables be displayed

in close proximity. In this manner, the user can see all semantically related information in one

location. Object integration requires multiple variables to be displayed in such a manner that the

variables appear to be part of a single object. In general, PCP suggests that the higher the level of

required integration, the higher the level of proximity the display should possess, and vice versa.

The lower the "fit" between the task and display proximity, the greater the "information access

cost" will be.

Hypothesis Development

Visualizations provide a method of understanding complex information by accumulating,

grouping, and displaying data in a manner that may be understood more effectively than by

viewing the details of the data. For decision makers performing a prediction task using

momentum accounting information, visualizations can be used as a tool to aid their understanding

of the underlying functional relationships8. Based on CFM and PCP, we expect that there should

be a difference in decision-making performance (prediction accuracy and time) based on the visual

representation used. Furthermore, we expect that the better the "fit" of the visual representation

to the dimensionality of the momentum accounting information, the more accurate the prediction.

In this case, accuracy is defined in terms of how close the subject’s prediction is to the momentum

accounting model prediction. In regards to the effect that rotation will have on decision-making

performance, the previous results have been mixed (Wickens, et al. 1994; Pani 1993). However,

due to issues related to occlusion, we believe that rotation may be capable of improving the

accuracy of the prediction.9 As such, our null hypothesis is:

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H1: Increasing the dimensionality of the visualization does not increase the accuracy ofpredictions of novices based on momentum accounting information.

For the purpose of this research, the dimensionality relationships are operationally defined as 2D <

3D < 3D rotatable. Based on these relationships, the null hypothesis implies decisions will not

differ as dimensionality increases from 2D to 3D to 3D rotatable.

In addition to prediction accuracy, the time to make a decision is important to the decision

process. Vessey (1991, 228) suggests that there are only two objective performance variables for

decisions: accuracy and decision time. Moriarity’s (1979) research with the multidimensional

Chernoff faces found significant decision time differences between experimental groups. Benbasat

and Dexter (1986) suggested that when using multiple forms of information representation to

solve problems, differences in time to solve problems might exist. These findings are in

agreement with the expectations set out by the CFM and PCP. However, there have been no

studies that have investigated the effects of 3D and rotatable 3D images on decision time.

Although from a CFM and PCP perspective, 3D and rotatable 3D images represent a more natural

"fit" for multidimensional information, due to issues related to occlusion and the mechanics of

rotating the 3D images, a decision-maker could take more time when using a 3D image than when

using a 2D image. Moreover, this increase in decision time when using 3D images could be even

more pronounced for novices, relative to experienced decision makers. As such, we also

investigate the following research question:

RQ1: How does the dimensionality of the visualization affect the time to make a predictionbased on momentum accounting information?

IV. METHOD

A laboratory experiment was conducted to investigate the hypothesis and research question.

This section describes methods used to develop the components of the experiment, including the

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experimental visualizations, task and reward system; the techniques used to select subjects and

companies are also described. Additionally, the dependent variables are identified and

operationalized.

Experimental Visualizations

Three visual representations were developed for this study (referred to as R1, R2, and R3).

Since the experimental task was an integrative prediction task (described below), it was expected

that the two-dimensional representation would be associated with the lowest subject performance

in the experiment. Each subject was exposed to only one of the three visual representations. The

first representation, R1, a two-dimensional line graph, demonstrated the functions of wealth,

momentum and impulse independently— three functions within momentum accounting (see Figure

1). Wealth was operationally defined as the market value of a company at a specific point in time;

momentum as the rate of wealth change (first derivative of the wealth function); and impulse as

the rate of momentum change (second derivative of the wealth function). Each graph contained

three lines, with each line representing a function for the wealth, momentum or impulse of a

company. This graph was a combination of the typical representations based on the physics

concepts that underlie momentum accounting (Brown, et al. 1995, p. 57; Halliday, et al. 1993, p.

21). Furthermore, since the experimental task (described below) was a prediction task, a line

graph seems appropriate. Users of the graph should be able to incorporate the rate of wealth

change (momentum) and rate of momentum change (impulse) when making their predictions of

future wealth.

The data displayed in this graph were semantically related and the task was integrative.

Therefore, a spatial proximity manipulation was used to make this graph as integrative as possible.

The graph displayed the relationships between the data in close proximity. To put the three lines

12

into close proximity required multiple y-axes and three different y-axes scales because of the unit

of measurement differences between the three functions. The first y-axis used wealth, the second

momentum, and the third used impulse. The momentum and impulse scales were multiplied by a

constant to allow similar relative values so that they were capable of being graphed in close

proximity with wealth. The x-axes, measured in months, ranged from one through 120 for each

of the representations. The lines were displayed to show the functions for months seven through

100 for a specific company. Each line on the visualization was displayed in a unique color. The

y-axes range, measured in dollars, varied based on the individual companies used for data.

(Insert Figure 1 here)

The second visualization, R2, used an object integration manipulation to maximize the level

of integration supported by this graph. It combined the three 2-dimensional lines from the first

representation into a modified trajectory line graph (see Figure 2). A trajectory line graph is a line

graph that curves through three separate dimensions (Harris 1996). This representation was

chosen to minimize differences between the representations; both are forms of line graphs. In our

modified trajectory line graph, time (month) was maintained as the x-axis, wealth as the y-axis,

and momentum was added as the z-axis. As a fourth dimension, we used the color of the line at

any point on the line to represent the impulse for a company at that point in time.10 The line was

plotted based on the values for the functions for the same time range used in the 2-dimensional

representation. This representation was displayed from a position of 30 degrees above the xz

plane and 35 degrees to the left of the yz plane.11

(Insert Figure 2 here)

The third representation, R3, looked identical to the R2 representation (see Figure 2). The

only difference was the ability of the subjects to rotate the image to view the data relationships

13

from different perspectives. By allowing subjects to rotate the image, issues related to occlusion

could be mitigated. The vertical rotation was allowed for 360 degrees (completely around the y-

axis) and the horizontal rotation was allowed for 180 degrees (the top half of the sphere divided

by the plane xz).12

Function Determination/Company Selection

The wealth function for a specific company was generated based on historical data for the

company’s monthly market equity (month-end stock price times the number of shares outstanding

at the end of the month). The derivative of the generated wealth function was taken (with respect

to time) yielding the momentum curve. A second derivative was taken to produce the function of

impulses. These three functions were used to generate the visualizations and were used for

predictive purposes.

The company data used in this study was selected from Compustat. Only those companies

that had monthly market values for November 1980 through May 1995 were selected. This

criterion was necessary to ensure that the companies were in business during the entire period for

which the wealth functions were to be generated. From these criteria, 188 companies were

selected that did not pay dividends during the period.13 These companies were ranked according

to total market value at the end of 1995; the group was then divided into thirds. Two companies

were selected from each of the high and low thirds, based on their relative rate of wealth growth

during the period, and total wealth. These companies are identified as large company/high growth

(LH), large company/low growth (LL), small company/high growth (SH), and small company/low

growth (SL). Two other companies were identified as having “interesting” patterns14 and were

used as training cases for the experiment.

14

The market values for the six experimental companies were used to generate an “nth”

degree polynomial to plot the data for each company. The polynomial was considered to be an

acceptable fit of the function when the graph displayed the major turns of the function and the R-

values for the polynomial generally were in the range of .7 to .9. After the generation of the

model functions and their first and second derivatives, 133 months of data were generated for

wealth, momentum, and impulse values for the each of the companies. Months 1-6 and 121-133

were eliminated, because of statistical issues that may exist in rounding endpoints when generating

equations from data points. Since months 101 - 120 were included the prediction period of the

task, they were not used. Months 7 - 100 were used to develop the visualizations used in the

experiment.

Measures

The data collected from the subjects included numerical values of wealth predicted for a

future period by each subject. For each company, the subjects predicted wealth for one, ten and

twenty month(s) beyond the values contained in the visualization. The dependent variable,

predicted wealth accuracy (WA), was measured for each subject, for each prediction period, by

subtracting the subject’s predicted wealth (S) from the model's predicted wealth (M).

WA = M - S (1)

The model predicted values were obtained from the wealth functions describe above for the

months of 101, 110 and 120. For data analysis purposes, we converted this measure to a

standardized measure that expressed the wealth accuracy relative (WAR) to the model's

prediction.

WAR = (M - S) / M (2)

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A second dependent variable examined consists of the time it takes a subject to process a

visualization and to make a prediction. This variable, prediction time, was operationalized as the

number of seconds expended since the previous response. This calculation was performed using

the internal clock of the PC. There was no fixed time limit imposed on the subjects although the

reward system, described below, was structured to provide incentives for speed if it was not

obtained at the expense of accuracy. Because of the method of collecting times, each prediction

generated an occurrence of the time variable.

Subject Selection

Subjects for this research were senior business school students at a major eastern state

university. These students were used because they are close to entering the job market in

positions that should require basic decision-making. They were a relatively homogeneous group

with basic training in financial decision-making. Although they had exposure to financial

statement representations, they were not biased for or against the “new” concepts presented by

momentum accounting. The usable sample consisted of 124 subjects allowing for the assignment

of approximately forty students to each of the three case groups.

Subjects were recruited from two courses at the university. One course was a senior-level

auditing course with class members being exclusively accounting majors. The second course was

an upper-level managerial accounting course with members being primarily of senior status and

business school, non-accounting majors. Each subject was randomly assigned and exposed to one

of the three visual representation groups.15

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Experimental Task

The experimental task was completed using personal computers, configured in a laboratory

environment. Each of the laboratory booths contained identical personal computers. Each

machine had a two-button mouse and a 15-inch color VGA monitor.

Upon entering an assigned booth, each subject read on-screen instructions and completed

practice predictions for one of the three visual representations.16 After the practice problems, all

participants were presented with visualizations for four companies and asked to make predictions

for three future periods for wealth. The predictions made by subjects required them to recognize

trends of wealth, based on the visualizations (R1-R3) presented.

The predictive results and additional information were collected on a diskette along with the

times each subject took to answer each question in the training session and actual case. The case

was similar to the case in DeSanctis and Jarvenpaa (1989).

Reward System

A reward system was developed to attract and compensate the participants. The

compensation package included guaranteed cash and extra credit in their course. The guaranteed

cash consisted of six dollars per hour, paid in one-tenth hour increments and the extra credit

received was a one percent bonus of the total possible points available in the course. Since no

subjects were members of both classes, the grade compensation was equal for all subjects. In

addition to the guaranteed segments of the reward system, each subject was entered into a “bonus

pool” with the chance of winning additional cash. The higher the performance of the subject, the

greater the likelihood of winning the additional cash. Three “pools” were established, one for

each type of representation (R1, R2 and R3), to eliminate compensation bias should one

representation be more effective than the others.

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V. RESULTS AND DISCUSSION

The experiment yielded twelve wealth predictions (three for each of the four companies)

and the associated prediction times for 124 subjects. The difference between the subject-

predicted value and the model-predicted value was used as the measure of the accuracy of the

prediction. Since the model-predicted value represents the “best” information that was available

to the subjects when making their decisions, it was used in this calculation. The model-predicted

value was determined by substituting the desired prediction period into the formula used to

generate the visualization. The data required for the research question were collected based on

the time required to make a prediction.

For each of the four case companies, each subject made three predictions for time periods

extending beyond the information provided. One would expect, as the times increased (the

predictions reaching further into the future) the accuracy of predictions would decline. These

expected differences suggest that the within-company predictions should be examined

individually, rather than in aggregate. In addition to the expected variability within company

predictions, a wide variation was expected between companies due to the characteristics of the

companies used in the experiment.17 Due to these expectations, it was determined that the

accuracy of the predictions for each company should be examined independently.

In order to evaluate the data independently with respect to company and prediction time

“distance," the accuracy data was segmented by observation made by the subjects. Each subject

made exactly one prediction for each time period for each company. A randomized block18 design

was used where the representations were blocked by subject observations. The mean for each

block was calculated providing the model with one observation per cell. These data, reported in

table 1, in conjunction with Friedman’s Rank Sums Test19, were used to test the hypothesis.20

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Friedman’s test (S= 7.17), using the representations as treatments, resulted in a p-value of .028.

This provides strong evidence that there were differences in the accuracy of predictions, based on

the visual representation used to make those predictions.

(Insert Table 1 here)

Although this evidence supports rejection of H1, a major issue in this research concerns not

merely the existence of treatment differences, but the direction of those differences. As described

earlier, it was expected that R3 would provide the highest accuracy of the treatments, R2 the mid-

range of accuracy, and R1 the lowest accuracy. With this expectation, Page’s (1963) test21 was

used to test for the direction of the relationships. Page's test (L= 155) resulted in a range of p-

values from 0.01 to 0.05. 22 This result suggests strong support for the order of accuracy of

representations where at least one of the inequalities was not a strict equality. In this instance,

this implies that as the dimensionality of the representation was increased, i.e., 2D to 3D to 3D

rotatable, the accuracy of the decision was improved. Evidence from Page’s test, in conjunction

with the result from Friedman's test, supports rejection of the null hypothesis (H1) and is

consistent with the alternative that proposed increased accuracy of predictions using

multidimensional representations of multidimensional data.

Results from the tests regarding H1 are consistent with several streams of research. First,

presentation format importance was confirmed. MacKay and Villarreal (1987) and Stock and

Watson (1984) all found that differences in decisions occur based on the format that the data were

presented to the decision-maker. Furthermore, Wickens, Merwin and Lin’s (1994) finding that

3D images are superior to 2D images when subjects are required to extract data was corroborated

by the current study. Within the accounting field, the current study findings were consistent with

19

the preferable decision outcomes when using multidimensional representations (MacKay and

Villarreal 1987; Moriarity 1979; Stock and Watson 1984.)

The research question suggests that there could be differences for time required to make a

prediction using the different visual representations. Again, Friedman’s test was used to examine

the research question. The means and ranks used to investigate the research question (R1 <> R2

<> R3) are included in Table 2. The results of the Friedman’s test (S= 15.5) indicate strong

support (p-value = 0.001) for differences between the three representations with respect to

prediction times between all three visual representations. We also investigated the three binary

comparisons between the three representations:

R1 <> R2, Friedman’s test (S= 1.33) indicate no support for differences (p-value = .248)

R1 <> R3, Friedman’s test (S= 12.00) indicate strong support for differences (p-value = .001)

R2 <> R3, Friedman’s test (S= 8.33) indicate strong support for differences (p-value = .004)

These results were consistent with prior research that suggests that time differences exist

when using multiple forms of information to solve problems (Benbasat and Dexter 1985).

(Insert Table 2 here)

Based on these results, we investigated the following relationships. Again, Page's test was used

to test the significance of the relationships.

R1 ≤ R3, Page’s test (L= 60) indicate strong support for differences (p-value = 0.000)

R2 ≤ R3, Page’s test (L= 59) indicate strong support for differences (p-value = 0.000)

R1 ≤ R2 ≤ R3, Page’s test (L= 159) indicate strong support for differences (p-values rangefrom 0.001 to 0.01)

R2 ≤ R1 ≤ R3, Page’s test (L= 162) indicate strong support for differences (p-values rangefrom 0.000 to 0.001)

20

From a practical perspective, these results imply that static visual representations (e.g., R1

and R2) may take less time to support decision making than dynamic visual representations (e.g.,

R3). In this instance, going from a 2D visual representation (R1) to a 3D visual representation

(R2) did not affect the amount of time to make the decision. Furthermore, the combined time and

accuracy results suggest that the static 3D (R2) visual representation may be more effective than

the static 2D (R1) or 3D rotatable (R3) visual representations. The R2 representation was more

accurate than R1 and took less time than R3. Furthermore, R2 seemed to take about the same

amount of time as R1. However, additional research is required to more fully explore these

relationships.

Although there was evidence that prediction time differences result from the different

treatments, there are several factors to consider in interpreting these results. One factor that may

have affected the time differences is the process by which individuals make decisions. Tan and

Benbasat’s (1993) study examines decision-making using 2-dimensional graphs and describes the

process used to make a decision. The process includes anchoring, disembedding, and projecting,

data points and values. It is also possible that a deeper knowledge of each of the visualizations

could impact the time differences noted in Research Question 1. Future research should include

additional training to mitigate any novice/expert effect of the representations. The relationship

between time and accuracy should also be considered. Furthermore, it is possible that R3 may

take less time than either R1 or R2 with a more difficult task. Additional research of the 3D

decision-making process considering these factors may provide insight into the intricacies of this

issue.

21

VI. CONCLUSION AND LIMITATIONS

The results of this study indicate that the form of the representation of data affects the

accuracy of the predictions novices make based on that data. Additionally, one can conclude that

multidimensional visual representation of complex multidimensional data results in greater

decision making accuracy because it facilitates the direct examination of the complex relationships

in the data. This conclusion has implications within the realm of accounting with respect to

decision-making when multiple variables are involved. As variables increase in complexity

(defined as dimensionality), there should be representations that show the interaction among the

variables to help enhance decision-making accuracy. Furthermore, with the trend towards

supporting decision-making with multidimensional data using on-line analytical processing

(OLAP), knowledge discovery, and data mining tools, this conclusion implies that in the future,

designers of advanced accounting information systems should be cognizant of the need to “fit” the

dimensionality of the data to the dimensionality of the visual representation. Otherwise, the

effectiveness of the decision maker may be compromised.

Although decision accuracy was improved by using the 3-D formats, the results do not

indicate that in this instance decision-makers use less time in forming their conclusions when using

these higher-dimension representations. The results do indicate that differences exist in decision

time, but these differences may be due to the physical limitations of rotating the graphic, lack of

familiarity with the visualization tool, or other factors not investigated here. Increased complexity

may add time to the decision-maker’s interpretation time, which is a possible explanation of the

data differing from the expectations given the minimal training that subjects received. It also is

possible that higher-dimension representations may only decrease decision making time with a

task more difficult than the one used in this study. Finally, it is possible that if the subjects are not

22

comfortable with the complexity of the task, they will take more time to investigate and

understand the visualizations.

A principal assumption of this study is that the visualization employed is appropriate for

momentum accounting information. In addition, other limitations may be identified with the

experiment. First, it is questionable whether the results reported in this paper can be generalized

beyond momentum accounting. Second, the results may have been partially confounded due to

the subject's lack of familiarity with momentum accounting and the multidimensional visualization

tool. Future research should conduct additional training to level the knowledge of the tools, prior

to the experimental trials. Expert users of the tools should also be considered in addition to the

inexperienced users examined in the current research. Finally, the issue of visual impairments and

color-blindness were not considered. Basic sight problems such as these may affect an

individual’s ability to use the presentations to make decisions.

Although research in accounting visualizations primarily has focused on simple graphics,

research in other fields has demonstrated benefits using data/information visualization

technologies. Further research into the application of these technologies to accounting problems

may yield similar results. Finally, visualization technologies may enable multidimensional

approaches to accounting problems, such as momentum accounting, to finally be comprehensible

and useful.

23

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FIGURE 1

R1 – 2 Dimensional Representation of Accounting Wealth, Momentum and Impulse

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FIGURE 2

R2/R3 – 3 Dimensional Representation of Accounting Wealth, Momentum and Impulse

Impulse Scale

x-axis – Monthy-axis – Momentum

z-axis – Wealth

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TABLE 1Standardized Wealth Accuracy

Means and (ranks) used with Friedman’s and Page’s tests for H1

Block\Representation R1 R2 R3Company 1: Obs 1 9.842 (2) 9.844 (3) 9.068 (1)Company 1: Obs 2 18.155 (3) 17.694 (2) 17.173 (1)Company 1: Obs 3 21.625 (3) 19.754 (1) 21.329 (2)Company 2: Obs 1 1.962 (2) 1.979 (3) 1.862 (1)Company 2: Obs 2 1.060 (1) 1.725 (3) 1.154 (2)Company 2: Obs 3 -0.020 (1) 0.141 (3) 0.091 (2)Company 3: Obs 1 -0.098 (1) 1.048 (3) 0.138 (2)Company 3: Obs 2 -0.689 (3) 0.010 (1) -0.256 (2)Company 3: Obs 3 -0.912 (3) -0.657 (1) -0.775 (2)Company 4: Obs 1 -0.977 (3) -0.945 (2) -0.933 (1)Company 4: Obs 2 -0.980 (3) -0.961 (1) -0.962 (2)Company 4: Obs 3 -0.983 (3) -0.973 (2) -0.971 (1)

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TABLE 2Question/Observation Response Time

Means and (ranks) used with Friedman’s and Page’s tests for RQ1

Block \Representation R1 R2 R3Company 1: Obs 1 45.4 (1) 50.3 (2) 52.6 (3)Company 1: Obs 2 25.9 (2) 22.6 (1) 35.1 (3)Company 1: Obs 3 19.3 (2) 15.4 (1) 29.4 (3)Company 2: Obs 1 43.4 (2) 42.1 (1) 52.9 (3)Company 2: Obs 2 22.0 (2) 21.9 (1) 32.4 (3)Company 2: Obs 3 20.3 (2) 15.6 (1) 22.6 (3)Company 3: Obs 1 39.3 (1) 47.7 (2) 53.5 (3)Company 3: Obs 2 18.9 (2) 17.6 (1) 41.2 (3)Company 3: Obs 3 14.6 (1) 17.0 (2) 21.4 (3)Company 4: Obs 1 30.3 (1) 44.9 (3) 42.3 (2)Company 4: Obs 2 22.5 (2) 18.8 (1) 25.0 (3)Company 4: Obs 3 15.2 (2) 13.4 (1) 16.8 (3)

33

ENDNOTES 1 Our reasoning for using momentum accounting (MA) rather than traditional concepts, was

twofold. First, given the functionality and derivatives associated with MA, it represents a “natural

occurrence” of multidimensional data within accounting. , MA thus appeared to be an ideal choice

to investigate the potential advantages of visualization technologies for presenting accounting

information. Second, for experimental purposes, it was deemed necessary to minimize subjects’

prior knowledge of the topic. Since student subjects used in the experiment had no exposure to

MA, there was little risk of them being biased either for or against the technique.

2 For a more complete description of visualization examples and issues, see Bertin (1983), Card,

et al. (1999), Cleveland (1993, 1994), Jones (1996), Kosslyn (1994), and Tufte (1983, 1990,

1997).

3 See Blommaert and Olders (1995) and Ijiri (1982, 1986, 1990) for a more complete description

of momentum accounting.

4 In addition to a traditional balance sheet, income statement and notes, the subjects received a

“Combined Momentum/Impulse/Action Statement” to convey the momentum accounting

information (Blommaert and Olders 1995, 17)

5 Chernoff used facial characteristics as variable representations for multivariate analysis

(Chernoff, 1973).

6 The experimental task used in this study is an integrative task.

7 The experimental visualizations used in this study were manipulated using spatial (2D

visualization) and object (3D visualizations) integration.

8 The experimental task used was similar to the task in DeSanctis and Jarvenpaa (1989)

34

9 In 3D graphics, if an object is occluded, then the observer cannot see it since it is covered by

objects that are "closer" to the observer. In this instance, it is possible for the trajectory line graph

to cover part of itself. As such, the only way the observer could see the entire graph is to rotate

it.

10 The use of a color overlay to add information to a graph is common when creating

visualizations. See Chapter 5 of Brown et al. (1995), Chapter 7 of Kosslyn (1994), and Chapter 5

of Tufte (1990).

11 This angle was selected through observations of other static 3-dimensional representations and

discussions with several pilot subjects. These individuals were allowed to rotate a graph and

asked what angle they would choose to display the graph for decision making, if the image could

not be rotated. With no exceptions, the individuals chose the approximate angle that was used in

this research.

12 A graphics expert suggested that subjects would receive no additional benefit from the bottom

half of the sphere (Lockhart 1997).

13 Companies that did not pay dividends were selected because dividends may have caused

discontinuities in the wealth functions used in the experiment.

14 Interesting as defined by a variety of directional moves relative to wealth, momentum and

impulse.

15 The random assignments were tested by statistically evaluating results based on gender and

college major. No differences were noted between groups.

16 Based on the results in DeSanctis and Jarvenpaa (1989), multiple practice predictions were

performed using the "interesting" (see footnote 14) firms. Prior to the experiment, each subject

35

was trained using an interactive automated routine. For each of two trial companies, three

practice predictions were made for wealth, three for momentum, and one for impulse. Each

practice prediction was followed by feedback that provided the model-predicted value for that

prediction interval. Each subject was exposed to only one type (dimension) representation for the

training and experiment.

17 One large, high growth company; one large, low growth company; one small, high growth

company; and one small, low growth company

18 This type of design is also known as a within-subject or repeated measures design.

19 Friedman’s Test is the nonparametric alternative to a repeated analysis of variance (SPSS, Inc.

1998). It is a distribution free test requiring data with one observation per block (Hollander and

Wolfe 1973.) The distribution free characteristic is important considering the unknown, non-

normal distributions of the samples collected in this research. To test the hypothesis of treatment

effect equality, Friedman’s Test ranks the observations within a block, and evaluates the rankings

for a specific treatment (Hollander and Wolfe 1973.)

20 The researchers analyzed the initial data, and various transformations (log, square root, and

inverse) of the data to determine if they met the normality of distribution and homogeneity of

variance assumptions for a classical Analysis of Variance test. The procedures used for this

analysis included the Kolmogorov-Smirnov Goodness-of-Fit Test, Levene’s Test and Bartlett’s

Test. After determining the data (and transformations) did not meet these assumptions,

nonparametric procedures were used to report results.

21 Page’s Test is a distribution-free test, based on the Friedman rank sums test. While Friedman’s

Test is used to look for the existence of differences between treatments, Page’s Test is used to

36

evaluate the order of those differences; the order should be identified prior to performing the test.

Each block is ranked by the relative position among the treatments.

22 P-values obtained from Hollander and Wolfe (1973, p. 372).