Comprehension of diagram syntax: an empirical study of Entity Relationship notations

Transcription

1 Comprehension of diagram syntax: an empirical study of Entity Relationship notations Helen C. Purchase*, Ray Welland*, Matthew McGill and Linda Colpoys International Journal of Human-Computer Studies, 6(2), pp87-203, * Computing Science Department, University of Glasgow 7 Lilybank Gardens Glasgow G2 8QQ Scotland School of Information Technology and Electrical Engineering University of Queensland St Lucia 4072 Brisbane Queensland Australia

2 Abstract Well-defined symbolic notations are essential for communication between teams of people working on any application. For large software implementations, UML is commonly used; for databases, entity-relationship diagrams are useful. However, the form of notation used in texts, papers, and documentation and learning materials is often different, and tends to reflect the personal preference of the author or publisher. The choice between semantically equivalent notations does not appear to be based on any consideration of the ease with which human readers could understand the notation. This paper addresses this notation comprehension issue by proposing an experimental methodology for determining which of two complete notations is easier to comprehend. The methodology also allows individual notational variants to be targeted. This methodology has been applied to two types of entity relationship notations: our experiment required subjects to indicate whether a supplied textual specification of objects and relationships matched each of a set of Chen [] and SSADM [2] entity relationship diagrams. The results reveal both better performance and higher preference for the more concise overall notation, with partial results with respect to individual variants within the notations.. Introduction There are many diagrammatic notations that may be used interchangeably in published texts, diagrammatic modelling systems, and in educational materials. Choices as to which notation to use are typically made with respect to personal preference, convention, or technical ease, rather than by taking into account the ease with which the notation may be understood or learned by humans. Some theoretical analytical work has been performed on software engineering notations and visual programming languages, but no empirical studies on human comprehension of these notations have been found. While software engineering notations have been analysed and compared using the Cognitive Dimensions framework [3,4] this framework is theoretical and these analyses, while providing interesting structured perspectives on the notational features, are not based on experimental data [5,6,7,8]. The methodology and experiment reported here complements such analytical work. Some experimental work has been performed on notational features for UML class and collaboration diagrams [9,0] using a similar methodology to that presented here. While the UML notation has been adopted as the defacto standard, it is ill defined with respect to some

3 of its specific syntax. These prior experiments considered only partial notational variations rather than complete UML notational formalisms. For example, the UML research considered the way in which cardinalities may be represented in UML class diagrams and the manner in which sequences are numbered in UML collaboration diagrams. The experiment reported here compares both two complete notations, as well as the notational differences within them. The aim of this research was to present an experimental methodology for comparing complete notational representational methods with respect to their comprehension by humans, and to demonstrate its use by applying it to the comparison between two entity relationship notations.. Experimental Aims The first aim was to raise the issue of the criteria by which a notation may be chosen. The assumption is made that the set of possible notations that may be used are all functionally equivalent (that is, they are all able to represent all the information that needs to be depicted), and that their difference lies in their syntax. The second aim is to propose a methodology to compare two complete notations, while targeting their specific differences. The possible outcome of such an experiment could be that one complete notation is deemed easier to understand than the other; however some of the individual notational differences may produce better performance. The third aim was to demonstrate an application of this experimental methodology, by performing an experiment to determine which of two Entity Relationship diagram notations is most suitable with regard to human comprehension and performance. The experiment asked subjects to perform comprehension tasks on the same application domain using each of the two notations..2 Entity relationship diagrams An entity relationship (ER) diagram is essentially a 'type' diagram that defines the structure of database instances. An entity is a thing about which we wish to store data, for example a student or a project, and is characterised by a set of attributes. An instance of an entity has a set of attribute values describing that instance.

4 A relationship defines the permissible associations between instances of entities. There are three important characteristics of a relationship: The entity types it connects. In our experiment we have assumed that all relationships are binary, i.e. involving only two entity types (or a recursive relationship associating instances of one entity type with other instances drawn from the same type). The cardinality of the relationship. This specifies the number of instances of an entity type that may be involved in any instance of the relationship type. The participation constraint. This indicates whether every instance of a given entity type must be involved in an instance of the relationship (i.e. mandatory or optional). Figure shows a small university system in which an academic may supervise students, who enrol in subjects, and work on projects. The system is displayed in both notations of the entity relationship diagrams notations used in the experiment reported in this paper. Academic supervises Subject enrolled in M Student works on Project Figure : The student application using the Chen notation [] Academic supervises Subject enrolled in Student works on Project Figure 2: The student application using the SSADM notation [2]

5 .3 The notations The experimental aim was to compare the performance of two ER notations with respect to a human comprehension task. This method is therefore different to our previous similar empirical studies on UML notations [9,0] when only parts of the notational syntax were investigated. One of the earliest forms of ER model was proposed by Chen [] and his basic notation (the 'Chen model') is still widely used today. More recently an ER model notation, called the Logical Data Structure (LDS), defined for SSADM [2] has become popular. These two notations are interesting to us because we can define the equivalent data model in the two notations; provided we make some simplifying assumptions, we can describe exactly the same ER model using different surface syntax. This experiment does not attempt to compare the effectiveness of the different modelling methodologies underlying the notations, but rather looks at the comprehension of the syntax of the notations themselves. We make no claim about these two methodologies..3. Simplifying Assumptions The Chen model includes attributes as part of the ER diagram, whereas the SSADM notation assumes that these are defined separately in some form of data dictionary (an Entity Description Form in SSADM terminology). We have ignored attributes for the purposes of this experiment to ensure comparability of the notations and to reduce diagram complexity. Another difference between the notations is that Chen allows attributes to be associated with relationships; ignoring attributes also hides this difference. The SSADM model allows the use of role names to distinguish the two constituents of a binary relationship. Again, for comparability, we have assumed that each relationship has a single name. The only similarity between the two notations is that the entities are represented in rectangles. Otherwise, the notations differ in three ways: (a) the representation of the cardinality of the relationships: one-to-one, one-to-many, or many-to-many. Cardinalities in the Chen notation are written as or M/

6 (representing many ) and are found on either side of the relationship diamond-shaped node. In the SSADM notation, cardinalities are displayed using either a single-line join at the entity node for depicting a relationship occurring only once, and a crow s foot for relationships in which the entity may participate many times. (b) the representation of whether the relationship is mandatory or not (its participation). The Chen notation denotes optional and mandatory relationships with a single and a double line respectively, while the SSADM notation denotes optional and mandatory relationships with a single broken, and single unbroken line respectively. (c) the naming of the relationships (in the example: works on, enrolled in, and supervises.) In the Chen notation, relationships are displayed inside diamond-shaped nodes, whereas in the SSADM notation, relationships are written alongside the edge joining the entities. 2. Experimental Method The comprehension task was that of matching a given textual specification against a set of diagrams, indicating whether or not each diagram correctly matches the specification. The set of diagrams included both correct and incorrect diagrams from the Chen and SSADM notations. 2. Experimental materials 2.. The application domain The entity relationship diagrams were based on a simple domain, which models a small organisation with a department that has an account section, and employees who work on projects that are paid for by a client account. The example includes 5 entities and 8 relationships (see Figure 3). A textual specification of this domain was produced in simple English (see Figure 4). The subjects were asked to match the experimental diagrams against this specification.

7 Supervises Supervises Employee Employee Manages Works for Assigned to M Manages Works for Assigned to Department Oversees Project Department Oversees Project Invoices for Pays for Invoices for Pays for Account Section Portfolio Client Account Account Section Portfolio Client Account Figure 3: The experimental application domain in the Chen and SSADM notations Tutorial and Worked Example A tutorial sheet explained the meaning of Entity Relationship diagrams, and, using a simple example, described the semantics of both notations. The order in which the notations were introduced was varied so that half of the subjects started with the Chen notation, while the other half started with the SSADM notation. The tutorial provided them with all the Entity Relationship diagram background information they required for the task. Subjects were not expected to have any prior knowledge of Entity Relationship diagrams. In fact care was taken so as to recruit first-year students who had not completed university subjects in which they had learnt about Entity Relationship diagrams as that may have biased them towards one particular notation over another. A worked example demonstrated the task the subjects were to perform, by presenting a small textual specification with four different diagrams, and for each diagram indicating whether it matched the specification or not. The example textual specification was written in the same form as the specification used for the experimental diagrams. Care was taken to ensure that neither the tutorial nor the worked example would bias the subjects towards one notation or the other by providing two examples from each notation.

8 A company consists of departments for which the employees work. The employees work on projects, which are overseen by departments, for clients. The projects are paid for by client accounts, which are in the portfolio of an account section. An Employee: must work for one department may manage one department may be assigned to many projects may be supervised by one employee may supervise many employees A Department: must be managed by one employee must be invoiced for by one account section must be worked for by at least one employee may oversee many projects A Project: must be assigned to by at least one employee must be overseen by one department must be paid for by one client account An Account Section: must invoice for at least one department must have in its portfolio at least one client account A Client Account: must be in the portfolio of one account section may pay for many projects Figure 4: The specification that subjects matched against the experimental diagrams.

9 2..3 The experimental diagrams The basic structure of the Entity Relationship diagram representing the domain was reproduced in six different layouts. Different layouts were required so that the subjects would not merely use visual pattern matching in performing the comprehension tasks. If all the diagrams had identical layout, the differences between them would be visually obvious and detectable without the subject needing to understand the information embodied in the diagram. Prior experimental work demonstrated the effect of diagrammatic layout features on the comprehension [,2], so each layout was constructed with a view to minimising the potential for any confounding layout factors. Thus each layout had a similar number of edge bends and sloping lines, no edge crossings, comparable orthogonality (the property of fixing nodes and edges to the intersections and lines of an invisible unit grid), and was of similar size. Using these six layouts of the diagram, the following experimental diagrams were produced: Correct diagrams: For each of the six layouts, both the Chen and SSADM notations were used to draw the application domain, giving a total of 2 correct diagrams. Account Section Portfolio Invoices for Client Account Department Oversees Pays for Works for Manages Project M Assigned to Employee Supervises Figure 5: Error operation (c) (Chen notation)

10 Supervises Employee Assigned to Project Works for Manages Oversees Pays for Department Client Account Invoices for Portfolio Account Section Figure 6. Error operation (b) (SSADM notation) Incorrect diagrams: For each of the 2 correct diagrams, three error operations (a, b, and c) were applied, making a total of 36 incorrect diagrams. Each error operation focussed on one of the differences between the notations (cardinality, participation, representation of relationships). The following error operations were used: Error operation (a) affected the cardinalities, where the cardinalities of three relationships were altered. Error operation (b) had the participation in three relationships altered. Error operation (c) swapped two of the relationship names. Figures 5 and 6 show the application domain in each of the notations, with error operations applied. These figures also demonstrate two of the alternate layouts used in the creation of the experimental diagrams. Separating the error operations in this way enabled the comprehension of the different notational differences to be studied independently: thus, it may be that one notation is better for representing cardinality, while another may be better for representing participation. However, both error operations (a) and (b) affect the representation of the nature of the relationship, rather than the name of the relationship. There is therefore a potential interaction between the representation of participation and cardinality, although this has not been

11 addressed in this experiment as no diagrams were produced that had both the error operation (a) as well as the error operation (b) applied. 2.2 Experimental Procedure 2.2. Preparation The students were given preparatory materials to read as an introduction to the experiment. These documents consisted of a consent form, an instruction sheet, a tutorial on Entity Relationship diagrams and notation, and a worked example of the experimental task. As part of this document set, the subjects were also given the textual specification of the case study to be used in the experiment: this was the specification that they would need to match the experimental diagrams against. The subjects were asked to study this specification closely, and memorise it if possible. The subjects were given 5 minutes to sign the consent form, read through and understand the materials, ask questions, take notes, or draw diagrams as necessary Online Task The subjects then used an online system to perform the experimental task. A copy of the text specification was placed in front of the computer for easy reference, and the experimental Entity Relationship diagrams were presented in random order for each subject. The subjects gave a yes/no response to each presented diagram, indicating whether they thought the diagram matched the specification or not: two keys on the keyboard were used for this input. 6 practice diagrams (randomly selected from the 48 experimental diagrams) were presented first. The data from these diagrams was not collected, all subjects saw the same practice diagrams, and the subjects were not aware that these diagrams were not part of the experiment. These diagrams gave the subjects an opportunity to practice the task before experimental data was collected. The 2 correct diagrams were viewed twice, while the 36 incorrect diagrams were viewed only once, a total of 60 experimental events. These 60 events were in a different random order for each subject, in blocks of eight, with a rest break between each block (the length of which was controlled by the subject). The final block comprised four diagrams.

12 Each diagram was displayed until the subject answered Y or, or 35 seconds had passed. A beep indicated to the subject when the next diagram was displayed after a timeout. A suitable period of time for each diagram to be displayed before timing out was achieved by running extensive pilot experiments. The practice diagrams helped the subjects become accustomed to the length of the allocated time period. A within-subjects design was used to reduce any variability that may have been attributed to differences between subjects: thus, all subjects saw all the diagrams (correct and incorrect), and each subject s performance on one notation was compared with his or her own performance on the alternative notation. The practice diagrams and the randomisation of the order of presentation of the experimental diagrams for each subject helped counter the learning effect (whereby a subject s performance on the task may improve over time, as they become more competent in the task) Data collection The response time and accuracy (number of errors) of the subjects responses to the 60 experimental diagrams were recorded by the online system. Subjects were also asked to complete a questionnaire at the conclusion of the online experiment, which gathered background data on the student (eg, experience) as well as preference data about which notation they preferred and why Subjects The 32 subjects were enrolled in first year Computer Science and Information Systems courses at the University of Queensland, and had not yet attended any university lectures on Entity Relationship diagrams. These subjects were therefore novices, unfamiliar with modelling methods. Students are typically initially taught one Entity Relationship notation, and may be introduced to another notation in later years. As we did not wish the subjects to be biased towards either of the notations being considered, it was important that they had not been introduced to any Entity Relationship modelling method prior to the experiment. We asked the subjects to rank their knowledge of entity relationship models: 28 of the 32 subjects had either not seen them or had only limited knowledge. We also asked the subjects whether they had seen either the Chen or the SSADM notations before: 3 had seen the Chen notation (or something similar), and had seen the SSADM notation.

13 The subjects were paid $5 for their time, and, as an incentive for them to take the experiment seriously, the best performer was given a CD voucher. 3. Data Both the speed and number of errors of each subject s responses were measured, enabling the analysis of two different measures of understanding. Analysis was performed on both the subjects average percentage performance in identifying the correct diagrams and their average percentage performance in identifying each category of incorrect diagrams. The aggregated data over all incorrect diagrams was also analysed. Preference data was also collected: students were asked which of the notations they preferred for the representation of cardinality, participation, and relationships, and which notation they preferred overall. They were also asked to state reasons for their preferences. 3. Performance data For both response time and error, four independent sets of data were collected: one for correct diagrams, and three for the three different error operations (Table ): Response time average Response time standard deviation Errors average Errors standard deviation Chen (correct) SSADM (correct) Chen (cardinality error) SSADM (cardinality error) Chen (participation error) SSADM (participation error) Chen (relationship naming error) SSADM (relationship naming error) Table : Averages and standard deviations for all experimental diagrams.

14 One set of data was derived: the response time and errors for all incorrect diagrams (Table 2): Chen (all incorrect diagrams) SSADM (all incorrect diagrams) Response time average Response time standard deviation Errors average Errors standard deviation Table 2: Averages and standard deviations for all incorrect diagrams. Average response time: correct diagrams Average errors: correct diagrams Average response time (seconds) Chen otation SSADM Average errors (percent) Chen otation SSADM Figure 7: The response time and error data for users on correct diagrams. Average response time: incorrect diagrams Average errors: incorrect diagrams Average response time (seconds) cardinality * participation relationship naming * Error operation applied overall * Chen SSADM Average errors (percent) cardinality participation relationship naming Error operation applied overall Chen SSADM Figure 8: The response time and error data for the incorrect diagrams: the significant differences are indicted by *. Analysis of the correct diagrams reveals no significant differences at the 0.05 level of significance. The data for the three categories of incorrect diagrams were analysed, as well as the derived data calculated from aggregating the incorrect diagram data. A significance level of was used, as a result of applying a Bonferroni correction in recognition of the fact that the data was analysed twice.

15 Using a two-tailed related t-test (df = n- = 3), the statistically significant results are: Identifying incorrect diagrams (error operation a: cardinality): The SSADM notation is faster than the Chen notation (p=0.08) Identifying incorrect diagrams (error operation c: relationship naming): The SSADM notation is faster than the Chen notation (p=0.0038) Identifying incorrect diagrams (overall): The SSADM notation is faster than the Chen notation (p<0.0036) There were no other significant results for either time or error data. 3.2 Correlation data Chen SSADM Correct diagrams (24 = 2 x 2) Error operation (a) incorrect diagrams (2 = 2 x 6) Error operation (b) incorrect diagrams (2 = 2 x 6) Error operation (c) incorrect diagrams (2 = 2 x 6) Incorrect diagrams (36 = 3 x 2) Table 3: Linear correlations between errors and response time: the shaded values are statistically significant (r>0.35) The correlations between time and errors were calculated, accumulated according to the correct/incorrect nature of the diagrams, and notation type (Table 3). This process was necessary to determine whether there was any relationship between our two dependent variables (time and errors) that would make it inappropriate to analyse them separately. The linear correlations that we were therefore most interested in were those relating to any significant results obtained from the t-tests that are related to both time and errors for any of the conditions, as they may change the way we interpret the results. As all our significant results were all based on conditions where the response time data was significant, there were no conditions for which a correlation between time and errors may have affected our interpretation of the t-tests.

16 The strong correlations between errors and time suggest that the slower the subjects responded, the less accurate they were. Observation of the data reveals that this is not due to a high number of time-outs (when subjects do not answer within the allotted time, and an incorrect answer is therefore registered), as might be expected. 3.3 Preference data Subjects were asked to state which of the notations they preferred with respect to the three notational variations, as well as with respect to the overall notation. They were also asked to provide reasons for their choice. One subject chose not to complete the questionnaire Quantitative preference data: Chen SSADM Cardinality preference (a) 20 Participation preference (b) 2 9 Relationship naming preference (c) 2 9 Overall preference 9 22 Table 4: Preferences (number of students): the shaded values indicate statistical significance (p<0.05) Using a binomial distribution, the statistically significant preference results are (Table 4): Subjects prefer the SSADM notation to the Chen notation overall (p=0.009) Subjects prefer the cardinality representation in the SSADM notation to that in Chen notation (p=0.039) There were no other significant preference results Qualitative preference data: Cardinality: The subjects reasons for their choice of SSADM for the cardinality notation were that it was a simpler notation and that they felt the symbolic crowsfoot was more easily understood than reading either a or. Of the subjects that preferred the Chen notation, the reasons for their choice were that the or was clearer than a crowsfoot and so was less confusing.

17 Participation: The reasons for subjects indicating that that the SSADM participation notation was more easily understood included: SSADM being simpler; there being a more obvious difference between dotted/non-dotted lines than single/double; and that dotted lines were indicative of an optional constraint. The reasons given as to why the Chen notation was preferred were that the difference between single/double lines was more pronounced than dotted/non-dotted lines and that double lines were more indicative of a mandatory constraint. Relationship naming: The reasons the subjects gave for the SSADM relationship naming notation being more easily understood were that it was simpler, and that placing a box around the relationship (as in the Chen notation) made it possible to confuse the relation ship with an entity. Those subjects that preferred the Chen notation listed their reason as being that placing it inside a diamond highlighted the relationship. Overall notations: Subjects justified their choice of the SSADM notation overall by stating that the diagrams in the SSADM notation appeared less cluttered and less complicated than their Chen notation counterparts. 4 Analysis The accuracy of the subjects responses showed no variation according to the overall notations or the notation components. The performance results show that SSADM is faster overall, and faster for the identification of cardinality and relationship naming operations. There was no significant difference between the two notations in the identification of participation errors. The preference data showed that the SSADM notation was significantly preferred overall, and there was significant preference for the SSADM representation of cardinality. 4. Discussion In interpreting these results, we infer that the overall SSADM notation is better understood than the Chen notation. The SSADM notation is more concise, with fewer shapes and text on the page. This conciseness may make it easier to understand. The only error operation that did not give any significant results was participation represented by single/double lines in the Chen notation, and as dotted/solid lines in SSADM. The diagrams which had participation errors introduced all had faster and more accurate results than diagrams with the other errors operations applied. This would imply that the

18 changing of the participation relationships was more obvious to the subjects than either the swapping of cardinalities or the swapping of relationship names. In both notations, participation was the only notational variant of the three that did not involve reading text or numbers, being represented solely as lines. We could infer from this that notations which represent information diagrammatically (rather than with the use of text) may result in better performance. These results, of course, need to be interpreted within the limitations of the formal experimental method. Any formal empirical study has limitations: in our case, we were using university students as subjects, rather than typical database diagram users, and the comprehension task and application were constrained to a simple domain, only two notations with three variants, and a binary matching task. Using a binary matching task introduces the notion of false positives : answers that are correct, but for the wrong reason. When subjects indicate that a diagram does not match the given textual specification, we do not know why they have done so we have assumed that it is because they have identified the planted errors, but it may be because they have misunderstood other aspects of the notation. Approximately 30% of all the correct diagrams (in both notations) were incorrectly identified as not matching the text. Two subjects indicated that all the correct SSADM diagrams had errors: this could indicate that they had a fundamental misunderstanding of this notation, or that they did not take the experiment seriously. This reveals a basic problem with quantitative experiments of this kind: we can measure and analyse behaviour, and attempt to choose tasks that demonstrate subjects comprehension, but we cannot measure actual understanding. In practise, comprehension of such diagrams is a fundamental activity in the maintenance of large database applications. We chose the task of noticing changes in cardinality, participation or the relationship between entities, as way of measuring the comprehension of the entire diagram with respect to notational variations. There are many other ways in which comprehension may be assessed. Case study investigations including, for example, the use of Entity Relationship modelling in a real world industrial application, the use of database support tools in practise, or the learning of modelling notations by students over an entire semester, would give greater insight into the suitability of the different notational variations from a human comprehension point of view. Such experiments may, in particular, relate the effectiveness of the variations according to the task for which the modelling language is being used. It may be the case, for example, that some variations may be preferable for learning the notation, but may need to be adapted for real world use on a multi-person project. In addition, the conventions and standards of different organisations may require use of one notation over another.

19 One important aspect of the comprehension of notations that we were not able to explore is that of scale. A real world data model will contain many more entities and relationships than our simple example and it would be interesting to determine whether comprehension decreases with scale, and if so, at what point. In comparing the notations it would be interesting to determine whether one notation supports the comprehension of larger diagrams more effectively than the other. 5 Conclusion We have demonstrated that it is possible to set up an experimental framework to systematically compare two diagrammatic notations, seeking to compare both overall comprehension and individual notational variations. We have applied this methodology to the comparison of two Entity-relationship diagram notations, and infer that one is preferable to the other. This approach can be used to compare other equivalent diagram notations that would benefit from empirical studies investigating their comprehension. Acknowledgements We are grateful to the students of the School of Information Technology and Electrical Engineering at the University of Queensland who willingly took part in the experiment, the Australian Research Council, which funded this research, and the anonymous reviewers who commented on an earlier draft of this paper. Ethical clearance for this study was granted by The University of Queensland, 200. References. Chen P., The entity relationship model - towards a unified view of data. ACM Trans on Database Systems, 976, (), pp Weaver P.L., Practical SSADM Version 4 A Complete Tutorial Guide. Pitman, Green, T. and Petre, M. Usability analysis of visual programming environments: A cognitive dimensions framework. Journal of Visual Languages and Computing, 996, 7, pp 3-74.

20 4. Blackwell, A. and Green, T. A Cognitive Dimensions Questionnaire Optimised for Users. Proceedings of the Twelfth Annual Meeting of the Psychology of Programming Interest Group, Corigliano Calabro, Cosenza, Italy, 2000, pp Kutar, M., Britton, C. and Wilson, J. Cognitive dimensions: An experience report. Proceedings of the Twelfth Annual Meeting of the Psychology of Programming Interest Group, Corigliano Calabro, Cosenza, Italy, 2000, pp Cox, K. Cognitive dimensions of use cases Feedback from a student questionnaire. Proceedings of the Twelfth Annual Meeting of the Psychology of Programming Interest Group, Corigliano Calabro, Cosenza, Italy, 2000, pp Gurr, C. and Stevens, P. A cognitively informed approach to describing product lines in UML. University of Edinburgh, Edinburgh, Scotland, Gurr, C. and Tourlas, K. To the principled design of software engineering diagrams. 22 nd International Conference on Software Engineering, Limerick, Ireland, 2002, pp Purchase, H.C., Colpoys, L., McGill, M., Carrington, D. and Britton, C. UML class diagram syntax: an empirical study of comprehension, Proceedings of the Australian Symposium on Information Visualisation, Eades, P. and Pattison, T. (eds), Sydney, 200, pp Purchase, H.C., Colpoys, L., McGill, M. and Carrington, D. UML collaboration diagram syntax: an empirical study of comprehension, Proceedings of the First International Workshop of Visualizing Software for Understanding and Analysis, Knight, C., Storey M-A. and Munro, M. (eds), Paris, 2002, pp Purchase, H.C., Which aesthetic has the greatest effect on human understanding?, Proceedings of Graph Drawing Symposium, Di Battista, G. (ed), Lecture otes in Computer Science 353, Springer-Verlag, Rome, 997, pp Purchase, H.C., Carrington, D.A. and Allder J-A. Graph Layout Aesthetics in UML diagrams: User Preferences, Journal of Graph Algorithms and Applications, 2002, 6(3), pp