A SCATTER PLOT FOR IDENTIFYING STIMULUS CONTROL OF PROBLEM BEHAVIOR

Line graphs that average response frequency over long periods obscure the major rate changes that indicate sources of behavioral control. A scatter plot can make patterns of responding identifiable and, in turn, suggest environmental features that occasion undesirable behavior. Use of scatter diagrams is illustrated in three cases.     

How are graphs read? An indication of sequence

Graphs are an extremely powerful communicative and analytical tool commonly used in both the behavioral sciences and computing (as well as many other fields). More than 2.2 trillion graphs are published annually, and these graphs are used to communicate a host of often very important information to readers. Yet despite the multitude of applications for which graphs are used, and despite the frequency of their use, little is known about how graphs communicate information or about the cognitive processes that readers use when they read and interpret the information presented within graphs. Insight into the answers to these questions can be obtained through the study of the techniques that people use to read graphs. This paper describes the research methodology and results of an empirical investigation into the viewing order in which readers choose to view the different components of graphs and into the length of time that readers spend studying each of these components.     

A comparison of sources of baseline data for treatments of problem behavior following a functional analysis

It is common practice in research on the treatment of problem behavior to compare levels of targeted behaviors during treatment to levels when treatment is not in place. Some researchers use data collected as part of a multielement functional analysis as the initial baseline, whereas others collect new baseline data following completion of the functional analysis. We evaluated whether the source of baseline data influences the reliability and efficiency of decision-making. Results suggest that similar decisions are made in regard to treatment efficacy using the different sources of baseline data, but using data from a multielement functional analysis as baseline may save time. Interrater agreement was adequate, but lower for some graphs than has been observed in past studies. Several potential explanations for this discrepancy are discussed.     

The monadic second-order logic of graphs XV: On a conjecture by D. Seese

A conjecture by D. Seese states that if a set of graphs has a decidable monadic second-order theory, then it is the image of a set of trees under a transformation of relational structures defined by monadic second-order formulas, or equivalently, has bounded clique-width. We prove that this conjecture is true if and only if it is true for the particular cases of bipartite undirected graphs, of directed graphs, of partial orders and of comparability graphs. We also prove that it is true for line graphs, for interval graphs and for partial orders of dimension 2. Our treatment of certain countably infinite graphs uses a representation of countable linear orders by binary trees that can be constructed by monadic second-order formulas. By using a counting argument, we show the intrinsic limits of the methods used here to handle this conjecture.     

Graphics in psychology: Pictures,data, and especially concepts

Over the last 50 years, psychologists have included numerous graphics in their journals and textbooks. The textbooks have contained mostly pictures, whereas the journals have contained mostly data graphs. Surprisingly, conceptual graphs (such as a network chart of the relations among types of memory) have been very infrequent. There are two main reasons for this absence of conceptual graphs: a lack of awareness of the important role that they have played in the history of our discipline, and a lack of knowledge about how to make them. Four types of conceptual graphs are presented here: mathematical graphs (e.g., Fechner’s law), geometric models (e.g., Henning’s smell prism), networks (e.g., Atkinson and Shiffrin’s STM-LTM model), and EulerVenn graphs (e.g., Shiffrin and Schneider’s model of control and automatic processes). Suggestions are offered forheuristics that can be used to facilitate the perception of conceptual relations in these graphs. It is argued that appropriate conceptual graphs can help researchers and theorists communicate the “big picture” relevant to their ideas, can help educators more effectively communicate with students, and may help clinical psychologists communicate their ideas to clients better.     

When Are Graphs Worth Ten Thousand Words? An Expert-Expert Study

This study analyzes the interpretive activities of scientists related to familiar and unfamiliar graphs. The analyses show that when scientists were familiar with a graph, they read it transparently and thereby leapt beyond the material basis to the thing the graph is said to be about. In contrast, when scientists were less familiar with the particular graphs, their reading turned out to be a complex iterative process. In this process, scientists linked graphs to possible worlds by means of complex inferences. They checked whether an expression referred to the actual properties of the worldly things the graphs are speaking of. They also checked graphical expressions themselves on the basis of certain circumstances. In a few instances, the scientists abandoned all attempts in interpreting the graphs and classified them as meaningless. Grounded in the data, a 2-stage model is proposed. This model accounts for different levels of reading graphs observed in this study.     

Effects of spatial compatibility on integration processes in graph comprehension

A precondition for efficiently understanding and memorizing graphs is the integration of all relevant graph elements and their meaning. In the present study, we analyzed integration processes by manipulating the spatial compatibility between elements in the data region and the legend. In Experiment 1, participants judged whether bar graphs depicting either statistical main effects or interactions correspond to previously presented statements. In Experiments 2 and 3, the same was tested with line graphs of varying complexity. In Experiment 4, participants memorized line graphs for a subsequent validation task. Throughout the experiments, eye movements were recorded. The results indicated that data-legend compatibility reduced the time needed to understand graphs, as well as the time needed to retrieve relevant graph information from memory. These advantages went hand in hand with a decrease of gaze transitions between the data region and the legend, indicating that data-legend compatibility decreases the difficulty of integration processes.     

存在图的逻辑地位——批评与回应

存在图是继欧拉图、文恩图和皮尔士一文恩图之后的又一种逻辑图。逻辑图是指用于表示命题和推理的二维图形。然而由于存在图之前的逻辑图在表达能力上的缺陷以及现代数理逻辑的成功,长期以来存在图并未引起人们的关注。直到近来计算机表示的图示推理发展起来以后人们才认识到它的重要性,并把它作为一种图式逻辑纳入了哲学逻辑的范畴。人们对存在图逻辑地位的认可经历了一个复杂的过程。存在图在被认可道路上遇到了逻辑系统身份、推理效率和阐述的精确性三个问题,随着这三个问题的解决,人们逐渐认可了存在图的逻辑地位。     

三维图形的视空间工作记忆容量研究

采用三维几何图形为材料,通过单探测变化觉察范式来测定视觉工作记忆的存储容量,并比较客体工作记忆和空间工作记忆容量的差异。实验1、2的材料分别为由颜色和形状两个基本特征组成的三维图形和由一个基本特征和一个细节特征组成的三维图形。两个实验结果显示,被试能在视觉工作记忆中存储约2-3个客体和4个空间位置,空间工作记忆容量显著大于客体工作记忆容量。进一步的比较发现,被试对由两个基本特征组成的三维图形的存储容量大于由一个基本特征和一个细节特征组成的三维图形。这表明,组成三维图形的特征类型对视空间工作记忆的存储容量有显著影响。     

A Field-Tested Task Analysis for Creating Single-Subject Graphs Using Microsoft<Superscript>®</Superscript> Office Excel

Creating single-subject (SS) graphs is challenging for many researchers and practitioners because it is a complex task with many steps. Although several authors have introduced guidelines for creating SS graphs, many users continue to experience frustration. The purpose of this article is to minimize these frustrations by providing a field-tested task analysis for creating SS graphs using Microsoft^® Office Excel. Results from the field test are presented and the task analysis, which includes steps for creating a variety of SS graphs, is provided. The article includes various illustrations, a list of prerequisite skills, tips, and troubleshooting items.     

CREATING SINGLE-SUBJECT DESIGN GRAPHS WITH MICROSOFT EXCEL™

Because single-subject design methodology is the cornerstone of behavior-analytic research, behavior analysts are often engaged in the practice of graph production. There are a variety of computer software packages on the market that can be used to create graphs; however, not all of them are suitable for producing single-subject design line graphs. Microsoft Excel 97 for Windows 95/NT and MacOS operating systems contains a variety of features that are conducive to producing reversal, multiple baseline, and multielement graphs (among others) that conform to many of the technical recommendations for publication in the Journal of Applied Behavior Analysis. We present detailed instructions on creating these graphs using Microsoft Excel.     

A graph theoretic approach to similarity relations

Summary A similarity relation is reflexive and symmetric. A graph may be regarded as a geometric representation of an irreflexive symmetric relation; anr-graph then coincides with a similarity relation. For the realization of psychophysical phenomena, the points of a graph stand for the stimuli and a line for indistinguishability of a stimulus pair. Not all graphs, however, are likely to arise as similarity relations in a real situation. A special class of graphs, called interval graphs, does have this realistic property. These graphs are described and characterized.The preparation of this article was supported by Grant NSF-G-17771 from the National Science Foundation.     

Recovering data from scanned graphs: Performance of Frantz’s g3data software

Recovering data points from scanned or photocopied graphs by hand is time consuming, prone to error, and it requires patience and a steady hand. An alternative is to use g3data-a program that reads many common image file types and allows accurate estimation of data point coordinates from the graphs contained in these files. Limits of the software are discussed, and validation of its accuracy using graphs with known data values is presented.     

Structure and strategy in encoding simplified graphs

Tversky and Schiano (1989) found a systematic bias toward the 45 degrees line in memory for the slopes of identical lines when embedded in graphs, but not in maps, suggesting the use of a cognitive reference frame specifically for encoding meaningful graphs. The present experiments explore this issue further using the linear configurations alone as stimuli. Experiments 1 and 2 demonstrate that perception and immediate memory for the slope of a test line within orthogonal "axes" are predictable from purely structural considerations. In Experiments 3 and 4, subjects were instructed to use a diagonal-reference strategy in viewing the stimuli, which were described as "graphs" only in Experiment 3. Results for both studies showed the diagonal bias previously found only for graphs. This pattern provides converging evidence for the diagonal as a cognitive reference frame in encoding linear graphs, and demonstrates that even in highly simplified displays, strategic factors can produce encoding biases not predictable solely from stimulus structure alone.     

Eye Movements Indicate the Temporal Organisation of Information Processing in Graph Comprehension

Hierarchical graphs (e.g. file system browsers and preference trees) represent objects (e.g. files and folders) as graph nodes and relations between them (e.g. sub‐folder relations) as lines. We investigated the temporal organisation of two processes that are necessary for comprehending such graphs—search for the graph nodes and reasoning about their relation. We tracked eye movements to change graphs while participants interpreted them. In Experiment 1, we masked the graph at a time when search processes had finished but reasoning was hypothetically ongoing. We observed a dramatic deterioration in comprehension compared with unmasked graphs. In Experiment 2, we changed the relation between critical graph nodes after search for them had finished, unbeknownst to participants. Participants mostly based their response on the graph as presented after the change. These results suggest that comprehension processes are organised in a sequential manner, an observation that can potentially be applied to the interactive presentation of graphs. Copyright © 2014 John Wiley & Sons, Ltd.     

Spatial legend compatibility within versus between graphs in multiple graph comprehension

Previous research has shown that spatial compatibility between the data region and the legend of a graph is beneficial for comprehension. However, in multiple graphs, data–legend compatibility can come at the cost of spatial between-graph legend incompatibility. Here we aimed at determining which type of compatibility is most important for performance: global (legend–legend) compatibility between graphs, or local (data–legend) compatibility within graphs. Additionally, a baseline condition (incompatible) was included. Participants chose one out of several line graphs from a multiple panel as the answer to a data-related question. Compatibility type and the number of graphs per panel were varied. Whereas Experiment 1 involved simple graphs with only two lines/legend entries within each graph, Experiment 2 explored more complex graphs. The results indicated that compatibility speeds up comprehension, at least when a certain threshold of graph complexity is exceeded. Furthermore, we found evidence for an advantage of local over global data–legend compatibility under specific conditions. Taken together, the results further support the idea that compatibility principles strongly determine the ease of integration processes in graph comprehension and should thus be considered in multiple-panel design.     

An evaluation of the agreement between the conservative dual‐criterion method and expert visual analysis

The conservative dual‐criterion (CDC) method was developed to standardize the analysis of single‐subject experimental designs data, but to date its accuracy has been evaluated only by comparing results to the statistical parameters of graphs. Our study investigated agreement between expert visual analysts and the CDC method on 66 AB tiers from published multiple baseline graphs. We found strong agreement between the two methods for certain types of graphs and discuss implications of the findings and areas for future research.     

The empirical investigation of factors affecting graphical visualization

An estimated 2.2 trillion graphs were published during 1994. These graphs used a multitude of different visual techniques in an effort to communicate information to a reader. Despite the many important applications for which graphs are used and the frequency of their use, little is known about what techniques make a graph most effective at communicating information to a reader. This paucity of knowledge stems largely from a dearth of empirical investigations pertaining to graphs. A major problem encountered by researchers who wish to undertake sound empirical research into the effectiveness of graphical presentations is the shortage of suitable tools. This article presents a computer software tool, Graphics Visualization, which offers the researcher an inexpensive yet accurate and reliable method of performing empirical research into factors that affect the accuracy and speed by which a reader can interpret data encoded within a graph.     

Judging proportion with graphs: the summation model

People take longer to judge part-to-whole relationships with bar graphs than with pie charts or divided bar graphs. Subjects may perform summation operations to establish the whole with bar graphs, which would be unnecessary for other graph types depicting the whole with a single object. To test this summation model, the number of components forming the whole was varied with bars, divided bars, reference bars, and pies in three experiments. Response time increased with the number of components for bar graphs but there was little increase for other graph types in Experiment 1. An accuracy emphasis in Experiment 2 produced generally longer response times, but had little effect on the time per summation. The summation operation was not used when graphs were displayed briefly in Experiment 3, although subjects still took longer with bars. The estimated time for a summation operation is consistent with estimates derived from other research. In general, the bar graph is not effective for proportion judgments, and its disadvantage becomes potentially greater as the number of components increases. © 1998 John Wiley & Sons, Ltd.