Drawing Graphs: Methods and Models

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Yet, it is challenging for most people to make sense of that much numerical information. You would have to look carefully at the entire table to see any trends. But if we take the exact same data and plot it on a graph, this is what it looks like Figure 2 :. Describing the graph: The x-axis shows the variable of time in units of years, and the y-axis shows the range of the variable of CO 2 concentration in units of parts per million ppm.

The dots are individual measurements of concentrations — the numbers shown in Table 1. Thus, the graph is showing us the change in atmospheric CO 2 concentrations over time. Describing the data and trends: The line connects consecutive measurements, making it easier to see both the short- and long-term trends within the data. On the graph, it is easy to see that the concentration of atmospheric CO 2 steadily rose over time, from a low of about ppm in to a current level of about ppm. Within that long-term trend, it's also easy to see that there are short-term, annual cycles of about 5 ppm.

Making interpretations: On the graph, scientists can derive additional information from the numerical data, such as how fast CO 2 concentration is rising.

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This rate can be determined by calculating the slope of the long-term trend in the numerical data, and seeing this rate on a graph makes it easily apparent. While a keen observer may have been able to pick out of the table the increase in CO 2 concentrations over the five decades provided, it would be difficult for even a highly trained scientist to note the yearly cycling in atmospheric CO 2 in the numerical data — a feature elegantly demonstrated in the sawtooth pattern of the line.

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Putting data into a visual format is one step in data analysis and interpretation , and well-designed graphs can help scientists interpret their data. Interpretation involves explaining why there is a long-term rise in atmospheric CO 2 concentrations on top of an annual fluctuation, thus moving beyond the graph itself to put the data into context. Seeing the regular and repeating cycle of about 5 ppm, scientists realized that this fluctuation must be related to natural changes on the planet due to seasonal plant activity.

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Visual representation of these data also helped scientists to realize that the increase in CO 2 concentrations over the five decades shown occurs in parallel with the industrial revolution and thus are almost certainly related to the growing number of human activities that release CO 2 IPCC, It is important to note that neither one of these trends the long-term rise or the annual cycling nor the interpretation can be seen in a single measurement or data point.

That's one reason why you almost never hear scientists use the singular of the word data — datum. Imagine just one point on a graph. You could draw a trend line going through it in any direction. Rigorous scientific practice requires multiple data points to make a clear interpretation, and a graph can be critical not only in showing the data themselves, but in demonstrating on how much data a scientist is basing his or her interpretation. We just followed a short, logical process to extract a lot of information from this graph.

Although an infinite variety of data can appear in graphical form, this same procedure can apply when reading any kind of graph. To reiterate:. Describe the graph: What does the title say?

Methods and Models

What variable is represented on the x-axis? What is on the y-axis? What are the units of measurement?

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What do the symbols and colors mean? Describe the data: What is the numerical range of the data? What kinds of patterns can you see in the distribution of the data as they are plotted? Interpret the data: How do the patterns you see in the graph relate to other things you know? The same questions apply whether you are looking at a graph of two variables or something more complex.

Because creating graphs is a form of data analysis and interpretation , it is important to scrutinize a scientist's graphs as much as his or her written interpretation. Graphs and other visual representations of scientific information also commonly contain another key element of scientific data analysis — a measure of the uncertainty or error within measurements see our Uncertainty, Error, and Confidence module. For example, the graph in Figure 3 presents mean measurements of mercury emissions from soil at various times over the course of a single day. The error bars on each vertical bar provide the standard deviation of each measurement.

These error bars are included to demonstrate that the change in emissions with time are greater than the inherent variability within each measurement see our Statistics in Science module for more information. Graphical displays of data can also be used not just to display error, but to quantify error and uncertainty in a system.

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For example, Figure 4 shows a gas chromatograph of a fuel oil spill. Peaks in the chromatograph the blue line provide information about the chemicals identified in the spill, and the peak size can provide an estimate of the relative concentration of that specific chemical in the spill. However, before this information can be extracted from the graph, instrument error and uncertainty must be calculated the red line and subtracted from the peak area. In this phase computes the line position of the straight lines representing the inheritance relations and segment position of association relationships between classes on the same layer or on adjacent.

The main difference between experiment A and experiment B was the way in which the experimental diagrams were produced. While experiment A used computational metrics to determine the presence of an aesthetic in a diagram, in experiment B, a separate human perception study was used to assess the extent to which aesthetics were perceived in a diagram. Another two other important aspects which differs Experiment B from Experiment are: choice of aesthetics and aesthetic variation.

nttsystem.xsrv.jp/libraries/64/dypi-sms-lesen-telekom.php The aim of experimental was to determine which of the aesthetics underlying common graph drawing algorithms are most suited to human comprehension of UML diagrams. By asking subjects University Students to perform comprehension tasks on the same UML diagram portrayed with different aesthetic emphases, we aimed to identify the aesthetic criteria that resulted in the best performance.

Graph drawing aesthetics used in two experiments are shown in Table 1. They suggested that additional semantic issues need to be considered when a layout algorithm is used in a domain-specific tool. UML class diagrams-state of the art in layout techniques: Overview of UML Tools shows that most of them are too implementation-specific. The abstract concepts like association classes, higher association, constraints and even comments, which cannot be directly realized in a programming language, cannot be visualized.

In most tools package-like elements like subsystems or models are not present. A class diagram can be described in terms of graph theory. It is obvious that classes, packages and rhombs representing n-ary associations map to nodes. Edges are mapping of the associations, dependencies as well as inheritance relations. Unfortunately most layout algorithms on class diagrams do not adhere to any aesthetic principles. Holger Eichelberger in his previous papers Eichelberger, discussed semantic based aesthetic criteria in order to provide intuitive rules for drawing class diagram which are shown in Table 2.

These rules lead to readable diagrams and therefore can reduce the cost of communication when interchanging software development diagrams. But validating these rules by user experiments is a hard task. The Algorithms in many CASE tools mainly focus on classes, inheritance relations and association relations but not on nested package and class structures and more sophisticated model elements like association classes, higher associations or constraints.

Table 3 shows a subset of proposal for aesthetic principles for class diagrams. As a consequence of applying these principles the readability and understandability is enhanced. Their proposed algorithm is capable of working on nested and structured elements and it can easily be updated. Although, adding more constraints to an algorithm can increase runtime and decrease quality, but introducing additional criteria into the new edge crossing reduction algorithm can be respected. They believe that additional minor update to the set of aesthetic principles is necessary.

Figure 3 depict one of the result produced by their algorithm. Three dimensional software modeling: They have used the third dimension to demonstrate a different kind of arrow in the same diagram. This has been presented by a series of 3D notations, which have a number of advantages over their 2D matching parts. The notations complement and are compatible with existing 2D notations such as those making up UML. In other word, it can thought of as a seamless combination of several 2D diagrams.

Software models, which support 3D, enable visualization of richer semantic then those of 2D models. The 3D notations they developed are: contract boxes, 3D sequence diagrams, nested and structured box diagram. The Contract boxes, as depicted in Fig. The 3D sequence diagram provides much richer visualizations where it is only possible with UML sequence and collaboration diagram. The 3D sequence diagram can also show message passing between objects and sets of objects. The nested box diagram is a combination of the contract box specifications with sequence diagram.

It visualizes the complete action design which includes the specifications of the sub-actions involved. The structured box diagrams are an extension of nested box diagrams to visualize looping and conditional behavior. Hence structured box diagrams show all aspects of the model on a single diagram.

All other diagrams may be considered as either sub-diagrams or projections of these. Experience in 3-dimensional visualization of java class relations: Syntax graph is a formal model considering the structure of a system which UML visualizes some parts of the syntax graph in 2D dimensions.

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Their approach is a combination of visualizing the syntax graph and the benefit of visualizing the large software systems structures in a 3D dimension view. They concentrated on the differences between 2D and 3D, so they selected out some aspects in 3D, which is much weaker in 2D. Those aspects were: transparency of objects, effect of depth, ordering in space and motion.