Tables and Graphs

6 Key excerpts on "Tables and Graphs"

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  eBook - ePub

  Statistical Techniques for Data Analysis

  • John K. Taylor, Cheryl Cihon(Authors)
  • 2004(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  CHAPTER 7 Presenting Data

  Data are commonly presented in tables, charts, and graphs and by mathematical expressions. The latter may be theoretical or empirical. This chapter consists of a brief discussion of these modes of presentation. Some of these modes provide ways not only to facilitate ready access to data but also to smooth out experimental variability in finished data. Excellent discussions of data presentation will be found in the literature, especially that of a number of years ago. Modern authors have dealt less extensively with this subject. The author grew up with the books cited in the following references and recommends them for their practical approach and ease of understanding of the subject matter presented [1 ,2 ].

  TABLES

  The use of tables is perhaps the most common method for presentation of data. The format will vary, depending on what information is needed to be conveyed. Even a cursory perusal of the scientific literature will reveal many examples of both good and poor tables. A good table is simply one that presents data in an easily understandable manner. Tables should be relatively simple in order to promote understanding and the columns should have a clear relationship to each other. Column titles should be as brief as possible, consistent with clarity. Footnotes may be needed in some cases to provide further explanation of the headings.

  Columns that are intended to be intercompared should be placed adjacently as possible. Unnecessary grouping of dissimilar materials in tables can lead to confusion, hence this should be avoided whenever possible. For example, the author has seen examples where several kinds of uncertainty estimates have been included in the same table for different substances, for apparently no reason. When the statistical parameters of the results for all substances in a given table are treated identically, intercomparisons are facilitated. Moreover, there is an advantage in achieving consistency among all tables in a single presentation, such as a paper or a lecture, and this should be done unless there is good reason to do otherwise. In the latter case, pointing out the reason for the varied presentations will give emphasis to the reasons therefore, and help to minimize confusion of intercomparison.

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  eBook - ePub

  An Introduction to Scientific Research Methods in Geography and Environmental Studies

  • Daniel Montello, Paul Sutton(Authors)
  • 2012(Publication Date)
  • SAGE Publications Ltd

    (Publisher)

  people lie to people – with intentionally poor data collection, analysis, and especially display.

  There are a variety of more or less standard graph styles available to the researcher, and new styles continue to be invented. Here are some guidelines for choosing among them; as guidelines , they should probably be ignored on occasion. The first consideration is whether you are graphing the distribution of one or more variables, or the relationship between two or more variables. Distribution graphs depict the distributions of variables, most often employing a two-dimensional space whose mapping onto data values is defined by two axes that meet at a right angle5 (but see our discussion below of dimensionality in graphs). The values or ranges of values of the variable are typically displayed on the horizontal X-axis or abscissa . The frequency (or relative frequency, and so on, as discussed above with tables) of each value or range of values is displayed on the vertical Y-axis or ordinate . Relationship graphs depict the form and strength of relationships between pairs of variables, again most often with a two-dimensional space. The values or ranges of values of one variable are displayed on the X-axis; those of the other variable are displayed on the Y-axis. More complex relationships, such as the relationship between two variables separately for each level of a third variable, can be displayed by using three spatial dimensions, using nonspatial symbols like color hue, showing separate two-dimensional graphs for each level of a third variable, and so on.

  Two additional considerations when choosing a graph style are whether variables are discrete or continuous, and the level at which they were measured. We present these together because their meanings, including the way they influence graph choice, are partially related; remember from Chapter 2 that nominal and ordinal variables must be discrete, but interval and ratio (metric) variables can be either discrete or continuous. Figure 11.3 shows schematic examples of various common graph styles. Distribution graphs of nominal or ordinal variables should generally be made with a discrete graph style, such as the bar graph (bar chart). Like tables of nominal variables, graphs of nominal variables should also order values according to some useful communication logic such as class magnitudes. Distribution graphs of discrete metric-level variables can use a discrete graph style such as the histogram , which is a bar chart whose bars’ widths represent the range of a quantitative class interval for a metric variable. For example, spectral frequency data generated by remote sensing are traditionally graphed with a histogram densely filled with bars. A style of distribution graph that necessarily shows relative frequencies (proportions) is the circle diagram , known by many people as the “pie chart.” They are a poor choice for variables beyond the nominal level because they force a confusing circular logic onto the linear sequential logic of ordinal and metric variables; cyclic variables such as measurements over 360° of direction or 12 months of a year might work fine, however. Distribution graphs of continuous variables should generally use continuous graphing styles, the most common of which is the line graph (polygon or “connect-the-dot” graph). That deserves emphasizing: Line graphs are strictly correct only for graphing continuous variables . That’s because a line itself is continuous, so that as a visual metaphor it implies continuously filled intervals between any two data values; it’s probably a good idea for those filled intervals to be conceptually possible. Finally, we should point out that distribution graphs sometimes show a statistical model of a distribution that has been fit to the data (Figure 10.3 in Chapter 10

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  eBook - ePub

  Statistical Literacy at School

  Growth and Goals

  • Jane M. Watson(Author)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  3Graphs—How Best to Represent the Data

  For many people the first word that comes to mind when they think about statistical charts is “lie.” No doubt some graphics do distort the underlying data, making it hard for the viewer to learn the truth. But data graphs are no different from words in this regard, for any means of communication can be used to deceive. There is no reason to believe that graphs are especially vulnerable to exploitation by liars; in fact, most of us have pretty good graphical lie detectors that help us see right through frauds.

  1

  3.1 Background

  Edward Tufte’s assessment of graphs as similar to words as a means of communication with no more or less potential to deceive is an important issue in considering the place of data representation in the data and chance curriculum. His view that most people have “pretty good graphical lie detectors,” however, is not borne out at the school level. It is there that a conscious effort needs to be expended to achieve the skills that will provide the lie detectors required by statistically literate adults.

  In contrast to sampling, graphing of data has a firm and explicit place in the data and chance curriculum. Even before the mathematics curriculum was expanded to contain coverage of data handling generally, many textbooks included exercises in graphing, leading for example to histograms. It is interesting that the link to algebraic graphs was often exceedingly tenuous although both types of graphs rely on a coordinate system. Although early in the last century some analytic geometry texts introduced the idea of “empirical curves,”2 only very recently have curriculum materials again sought to establish meaningful links between graphs of data sets and the graphs of equations that might describe them more formally.3

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  eBook - ePub

  Social Research Methods

  The Essentials

  • Nicholas Walliman(Author)
  • 2015(Publication Date)
  • SAGE Publications Ltd

    (Publisher)

  Thirteen Presenting Data Graphically

  A picture is worth a thousand words, so goes the saying, and there is an element of truth in this, but only if the picture is a true reflection of the data. The best way to present data is in graphical form, which can provide a compact list of the results, describe the data according to some criteria of measurement or bring them into relationship with other data. In the previous chapters on data collection and analysis, various ways of presenting data have been mentioned in the text. This chapter illustrates examples of a wide selection of these graphics, and provides some advice on their features and how to use them appropriately.

  In general, in order to present data effectively in graphics, you have to do several things at once to make sure that it:

  1. Accurately illustrates the data
  2. Presents the data as simply as possible
  3. Uses colour to clarify the message
  4. Is consistent across comparative presentations.

  Graphics should be used to stimulate thinking by enabling the interpretation of data. You can use them effectively to reduce the amount of textual explanation when describing trends, relationships and comparisons. It is, of course, important to use the right type of graphic to portray your ideas. As a rule you should ensure that each graphic has a heading and that the components are labelled and the data sources are indicated.

  With all graphics, you should devise a title or caption that provides enough detail that the reader can understand the content without needing to consult the accompanying text. Number them too – tables are usually numbered separately from other graphics and pictures – entitled ‘figures’. In longer texts such as dissertations, you will need to provide a list of tables and figures with their page numbers at the beginning with the contents list. You can use the ‘insert caption’ facility in your word-processor to make this simple.

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  Single Case Research Methodology

  Applications in Special Education and Behavioral Sciences

  • Jennifer R. Ledford, David L. Gast(Authors)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  Before analyzing graphically displayed data, it is important to evaluate the appropriateness of the format to display your data. The primary function of a graph is to communicate without assistance from the accompanying text. This requires that you (a) select the appropriate graphic display (line graph, bar graph, or cumulative graph) and (b) present the data as clearly, completely, and concisely as possible. How data are presented and how figures are constructed directly influences a reader’s ability to evaluate functional relations between independent and dependent variables. Though there are few hard and fast rules that govern figure selection, graph construction, or data presentation, there are recommended guidelines for preparing graphic displays (APA, 2009; Parsonson & Baer, 1978; Sanders, 1978). Following these guidelines should facilitate objective evaluations of graphically displayed data.

  Figure Selection

  When plotting time series data, you should generally use a line graph, and when plotting summative data, you should generally use a bar graph. Cumulative records are helpful when sessions represent a single opportunity to respond, or when reaching a cumulative number is critical (often true in experimental analyses with non-human subjects). Combination bar and line graphs are sometimes used when two or more variables are measured to simplify display (cf. Shepley, Spriggs, Samudre, & Elliot, 2017), even if all data are collected over time (e.g., when we would generally recommend using a line graph). For example, if two data paths are likely to have similar values throughout the study, a researcher might decide to present one as a bar graph and another as a superimposed line graph. Although this goes against advice above regarding representing time series data in bar graphs, in some situations, it can improve accessibility and decrease confusion. As previously mentioned, avoiding clutter by keeping the number of behaviors plotted on one graph to a minimum is a key component to a well constructed graph; with more than three data paths on a single graph, “the benefits of making additional comparisons may be outweighed by the distraction of too much visual ‘noise’ ” (Cooper et al., 2007, p. 132).

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  Effective Writing

  Improving Scientific, Technical and Business Communication

  • John Kirkman, Christopher Turk(Authors)
  • 2002(Publication Date)
  • Routledge

    (Publisher)

  We have argued earlier that the way a text is organized and laid out, and the rate at which information should be ‘unloaded’ or packed into our pages, must be varied according to the function of the text. In a dictionary or a parts list, it is effective to pack together a great deal of information tightly and economically, because these texts are designed for reference, for scrutiny and cross-checking of particular items. We must make it easy for ‘readers’ to find their way into and around the assembled information, but we do not have to construct a coherent discourse; the entries are not statements in a connected argument. Tactics of selection and organization are different from those used in a report or an instruction sheet.

  In just the same way, tactics in using tables and graphic techniques must be related to the precise function of the document as a whole and of the visual items in particular. Distinguish between tables and charts that are to be used for reference, as stores of classified and juxtaposed information, and visual statements that are to be used to make a point in an explanation or argument. Tables and drawings designed as reference material (such as wall-charts or timetables) can be packed tightly in the equivalent of dictionary or parts-list form. They are usually best separated from the main text of a report or paper so that they are not an obstacle to the readers’ smooth progress through the argument. Tables and drawings that are designed to make a point as part of an argument should have simple structures and carefully judged information-loads. They should be placed as close as is physically possible to the point in the prose text at which you want readers to take in the information they provide. For example, Fig. 10.1 shows a very detailed chart, providing a mass of information about the enthalpy of methane for reference and for scrutiny of detail. In most circumstances, it would distract the reader if it were part of the text, and it would be best placed in an appendix. Fig. 10.2 shows a specially drawn graph, based on the same information as Fig. 10.1 ; but it is a simpler statement designed to make one particular point. It was placed within the prose text of a report, close to the point in the argument at which the visual point was needed.

  A practical tip: abstractions of information like this can often be made simply by putting tracing paper over a complicated original and inking in the significant lines. The traced outline can then be photocopied (perhaps even reduced) and included conveniently within a typewritten report or paper.

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