Line Graphs

6 Key excerpts on "Line Graphs"

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  eBook - ePub

  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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  Statistical Literacy at School

  Growth and Goals

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

    (Publisher)

  Points, wherever found, are often considered as representing single entities. In fact this is true in a scattergram but the entity has two defining characteristics that determine its location in a setting where the trend over many entities is important. Following on from work with “people graphs” for very young children to report frequency by having them line up behind the characteristic with which they are associated, people graphs also can be very helpful with older students to help distinguish two variables and their relationship to the point represented. 23 Laying out the perpendicular axes, with the origin, on the floor or playground, students can stand on a point, facing the origin, and extend their arms at right angles to indicate the measurements on each axis that determine where they are standing on the scattergram. Anecdotally this has been found to be a very useful technique. 3.6 Graph Interpretation: the Case of Bar Charts Bar charts, perhaps as derivatives of pictographs, are the graphs met most frequently by students in the elementary school years. As such they provide links to other basic aspects of the mathematics curriculum, particularly for younger children. One-to-one correspondence, addition, and subtraction, for example, are involved in the basic interpretation of bar charts, and judicious questioning can also focus discussion on issues related to the building of proto-statistical intuitions. Consider, for example, the bar graph in Fig. 3.15 that records how children in class arrive at school. This particular version of the bar graph, which is often a basis for this theme, has moveable bars that disappear in a slit at the base line. 24 Asking students what they can tell from the graph allows for a display of the natural starting points for graph interpretation. Some students, often FIG

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  Essential Mathematics and Statistics for Forensic Science

  • Craig Adam(Author)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  This chapter will start by using examples to illustrate the variety of types of graph encountered within the forensic discipline. The main focus will be, however, on applications where an empirical or first-principles mathematical model may be found that explains the trends displayed by the experimental measurements. The basis of this technique is an understanding of the linearization of equations and the fitting of linear trend-lines to graphs. Once these topics are fully assimilated, you will be able to construct your own graphs and fit a variety of types of model to such data, including the use of calibration graphs for the chemical or spectroscopic analysis of evidence.

  5.1 Representing data using graphs

  Wherever possible, it is a good idea to display information, numerical data or experimental results using a graph. However, it is important to think carefully about the type of graph that best illustrates the implications of the data and how this graph aids your interpretation of it.

  1. Graphical representation may be used simply to display numerical information in order to con vey similarities and differences. For example, from a survey of the occurrence of the five Galton-Henry fingerprint classes in a sample of the UK population (Cummins and Midlo, 1961) it was found that some classes are far more common than others. As this form of data corresponds to a set of numbers related to particular items or classes, it is best represented by a bar chart or a pie chart (Figure 5.1 ).

  Figure 5.1 Distribution of the fingerprint classes amongst the UK population

  2. A further use of graphs is to display trends in a dataset, often over time. Here, there must be two sets of numbers such as a year and number relating to some measured quantity in that year. An important feature of this type of data is that we do not expect that there will be any correlation between the two sets of numbers, which would enable us to predict what the graph would look like if extended in either direction. For example, crime statistics that are published annually by the Home Office in England and Wales include data on the number of recorded offences per 100000 of the population. Retrospectively, these are of interest to determine trends but this data does not allow prediction of what the level of offences might be five years into the future. Either a bar chart or a line graph may be appropriate to display such data, but note here that as the data for earlier years is not annual, the bar chart gives a misleading impression as to the rate of change of these figures with time (Figure 5.2

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  Statistics for Exercise Science and Health with Microsoft Office Excel

  • J. P. Verma(Author)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Although graphic representation has many forms, only those forms that are useful in visualizing the important properties of frequency distribution and that facilitate comparison of two or more frequency distributions are discussed in this chapter. The latest software packages have helped students in creating different types of graphs with varied options, and therefore, it is recommended that students understand the concepts discussed in this chapter, which explains various graphical designs. Before discussing the construction of different types of graphs, the general guidelines common to most of the graphical presentation are discussed first.

  3.2 Guidelines for Constructing a Graph

  There are varieties of graphs that can be used to show the results of research data. The selection of a graph depends on the nature of the data. Irrespective of the graphic option that one may choose, there are some guidelines that are common in constructing most graphic display.

  3.2.1 Defining the x–y Axis

  There are two elements of measurement in a two-dimensional graphic display. The independent variable is measured along the horizontal axis and is known as abscissa or the x-axis. The dependent variable is measured along the vertical axis and is called the ordinate or the y-axis. In the case of grouped data, class interval is taken along the x-axis and frequencies along the y-axis.

  3.2.2 Taking Origin as Zero

  The scale of y must begin with zero as the origin. In case the frequency starts from 25 and ends at 35, then a cut is marked on the y-axis near zero in order to accommodate the frequency from 0 to 25 and then frequencies are marked from 25 onwards. Similarly, if some values of x need to be accomodated, then a similar cut should be made along the x-axis near the origin (Figure 3.1 ).

  Figure 3.1

  Marking scales on the x- and y-axis.

  3.2.3 Using a Single Vertical Scale

  If two curves are to be compared in a single graph, one should use only one vertical scale. This provides a real comparison of the data. If two different vertical scales are used on the left and right sides of the graph, then a valid visual comparison of the two curves cannot be made.

  3.2.4 Deciding the Scale Unit

  The scale unit is decided based on the nature of the data and their fluctuations. For example, stretching the x-axis will tend to de-emphasize fluctuations while stretching the y-axis will tend to overemphasize them. As a convention, the proportion of y and x

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  Intermediate Algebra

  • Lisa Healey(Author)
  • 2021(Publication Date)
  • Chemeketa Press

    (Publisher)

  In this section, we will see that, even without using numbers, a graph is a mathematical tool that can describe a wide variety of relationships. For example, there is a relationship between outdoor temperatures over the course of a year and the retail sales of ice cream. We can describe this relationship in a general way using a qualitative graph. As you study this section, you will learn to:

  ♦  Read and interpret qualitative graphs ♦  Identify independent and dependent variables ♦  Identify and interpret an intercept of a graph ♦  Identify increasing and decreasing curves ♦  Sketch qualitative graphs

  A. Reading a Qualitative Graph

  Both qualitative and quantitative graphs can have two axes and show the relationship between two variables. We also read both types of graph from left to right — just like a sentence. The difference is that

  quantitative graphs

  have numerical increments on the axes (scaling and tick marks), while

  qualitative graphs

  only illustrate the general relationship between two variables.

  Example 1

  Use the qualitative graph, Figure 1 , and the quantitative graph, Figure 2 , to answer the following questions.

  Figure 1. The sale of ice cream at Joe’s Café (a qualitative graph).

  Figure 2. The population of Portland, Oregon (a quantitative graph).

  1.

      What does the qualitative graph tell us about ice cream sales at Joe’s Café? Do we know how many servings were sold in June?

  2.

      What does the quantitative graph tell us about the population of Portland, Oregon? What was the population in 1930?

  Solutions

  1.

    Ice cream sales are lowest at the beginning and at the end of the year and highest during the middle months. We cannot tell from this graph exactly how many servings are sold in any given month.

  2.

    The population of Portland, Oregon, has been increasing since 1850, except for a slight decrease in the 1950s and 1970s. The population in 1930 was about 300,000.

  B. Independent and Dependent Variables

  A qualitative graph is a visual description of the relationship between two variables. The graph tells a “story” about how one quantity is determined or influenced by another quantity. For example, the number of calories one consumes in a week determines the number of pounds one will lose (or gain) that week. Another way to say this is that the change in a person’s weight is dependent on the number of calories they consume.

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  eBook - ePub

  Strategies and Tactics of Behavioral Research and Practice

  • James M. Johnston, Henry S. Pennypacker, Gina Green(Authors)
  • 2019(Publication Date)
  • Routledge

    (Publisher)

  Panel B shows the correct temporal distribution for the data. By including on the horizontal axis times when sessions did not occur, the data in Panel B reveal a fairly regular pattern not evident in Panel A. In the first session following a day or two without sessions, responding was usually higher than in subsequent sessions. Knowing that encourages us to ask why. If the data came from an actual study, we would be able to consider possible explanations for that pattern. If sessions were not held on weekends, for instance, it could mean that something about weekend activities affected responding on Mondays. The point is that the behavior of participants during sessions can be influenced by events occurring between sessions. Displaying data across continuous representations of time allows discovery of such influences.

  FIG. 14.7. Graphs showing data displayed across discontinuous (Panel A) and continuous (Panel B) representations of time on the horizontal axis.

  A third aspect of how units of some dimension are mapped onto axes applies to both vertical and horizontal axes. Different ways of spacing intervals on the axis unavoidably affect the slopes of connecting lines. Figure 14.8 illustrates that impact by showing the same two values on two graphs in which time is mapped differently on the horizontal axis. In the graph on the left, a year’s time is displayed in successive months, whereas in the graph on the right, the same year is divided into three 4-month seasons. The larger units of time are mapped onto the axis with shorter spaces between intervals. As a result, the slope of the line is steeper on the right graph than on the left. Both ways of constructing the axes are acceptable, but viewers might respond differently to each depending on what the data represent.

  A fourth issue is most often relevant to the vertical axis. In selecting the range needed to display the data, it is important to create a display that suggests a fair and meaningful interpretation. It is not appropriate to encourage conclusions that might be considered misleading. Figure 14.9

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