 |  Statistics for the Behavioral Sciences, 4/e Michael Thorne,
Mississippi State University -- Mississippi State
Martin Giesen,
Mississippi State University -- Mississippi State
Graphing Data
Chapter Overview| Before discussing specific types of graphs, two graphing conventions are presented. The first convention is the three-quarters rule, which states that the Y axis should be approximately three-fourths as long as the X axis. The second convention is that the values on the Y axis generally should begin with 0, and the units on the axis should reflect reasonable deviations in the data.
The frequency polygon is constructed by plotting the scores on the baseline, or X axis, and plotting the frequency of each score along the Y axis. The axes of the frequency polygon are labeled with the word "Score" below the X axis and the word "Frequency" to the left of the Y axis. In addition, each graph should have a caption describing the source of the data. If you want to compare two or more sets of data on a single set of axes and the sample sizes differ, the frequencies must be converted to percentages before plotting.
One common and very important curve is the normal or bell-shaped curve. The normal curve is symmetrical, in contrast to skewed curves, in which a large number of scores are piled up at one end or the other end, with a tail at the opposite end. Positively skewed curves have a tail toward the upper end of the X axis, and negatively skewed curves have a tail toward the lower end of the X axis.
The cumulative frequency or cumulative percentage polygon can be plotted from a frequency distribution. In this curve, cumulative frequency (or percentage) is plotted over the scores. The cumulative frequency curve is useful for determining the relative position of any individual.
The only difference between the frequency polygon and the histogram is that dots are plotted over the score values in the polygon, whereas rectangular bars are plotted over the values in the histogram. The bar graph is a type of histogram used to plot categorical or nominal scale data. A bar is drawn over each category, with its height indicating frequency; the bar's width is arbitrary.
The stem-and-leaf plot has features of both the frequency distribution and the frequency histogram. To construct it, each data point is split into two parts: a stem (the first digit[s]) and a leaf (the last digit[s]). For example, a score of 155 has a stem of 15 and a leaf of 5. If a stem-and-leaf plot is rotated 90° counterclockwise, it becomes a histogram with digits over the scores (stems) rather than bars. Another useful feature of the stem-and-leaf plot is that it can be used to compare two groups of data.
In a line graph, an independent variable is recorded on the X axis, and some measure of the dependent variable is shown on the Y axis. The independent variable is assumed to be continuous, and a line is used to connect the plotted points. |
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2003 McGraw-Hill Higher Education