When analyzing results, researchers start by constructing a frequency distribution of the data. A frequency distribution indicates the number of individuals who receive each possible score on a variable. Frequency distributions of exam scores are familiar to most college students—they tell how many students received a given score on the exam. Along with the number of individuals associated with each response or score, it is useful to examine the percentage associated with this number.
It is often useful to graphically depict frequency distributions. Let’s examine several types of graphs: pie chart, bar graph, and frequency polygon.
Pie charts Pie charts divide a whole circle, or “pie,” into “slices” that represent relative percentages. Figure 12.1 shows a pie chart depicting a frequency distribution in which 70% of people like to travel and 30% dislike travel. Because there are two pieces of information to graph, there are two slices in this pie. Pie charts are particularly useful when representing nominal scale information. In the figure, the number of people who chose each response has been converted to a percentage—the simple number could have been displayed instead, of course. Pie charts are most commonly used to depict simple descriptions of categories for a single variable. They are useful in applied research reports and articles written for the general public. Articles in scientific journals require more complex information displays.
Bar graphs Bar graphs use a separate and distinct bar for each piece of information. Figure 12.2 represents the same information about travel using a bar graph. In this graph, the x or horizontal axis shows the two possible responses. The y or vertical axis shows the number who chose each response, and so the height of each bar represents the number of people who responded to the “like” and “dislike” options.
Bar graph displaying data obtained in two groups
Frequency polygons Frequency polygons use a line to represent the distribution of frequencies of scores. This is most useful when the data represent interval or ratio scales as in the modeling and aggression data shown in Table 12.1. Here we have a clear numeric scale of the number of aggressive acts during the observation period. Figure 12.3 graphs the data from the hypothetical experiment using two frequency polygons—one for each group. The solid line represents the no-model group, and the dotted line stands for the model group.
Histograms A histogram uses bars to display a frequency distribution for a quantitative variable. In this case, the scale values are continuous and show increasing amounts on a variable such as age, blood pressure, or stress. Because the values are continuous, the bars are drawn next to each other. A histogram is shown in Figure 12.4 using data from the model group in Table 12.1.
What can you discover by examining frequency distributions? First, you can directly observe how your participants responded. You can see what scores are most frequent, and you can look at the shape of the distribution of scores. You can tell whether there are any outliers—scores that are unusual, unexpected, or very different from the scores of other participants. In an experiment, you can compare the distribution of scores in the groups.
Frequency polygons illustrating the distributions of scores in Table 12.1
Note: Each frequency polygon is anchored at scores that were not obtained by anyone (0 and 6 in the no-model group; 2 and 8 in the model group).
Histogram showing frequency of responses in the model group