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| Visualizing Statistical Concepts |
| Columns - Research to Practice | |
| Written by Michael J. Taleff, PhD, CADC, MAC | |
| Friday, 31 May 2002 | |
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If you have ever read any of the free government books like the Alcohol and Health: Special Report to the U.S. Congress, you will notice the many types of graphs and plots used to illustrate sets of numbers. Many of the more recent textbooks on addictions studies have begun to include more diagrams to help the reader understand the vast amount of information that is available to the field these days. It is critical to not only understand them, but to know how create them. Trying, however, to explain these things through words has limits. Therefore, we will use a figure to make sense of a mean and standard deviation; and show how you can understand large sets of numbers more easily by using plots and graphs.How practical are charts? Most addictions counselors don't use plots or graphs. Yet, there are good reasons to do so. For example, using some graph paper, you could have a client plot out days, or hours in the day, in which they experience strong urges. Eventually, a pattern would show itself that would identify specific triggers so an intervention could be used to address those urges. The point is to get the whole pattern in a figure form and not rely on memory. Actually seeing patterns could add power to the counseling process. This type of charting can apply to a host of other client variables. For a program example, you could begin to track admissions in terms of chemical choice, associated pathology, age, or any number of variables. Summarizing this information and placing it in bar graph form would demonstrate trends within your program that simple numbers could not quite convey. Armed with such visuals all program staff could then better understand the ebb and flow of how your facility is performing. Descriptive statistics placed in figure form are quite useful to clinicians. Portrait of a mean and standard deviation Let's revisit two concepts outlined in the last column, the mean (the average of set of numbers), and a standard deviation (measure of spread from a mean). How does one picture those definitions? The standard method is through a figure called the normal or bell curve. Here a curve is framed over a set of values on a horizontal line with the frequency of those values plotted on a vertical line (Jaeger, 1993; Salkind, 2000). For example, suppose you are at a large drug and alcohol conference and decide to sample the heights of those attending (not meaningful information, but it demonstrates the normal curve point). You walk around the conference and stop people at random and accost them with a tape measure. Keeping a log of your entries you next need to make sense of your data. For our purposes, you assign different colored poker chips to various heights. For example, those at 5'10" are assigned the color yellow, and those at 5'9" are assigned blue chips and so on. You then stack your chips according to your data. So, people of average height will have higher stacks of chips than the very tall and very short. Next, place all your chips in a single line, and it turns out that highest chips are in the middle, while lowest stakes are at the ends. Then you look at the side profile. If addictions counselors are anything like the rest of the population, they will start to resemble a bell-shaped pattern as shown in Figure 1. Note that the vertical line is the mean and the horizontal line with the hash marks is the distance from the mean or the standard deviation. In figure form, that represents a mean and standard deviation. However, not all curves assume this shape, some are flatter and others thinner (Newton & Rudestam, 1999). Other figures We also use an illustration to understand the major points of bar graphs, line plots, and pie charts. Not to long ago, I did a little survey to gauge the effects of a table display filled with alcohol information on a student's choice to drink. (Now my sample was small, and small samples are not to be trusted, but for our purposes, this example will suffice.) I asked a number of questions, but the one I was most interested in was whether such table displays alter in any way the student's decision to drink. This was asked using a five point Likert scale (1 = Not at all to 5 = Yes, very much). A little over 60 percent of that sample indicated that such displays would not alter their decision to drink, a little over 20 percent were between no effect and some effect, and 12 percent indicated that such displays would somewhat alter their decision to drink. No one indicated that the table displays used that day would alter their decision to drink. Describing the outcome of this small survey is a bit ambiguous, but I converted that data into a bar graph for Figure 2, note the striking results. Bar charts generally are best used for showing how data changes over time or comparing different categories. For the purposes of demonstrating other graphic forms, the next two illustrations used the same data, but I converted the bar graph to a line plot (Figure 3), and then a pie chart (Figure 4). Line plots generally show trends with equal intervals and pie charts are best showing proportions (Salkind, 2000). As you can see, graphs give numbers more clarity, have a much stronger visual impact than paragraphs of text, and can be quite practical for your program or individual counseling. Graphs of all types are easily created by any computer spreadsheet or statistical software package. Next we will explore correlations and in regression analysis. References Jaeger, R.M. (1993). Statistics: A spectator sport (2nd). Thousand Oaks, CA: Sage. Newton, R.R. & Rudestam, K.E. (1999). Your statistical consultant. Thousand Oaks, CA: Sage. Salkind, N.J. (2000). Statistics for people who (think they) hate statistics. Thousand Oaks, CA: Sage. Michael J. Taleff, PhD, CADC, MAC, is the Alcohol & Drug Education Program Coordinator for the University of Hawai'i at Manoa.              |
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