# Demographic data and demonstrations of difference.

An article in this issue, entitled "Executive Function and Behavioral Problems in Students with Visual Impairments at Mainstream and Special Schools," by Heyl and Hintermair, offers a good example of how statistics should be used to illustrate differences in data that might, without the guidance of statistics, be given too much or not enough consideration by readers. In Table 1 of this article, the authors list several demographic variables (measures that describe the participants who took part in the study). It is very useful for authors to provide such a table that includes information about means and standard deviations--not only for descriptive characteristics of their participants, but also for their experimental measures. Providing such information offers readers a sense of the overall scope of the data and sometimes reveals general patterns in the data. Since means and standard deviations are generally the building blocks upon which further statistical testing is based, such information can also offer a way to analyze whether the statistical results are reported accurately and what the clinical or practical meaning of the statistical testing might be.

A useful preliminary analysis of data, before the primary statistical testing is performed, is to look at reported demographic variables to see whether there are any important ways in which the participants varied as individuals within the group. Finding such differences might have an effect on how later analyses are conducted or even whether the results are meaningful at all.

What Heyl and Hintermair have done in Table 1 is to present the demographic variables they consider might potentially impact the outcomes of the study and judge whether these variables are significantly different for the two main conditions of their study (mainstream schools and special schools) by conducting a [chi square] (pronounced "chi square") test on these variables that looks at the frequencies of categorical variables. Any significant differences identified in Table 1 would then have to be taken into account in further analyses or an explanation would have to be offered as to why the differences would not impact the outcomes significantly.

When a variable is made of categories (like "cold," "warm," and "hot" as opposed to numerical values for temperatures), the [chi square] test compares how well the frequency of occurrence for each of the categories of one variable are similer to the categories of another variable. In Table 1, for example, the genders of the participants was compared to the type of schools they attended. The data in the table show that in the mainstream schools there were 43 males and 47 females and in the special schools there were 78 males and 58 females. By this count, the mainstream schools had more females and the special schools had more males. If only this information were provided, it would not be possible to determine whether this difference in gender between the two types of schools is enough to raise concern.

The [chi square] test for these two variables (reported in the table as [chi square] = 1.99) shows that this difference in gender was not statistically significant. The authors indicate the lack of significance by not putting an asterisk by the result; such notation is a kind of shorthand that is often used in reporting results in tables. If the [chi square] test result was reported in the text of the article, it would look more like this: [chi square](1) = 1.99, p .05. The first part indicates it is a chi-square test, and the number in parentheses represents the degrees of freedom. This information reveals that this test is comparing two variables with two groups each (male/female versus mainstream/special school). The "1.99" is the numerical result of the test, and the "p" value represents the significance level. Significance will undoubtedly be addressed in a future Statistical Sidebar; for now, readers should understand that significance is an indication of whether the statistical result is likely to have happened by chance or is due to true differences in the data.

By laying out the demographic data as the authors did in Table 1, and indicating any statistically significant differences, they are providing readers the best chance to fully appreciate any differences in the data and to make sense of any further statistical analyses.

Robert Wall Emerson, Ph.D., consulting editor for research, Journal of Visual Impairment & Blindness, and professor, Department of Blindness and Low Vision Studies, Western Michigan University, 1903 West Michigan Avenue, Kalamazoo, MI 49008; e-mail: <robert.wall@wmich.edu>.
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