Marginals

As it applies to survey research, a marginal is a number “at the margins” (at the edge or perimeter) of a cross-tabulation table of two or more variables. Statistical software that is used by survey researchers, such as SAS and the Statistical Package for the Social Sciences (SPSS), routinely create cross-tabs with the marginals showing as the default setting.

Table 1 shows a cross-tabulation between two variables—educational attainment (Not High School Grad, High School Grad, College Grad) and belief in the existence of extraterrestrial life (Believe, Not Sure, Do Not Believe)—from a survey conducted in 1996. This table displays the number of respondents (i.e. absolute frequency counts) that fall into each of the conditions (cells) shown in the table. The marginals in the Total column show the number of [Page 450]respondents out of the total 839 surveyed who gave each answer when asked about whether or not they believed “in the existence of life somewhere else in the Universe than on Earth.” Of the 839 adults surveyed, 420 said they did believe, 248 said they were not sure, and 171 said they did not believe. From the information in Table 1, one can quickly surmise that nearly half (420 out of 832) said they did believe. The marginals along the Total Row at the bottom of the table show the number of respondents among the total 839 in each of the three educational attainment categories. From these marginals, one can surmise that about 3 in 5 (507 out of 832) of those surveyed graduated from high school but not from college.

Table 2 shows the results of the same survey data except that it is the relative frequencies (percentages) that are displayed across the rows, down the columns, and as the marginals in each of the cells for the table. The top percentage in each cell is the row percentage for each educational level and the bottom percentage in each cell is the column percentage for each answer to the belief question. The margins, however, show the percentages for either that row or that column.

The information in Table 2 is more informative to a consumer of these data because it conveys information about both the answers to each variable and the interrelationship between the two variables in a way that is easy and quick to understand. For example, it is not clear from the results presented in Table 1 how the two variables are related, but from Table 2 it is readily apparent by looking at the row percentages that as educational attainment increases, so does the portion of people who believe in the existence of extraterrestrial life. Furthermore, as long as one knows the total number of respondents who were surveyed, then the absolute frequencies for each cell can be reproduced from the percentages in Table 2.