Chapter 18 Page 4

Introduction

Bivariate
analysis:
nominal
variables

Bivariate
analysis:
ordinal
variables

Statistical
tests of
association

Aids

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Table 18.2, we think you will agree, is much easier to read. The differences in percentages stand out much clearer without the frequencies; yet all the data a reader needs to understand the table is there.

Box 18.1. Guidelines for reading a bivariate table

Establish the direction in which the percentages are calculated. In a properly constructed table, this direction will be shown by the row or column labeled "percent" - in the right-hand column or across the bottom of the table. When the percentages are listed in columns, they should add to 100 or close to it at the bottom. In this case, the table has been percentaged down, as we did in Table 18.1. When the totals for percentages are listed in a column at the right, the table has been percentaged across rows.
To interpret a table, read in the opposite direction from the way the percentages were added. When a table is percentaged down, interpret the results by comparing across the rows. This is how we interpreted the results in Table 18.1. We compared the percentages of females and males who gave favorable responses. These percentages were found in the same row. When percentages are totaled across rows, read by table by comparing results down the columns.
In tables you construct, we recommend that you percentage down and then interpret them by comparing across the rows, as we did for Table 18.1. Readers seem to be able to make comparisons within rows and across columns rather than the reverse.

Beyond the 2x2 table

Table 18.2 has only two columns and two rows, not counting the total column or the total across the bottom of the table. A table with only two attributes for each variable is often called a 2x2 (two by two) table. Bivariate tables, however, can be extended, depending on the number of attributes for either of the two variables. With more attributes, there are more columns or rows or both. Thus, a table might have 3 or 4 or more columns and as many or more rows. Generally, readers can quickly grasp tables with 3 or 4 columns and rows, but as the number of columns and rows increase, tables become more difficult to read and interpret. With more cells, there are just too many percentages to compare. When there are a large number of attributes, represented by many columns and rows, it is better to use other measures of association. In the next chapter we describe some measures you can use.

Bivariate analysis: ordinal variables

With ordinal measurement, the attributes for a variable can be arranged from low to high along some dimension. Thus, in testing for a relationship between two ordinal variables, we can determine whether the relationship is:

Positive — as one variable increases, so does the other (persons with more schooling, for example, tend to earn more money); or
Negative — as one variable increases, the other tends to decrease (females with more schooling tend to have fewer children)

Positive relationship. Halim (1995) wanted to know if there was a relationship between levels of education among a sample of women and their attitudes toward holding a job after completing their education. She created three categories for level of education, secondary, university, and post-graduate. She also used three categories to measure responses to a question whether women should work after completing their education. Responses were "strongly agree," "uncertain," or "disagree." Using these ordinal data, she created the 3x3 table shown as Table 18.3. There was a clear positive relationship between the level of education of women and their attitudes toward holding jobs after they complete their education. Only 36% of the women with secondary schooling expressed agreement with this view while 100% of the women who had a post graduate level of education did, as did 99% of those with a university or special college education.

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