Construction and Interpreting a cross tabulation

Since quite representative of a typical cross tabulation, it can be used in making five observations or comments that can be of help to students when constructing and interpreting cross tabulations.

At the beginning of this discussion on cross tabulation it was pointed out that there are two types of categorized variables: type A, ones in which the different categories of the variable cannot be quantified, such as blue collar and white collar occupations; and type B ones in which the different categories are associated with quantifiable numbers (such as age and income) or imprecisely quantifiable numbers (such as “likely to buy” data). Cross tabulation is used on both types of categorical variables, but the comments below are more applicable to the type B categorical variable.

It is common practice to assign the categories associated with the dependent variable to the rows of the cross tabulation, and to assign the categories associated with the independent variables(s) to the columns of the cross tabulation. In attitude toward the pizza truck is the dependent variable, and level of awareness and knowledge is the independent variable.

It is also common practice to assign the top row to the dependent variable category with the largest quantifiable number. Each succeeding row is assigned a category with a progressively lower quantifiable number. Alternatively, the top row can be assigned to the highest or most desirable category, while the bottom row can be assigned the lowest or most undesirable category.

Similarly, the independent variable category with the largest quantifiable number is assigned to the rightmost column, and the category with the smallest quantifiable number is assigned to the leftmost column. As an alternative, the rightmost column can be assigned to the highest or most desirable category, and the leftmost column to the lowest or most undesirable category. Thus, in the left column is for “unaware” respondents while the right column is for “aware and knowledgeable” respondents.

It is usually preferable to calculate percentages so that each column’s percentages total 100.

To interpret the cross tabulation, analyze the pattern of percentages across each row separately. If the percentages increase from left to right, the dependent variable category is positively associated with the independent variable. A favorable attitude is positively associated with increasing awareness and knowledge of the pizza trucks. If the percentages decrease from left to right, the dependent variable category is negatively associated with the independent variable. Undecided is negatively associated with increasing awareness and knowledge of the pizza trucks.

When the Cross Tabulation is from Type A categorical Variables:

Comments on the above points do not apply if type A categorical variables are used to construct the cross tabulation. This is because in type A variables the categories are not in any way quantifiable or progressive from high to low values, or vice versa. Therefore, when a cross tabulation is to be made from type A variables comments above can be helpful in constructing and interpreting such a cross tabulation.

Three Useful Questions for Evaluating Cross Tabulations:

Researchers find it useful to answer the following three questions when evaluating a cross tabulation that appears to explain differences in a dependent variable.

1. Does the cross tabulation show a valid or a spurious relationship?
2. How many independent variables should be used in the cross tabulation?
3. Are the differences seen in the cross tabulation statistically significant, or could they have occurred have occurred by chance due to sampling variation?

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