Hibiscus B

### Survey Questionnaires and Graphs (303138)

**Ioana Schiopu Kratina, University of Ottawa*

*Kyle Trepanier, University of Ottawa*

*Christina Maria Zamfirescu, Hunter College*

**Keywords:** questionnaire design, acyclic digraph, statistical analysis, finite probability space, expected number of questions

The presentation expands on “Survey Questionnaires and Graphs” by I. Schiopu-Kratina, C.M. Zamfirescu, K. Trépanier, and L. Marques, EJS 9 (2015). We introduce a new type of graph---survey charts---and use them to improve survey questionnaires. By means of transformations of the survey chart, we simplify the structure of the questionnaire to facilitate testing and analysis. We also reduce the response burden associated with the questionnaire. Our methods are illustrated on an actual questionnaire with hundreds of questions.

Some desirable characteristics of a questionnaire are (i) each question should be asked only of a predetermined population, called the coverage of that question; (ii) for each surveyed subpopulation, the questions should be sequenced in a logical order; and (iii) it should collect the required information with a minimum response burden.

To attain these goals, we start with the flow chart used in survey practice. We turn it into what we call a survey chart, which is a special type of graph. We associate to it a finite probability space, called the analytical potential of the questionnaire. It contains all the information the questionnaire can collect, which should still be available at the end of each transformation. The probability measures on this space are defined to assess the response burden incurred by the questionnaire. We give simple examples to illustrate all these concepts.

Our transformations lead to a survey chart, on which one can clearly see (i) the coverage of each question; (ii) the paths taken by subpopulations of analytical interest; and (iii) the logic of sequencing the questions. The constraints imposed on our transformations are (i) the analytical potential is preserved by each transformation; (ii) the expected number of questions does not increase; and (iii) the change in the text of the original questions is minimal.

Our novel approach compares favorably with other methods that improve the questionnaire structure.