AU2002100348A4 - Method for measuring uncertainty in questionnaire reponses - Google Patents

Description

Measurement of Uncertainty in Questionnaire Responses.

Questionnaires often use a rating scale, which may range from two points to eleven or more. Examples include Yes No, In Favour Undecided Against, and any number of points displayed as arrays of boxes or other marks. In order to register an opinion, a questionnaire respondent is invited to select one of the presented options.

Questionnaires usually allow respondents to mark a Don't Know category, or to leave an item blank, if they do not wish to provide an answer. Such responses, which are not part of the rating scale are usually referred to as "missing values". Analysis of questionnaires is greatly complicated by missing values.

Questionnaire analysis programs need to count them, and to use the counts in calculating averages and tests of significance.

This invention eliminates the problem, by permitting respondents to select more than one point on the rating scale, or equivalently by treating an unanswered question as the selection of all points on the rating scale. All responses are then treated as ranges, where the range may consist of any number of contiguous scale points.

For example, consider an 11-point scale, where the left-most point takes the value 100, the right-most the value 0, and the intermediate points values between 100 and 0 in steps of 10. A response comprising the left-most five points would indicate a response that is the range 100-60.

We define the "uncertainty" in the response as the difference between the extreme points of the selected range. In this example, the uncertainty is 100 minus 60 40. The "certainty" in the response is the difference between the extreme points of the scale minus the uncertainty. In this example, the certainty is 100 minus 0 minus 40 Averages of questionnaire responses are calculated by averaging the maximum points, the minimum points and the uncertainties. If there are N questionnaire items, there will be N maximum points, N minimum points, and N computed uncertainties. The averages are computed simply from separate totals for the maxima, minima and uncertainties, each divided by N.

For example, suppose there are just three responses, 100-60, blank and 40-40.

The blank response is treated as 100-0. The average maximum is (100+100+40)/3 and the average minimum is (60+0+40)/3 33.3. The average uncertainty is (40+100+0)/3 46.6, and the average certainty is (60+0+100)/3 53.3. The sum of uncertainty and certainty is always equal to the maximum range of the rating scale. This method of calculation is intuitively appealing for reflecting overall certainty of viewpoint within range calculated, for the group of respondents.

We can also use certainty as a weight, and calculate weighted averages, using the middle point of the response range. In this example, the middle points are (100+60)/2 80, (100+0)/2 50, and (40+40)/2 40, and the weights are 60, 0 and 100 respectively. Note that the blank response is eliminated from the average because of its zero weight. The weighted average in this example is (80*60+50*0+40*100)/160 55. This method of calculation is intuitively appealing for reflecting the balance of opinion in the group of respondents.

A summary of the questionnaire responses would present the results from both methods of calculation.

Typical questionnaire analyses present ranges and standard deviations. The usual "range" can be approximated in this invention by the minimum of the middle points to the maximum of the middle points. However, this method does not exclude blank response, because it treats them as if the middle point were Our recommendation is that the usual range be replaced by the above computation, in which we calculate the average of the minima and the average of the maxima as the "range". Standard deviations can be computed over maxima, minima and middle points.

Claims (6)

1. A method for the measurement of uncertainty in questionnaire responses, which solves the problem of missing values.

2. The method of claim 1, wherein responses on a rating scale may comprise one or more contiguous points on the scale.

3. A potentially missing response of claim 2 represented as a response comprising all points on the scale.

4. Every response of claim 2 partitioned into two components, uncertainty and certainty.

Averages of responses of claim 2 computed as a range from the average minima to the average maxima of rating scale points.

6. Averages of the middle points of the responses of claim 2 weighted by the certainty of claim 4.