FIRST DRAFT (1 page)

The following is a quick sketch of my approach to a report of a survey.

  The survey

.(1) Each question in a survey refers to a variable.

.(2) The variable is sometimes continuous.

.(3) Usually just a few options are offered.

.(4) I refer to these as surface options because the underlying variable is continuous.

.(5) The number of options used seems to be somewhat arbitrary.

  The responses and the tables

.(6) The responses are aggregated to give raw percentages for each of the options, presented as a table.

  The report

.(7) The raw option percentages are processed in some way.

.(8) Sometimes one-sided aggregate percentages are reported.

.(9) The text of the report selects a few percentages to present in a somewhat haphazard way.

  Better

.(10) Rather than a one-sided percentage, a net aggregate percentage, x, is sometimes presented – in other words aggregate percentages plus or minus either side of some middle.

.(11) A refinement takes account of the number n of options to give the corrected net aggregate percentage, c.

. c = r x where r = ((n-1)/n).

For two options r=1/2; three options, r=2/3; four options, r=3/4; five options, r=4/5.

.(12) Both x and c are still aggregates, and so it is better to give scores to each option and to calculate the mean score.

.(13) One approach is to assume a standard underlying continuum with scores in the interval [-1,+1]. The interval is divided into n equal subintervals corresponding to the n options. The score for each subinterval is its midpoint.

.(14)