## 2pSPa2. A method for analyzing rating scale data.

### Session: Tuesday Afternoon, May 14

### Time: 1:25

**Author: Harry Levitt**

**Location: Ctr. for Res. in Speech and Hearing Sciences, Graduate School and Univ. Ctr. of the City Univ. of New York, 33 W. 42nd St., New York, NY 10036**

**Abstract:**

Subjective ratings are often used in the evaluation of hearing aids,
loudspeakers, speech processors, and other systems involving sensory stimuli.
The analysis of rating data, however, presents problems since the usual
parametric assumptions underlying standard statistical techniques (e.g., t
tests, analysis of variance) are not applicable to subjective ratings. A
nonparametric method of analyzing rating data is described using concepts
derived from signal detection theory. In order to compare two sets of ratings, a
nonparametric estimate of the area under the ROC curve is obtained by first
deriving the correlation function relating the two sets of ratings and then
summing over half the range of the correlation function. This statistic, the
half summed correlation (HSC), is relatively easy to compute and can be used to
test, with known statistical power, for various differences between two sets of
ratings (mean differences, variance differences, mean plus variance
differences). It is also possible to rank sets of ratings using this statistic
and to apply various multidimensional techniques designed for ordinal data. A
variation of the analysis of proximities using HSC's will also be described.
[Work supported by NIDCD.]

from ASA 131st Meeting, Indianapolis, May 1996