Abstract:
|
Background: For numerical rating scales and other ordinal variables, neither means nor medians are satisfactory as summary location measures. The mean is usually not a preferred measure for ordinal data, while the median is too discrete to be very informative and typically useless for informal discrimination between groups. Methods: The 'continuous median' or the 'c-median' is defined and proposed as a simple summary location parameter for numerical rating scale variables. The c-median is up to 0.5 units higher or lower than the integer-valued median depending on the proportion of the distribution below, equal to, and above the median. Intuitively, when rounded the c-median is equal to the median. Other 'c-quantiles' are defined in a similar way to the c-median; thus a 'continuous inter-quartile range' (c-IQR) can also be constructed. Results: (i) Real-life examples are shown demonstrating the utility of the c-median. (ii) A method for constructing confidence intervals is given and coverage probability is assessed with simulations. (iii) Use of the difference in c-medians as the basis of a statistical test is compared with other two-sample tests.
|
ASA Meetings Department
732 North Washington Street, Alexandria, VA 22314
(703) 684-1221 • meetings@amstat.org
Copyright © American Statistical Association.