Note on sample quantiles for ordinal data

Uwe Hassler

Statistical Papers, 2020, vol. 61, issue 6, No 7, 2383-2391

Abstract: Abstract The arithmetic mean computed over ordinal data has to be interpreted with care. Instead it is often recommended to compute the sample median, or more generally sample quantiles. The virtue of raw quantiles is that they are not affected by an arbitrary rescaling of the data. Unfortunately, they are not very informative when an ordinal variable falls into only few categories. The informational content is larger for so-called grouped quantiles interpolating around one possible value. In this note we show, however, that they turn out to be not invariant with respect to strictly monotonous transformations as long as the possible outcomes are not equidistant. This motivates to suggest the new centered interpolated quantiles. They are designed to be invariant with respect to transformations that preserve the ranking of the possible values.

Keywords: Likert response format; Interpolated quantiles; Invariance under strictly monotonous transformations; 62-07; 62P10; 62P15; 62P20; 62P25 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-018-1054-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-1054-5

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-018-1054-5

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().