Nanova is a new procedure I developed for analyzing nominal data collected using factorial experimental designs.

Nominal responses are the natural way for people to report actions or opinions. Because nominal responses are not numerical values, they have been under-utilized in behavioral research. On those occasions where nominal responses are elicited, the responses are customarily aggregated over people or trials so that large-sample statistics can be employed. The new analysis directly associates responses with sources in factorial designs. A pair of nominal responses either matches or does not; when responses do not match, they vary. That analog to variance is incorporated in the Nominal Analysis of “Variance” (Nanova) procedure, wherein the proportion of non-matches associated with a source plays the same role as sum of squares does in analysis of variance. Because there are no distributional assumptions associated with nominal data, the significance levels of the N-ratios formed by comparing proportions are determined by resampling. The Nanova table has the same structure as an analysis of variance table.

Please be warned, however, that for a large design, say one with several hundred scores, resampling can take a lot of computer time, even on a fast machine. When I employ the 100,000 iterations recommended for publication-level analyses, I usually allow the program to run overnight.

Version 3.1.2 of the NANOVA computer program I wrote to carry out this analysis is available here. (If you previously downloaded Version 1.x or 2.x, please replace it. The primary virtue of Version 3 is that it accommodates up to six factors, whereas earlier versions were limited to four. Version 3.1 added some minor cosmetic improvements.) The program employs the same user-friendly interface as the CALSTAT suite that accompanies my Analysis of Variance (without quotes) textbook. Screen shots of the NANOVA program are shown here.  Some operational issues common to both NANOVA and the CALSTAT suite are discussed on the FAQ page for the textbook.

A paper that describes the theory underlying Nanova, and that presents illustrative applications, is available here. The paper has been published in Behavior Research Methods. Examples of Nanova analyses, including some not included in the paper, are shown here. A published paper illustrating how nominal data can be analyzed in a Functional Measurement context is also available.

The development of NANOVA was partially supported by the United States Department of Homeland Security through the Center for Risk and Economic Analysis of Terrorism Events (CREATE) under grant number 2007-ST-061-000001. However, the program is the responsibility of the author and does not necessarily reflect views of the United States Department of Homeland Security.