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Testing for co-directional interactions using union--intersection and intersection--union methods

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  • Patrick D. Gerard
  • Julia L. Sharp

Abstract

When interaction terms exist in a two-factor, factorial experiment, the consideration and analysis of main effects are often restricted to those situations where the interaction between factors is not significant. Hinkelman and Kempthorne [4] softened that stance somewhat and advocate testing main effects when the interaction is deemed co-directional but not anti-directional. A test for the main effects in that situation may be pragmatic to the practitioner and appealing to researchers in other disciplines. Intersection--union and union--intersection methods are examined for assessing the directional nature of significant interactions so that the main effects in a two-factor factorial may be evaluated. The tests suggested are conceptually straightforward and practical and maintain the nominal Type-I error rate. Examples are provided to illustrate the methods.

Suggested Citation

  • Patrick D. Gerard & Julia L. Sharp, 2011. "Testing for co-directional interactions using union--intersection and intersection--union methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1347-1358, May.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:7:p:1347-1358
    DOI: 10.1080/02664763.2010.498506
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