Title page for ETD etd-05112006-154754

Type of Document Dissertation
Author Kuzmak, Barbara R.
URN etd-05112006-154754
Title An examination of outliers and interaction in a nonreplicated two-way table
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Smith, Eric P. Committee Chair
Foutz, Robert Committee Member
Myers, Raymond H. Committee Member
Reynolds, Marion R. Jr. Committee Member
Terrell, George R. Committee Member
  • Analysis of variance Research
Date of Defense 1990-12-05
Availability restricted

The additive-plus-multiplicative model, Υij = κ μ. + (αi + βj + ΣλρτριΥρj / ρ=1, has been used to describe multiplicative interaction in an unreplicated experiment. Outlier effects often appear as interaction in a two-way analysis of variance with one observation per cell. I use this model in the same setting to study outliers. In data sets with significant interaction, one may be interested in determining whether the cause of the interaction is due to a true interaction, outliers or both. I develop a new technique which can show how outliers can be distinguished from interaction when there are simple outliers in a two-way table. Several examples illustrating the use of this model to describe outliers and interaction are presented.

I briefly address the topics of leverage and influence. Leverage measures the impact a change in an observation has on fitted values, whereas influence evaluates the effect deleting an observation has on model estimates. I extend the leverage tables for an additive-plus-multiplicative model of rank 1 to a rank k model. Several examples studying the influence in a two-way nonreplicated table are given.

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