Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

Ronald V. Canfield


Ronald V. Canfield


David L. Turner


Charles Romesburg


If experimental data are obtained according to an experimental design for which analysis of variance (AOV) is appropriate, the result of the analysis is one of the following decisions:

1. A significant difference exists among treatment effects.

2. No significant difference exists.

Interpretation in the first case has been studied very thoroughly by many statisticians resulting, for example, in the multiple comparison procedure. Too often, in the second case, the AOV analysis is thought to be completed with no further attempt to interpret a nonsignificant outcome.

Of the many possible explanations for significance in the first case, the multiple comparison procedure seeks to find the most plausible explanation. Similarly, there are two possible explanations for the non-significant result:

1. There is truly no meaningful difference among the treatments.

2. The experimental design did not offer sufficient precision to detect differences which may be of interest.

In this paper a method is sought which gives some indication of the most plausible explanation for a non-significant result.

There are two main objectives For developing this report.

1. To develop an analysis following a non-significant AOV result that provides a plausible interpretation of the reason for non-significance.

2. To present the analysis procedure in such a way that experimenters not highly trained in statistics can easily perform the calculation.