TITLE:
Using Excel to Explore the Effects of Assumption Violations on One-Way Analysis of Variance (ANOVA) Statistical Procedures
AUTHORS:
William Laverty, Ivan Kelly
KEYWORDS:
Excel, One-Way ANOVA, Assumption Violations, t-Distribution, Cauchy Distribution
JOURNAL NAME:
Open Journal of Statistics,
Vol.9 No.4,
August
13,
2019
ABSTRACT: To understand any statistical tool requires not only an understanding of
the relevant computational procedures but also an awareness of the assumptions
upon which the procedures are based, and the effects of violations of these
assumptions. In our earlier articles
(Laverty, Miket, & Kelly [1]) and (Laverty & Kelly, [2] [3]) we used Microsoft Excel to simulate both a Hidden Markov model and
heteroskedastic models showing different realizations of these models and the
performance of the techniques for identifying the underlying hidden states
using simulated data. The advantage of using Excel is that the simulations are
regenerated when the spreadsheet is recalculated allowing the user to observe
the performance of the statistical technique under different realizations of
the data. In this article we will show how to use Excel to generate data from a
one-way ANOVA (Analysis of Variance) model and how the statistical methods
behave both when the fundamental assumptions of the model hold and when these
assumptions are violated. The purpose
of this article is to provide tools for individuals to gain an intuitive
understanding of these violations using this readily available program.