One-way ANOVA is an ANOVA model with one categorical factor. For observation 
at factor level 
, the fixed effects model
is
 |
where the errors are commonly assumed independent, normally distributed, and to have a common variance. The null hypothesis states that all factor-level means are equal.
The ANOVA 
statistic compares variability of the level means with variability of observations
within levels. A significant result indicates that the means are not all equal, but
does not by itself identify which pairs differ. One-way ANOVA can be balanced or
unbalanced according as the factor levels have equal
or unequal sample sizes.
