**Factor**: A source
of variance in the response. A categorical factor is measured in categorical
levels, whereas a covariate factor is measured on a scale of continuous (or
sometimes ordinal) variation. A statistical model might be constructed to test the
influence of a factor as the sole explanation (Y = A + ε) or as one of
many factors variously crossed with each other or
nested within each other.

A *fixed* factor has
levels that are fixed by the design and could be repeated without error in
another investigation. The factor has a significant effect if sample means
differ by considerably more than the background variation, or for a covariate,
if the variation of the regression line from horizontal greatly exceeds the
variation of data points from the line.

A *random* factor
has levels that sample at random from a defined population. A random factor
will be assumed to have a normal distribution of sample means, and homogenous
variance of means, if its MS is the error variance for estimating other effects
(e.g., in nested designs). The random factor has a significant effect if the
variance among its levels is considerably greater than zero.

Doncaster, C. P. & Davey, A. J. H. (2007) *Analysis of Variance and Covariance: How to
Choose and Construct Models for the Life Sciences*. Cambridge: Cambridge
University Press.

http://www.southampton.ac.uk/~cpd/anovas/datasets/