Can any of my fellow Tipsters who are experienced at teaching statistics
help me?
I am currently teaching the wonders of ANOVA and have come across a
situation I cannot explain and cannot find an explanation for in any of
my textbooks.
The basic structure of the F-ratio for ANOVA is:
variance between treatment/variance within treatment
The source of the variance for these two components is:
Between treatment variance = 'Treatment Effect' + 'Individual
Differences' + 'Experimental Error';
Within treatment variance = 'Individual Differences' + 'Experimental
Error';
Therefore if there is no treatment effect the F-ratio will be around
1.00 because the numerator & denominator are both measuring the same
variance ('Individual Differences' + 'Experimental Error').
So far so good, but IF the variance WITHIN treatments is great and the
variance between treatments is negligible the F-ratio falls well below
1.00 (I have some data which has resulted in the F-ratio being 0.01).
I am trying to find a simple explanation for this that I can give to my
students, can anyone help?
Thanks (in hopeful anticipation)
Antoinette Hardy
