appropriate degrees of freedom. The value of Fc is
calculated by dividing the mean square of the additional
term by the mean square error or

 Fc = 0.3477 / 0.0868
 = 4.0058

 d.f. = (1) and (n-k-l) or 1 and 3

 In comparing the calculated value of Fc with the
value of F in the table, it is found that the additional
term is not significant. This means that, according to
this test, the quadratic equation does not result in a
better representation of the response surface than the
linear equation. But this is a contradiction of earlier
findings. Which of the statistical tests can be believed?
What can be concluded? If statistics is a precise
science, how can it result in contradictory conclusions?
Can we not have confidence in statistics? Some of these
questions are answered in the following section.

A Priori and A Posteriori Information

 Statistics is not a science in itself. Rather it is a
tool to aid in scientific studies. Isolated from reality,
statistics produces little information. For this reason,
it is necessary that researchers know their data and have
a sound base in the theory of their science. Above all,
experience is highly valuable to the researcher when
analyzing and interpreting information collected from
experiments and other research.
 In Figure VI-8 the rice data and the two curves which
were calculated are plotted. The problem is to choose
between the two curves -- is the quadratic or is the
linear more representative of reality? Table VI-4 is a
summary of the statistical values calculated for the two
equations. The value of Fc for each of the equations is
similar and both are significant at the 5% level of
confidence. However, the F test of the quadratic term
indicates that it does not significantly improve the
representation of the response phenomenon. This is
supported by the lower value of t of the quadratic
coefficient, which is significant only at the 10% level.
On the other hand, the variance or standard error of the