Step 4. In the analysis of variance for a 2" factorial,
one degree of freedom is always assigned to each factor or
interaction of factors because the factor effect is
calculated by comparing two levels of the factor or
interaction and one degree of freedom is lost in the
estimation.
 Perform the analysis of variance (ANOVA):

TABLE III-5. ANOVA for the 23 factorial

Source of Degrees of Sum of Mean Fc
variation freedom Squares Squares
Blocks (b-l)=l 1.05 1.05 6.77 *

Treatments (t-l)=7 28.46 4.066 26.23 **

 Factor P 1 7.77 7.77 50.129 **
 N 1 4.95 4.95 31.935 **
 V 1 15.016 15.016 96.88 **
 PN 1 .681 .681 4.39 NS
 PV 1 .0056 .0056 .036 NS
 NV 1 .000625 .000625 .004 NS
 PNV 1 .1056 .1056 .68 NS

Error 7 1.084 .155
Total 15 30.594
CV = 6.38%
* Significant at 5% level
** Significant at 1% level

Interpretation of Results

 By examining the treatment mean yields in Table
III-3, and the analysis of variance, Table III-5, it can
be determined that each of the three factors individually
(plant density, nitrogen, and variety) had a highly
significant effect on yield. Out of the three factors,
the new variety (V) produced the greatest increase (2.05
kg/plot), and plant density (P) was second with a 1.1
kg/plot increase. Although nitrogen (N) had a significant
effect, increasing the yield by 21%, an economic analysis
should be conducted to determine whether its application
is an economically good choice. (Does the yield increase
cover the cost of buying and applying the nitrogen