Volume I - Section VI - Statistical Analysis 
Page VI - 5 
6.1.8 ANOVA 
The standard deviation, t-test, and correlation coefficients involve variance in the concepts and/or 
calculation methods. Use of the phrase “analysis of variance” (ANOVA) is reserved for a broad 
range of analytic techniques that address questions of statistical significance through calculation 
methods that divide overall variance into components. The calculation method uses a technique 
involving the ‘sums of squares.’ In one-way ANOVA, the following are calculated: the total 
sums of squares, sums of squares among groups, and residual sums of squares. Dividing each 
sums of squares by its associated degrees of freedom results in values called mean squares. 
Instead of calculating a t-test, ANOVA requires calculation of the F-ratio. Dividing the mean 
square among groups by the mean square yields the F-ratio. Traditionally, one would consult a 
table to locate the p-value associated with a specific combination of F, degrees of freedom for 
groups, and degrees of freedom for the error term. Today’s use of computers makes the process 
of obtaining p-value easy. See T. Lee (1995) for further details. 
Table 6.01 shows a sample of a single factor ANOVA test performed on the first three cases 
(basecase, case 02, and case 03) of this research on the cage occupied zone averaged 
concentration values. The summary section shows the number of cages in each group, the sum of 
the concentration values in all cages in a group, the mean average concentration values in all 
cages in a group, and the variance around the mean. The ANOVA test itself reports an F and an 
F C rit value. If F cr j t is less than F it can be said that there is a statistical difference between the 
members of the group. This is true for the sample given below and for all other groups of whole 
room runs. 
Table 6.01 ANOVA Example for Concentration (basecase, case 02, and case 03) 
SUMMARY: 
Groups 
Count 
Sum 
Average 
Variance 
Basecase 
210 
0.5774 
0.0027 
2.09E-07 
Case 02 
210 
0.4556 
0.0022 
1.67E-07 
Case 03 
210 
0.4196 
0.0020 
1.90E-07 
ANOVA: 
Source of 
Variation 
SS 
df 
MS 
F 
P-Value 
Fcrit 
Between 
Groups 
6.51E-05 
2 
3.26E-05 
172.3 
2.27E-60 
3.0101 
Within 
Groups 
0.00012 
627 
1.89E-07 
Total 
0.00018 
629 
