(1) V B(A) ¼ S B(A) /ν B(A)
(2) V A ¼ S A /ν A
(3) V A Â C ¼ S A Â C /ν A Â C
(4) V C ¼ S C /ν C
(5) V E ¼ S E /ν E
– Procedure (5): Calculate an alpha statistic (i.e., level of significance) using the
next expressions (1–4). The following values were obtained according to the
F-distribution. Here, the F-distribution is a consecutive probability distribution
used in statistics and probability theory. It is used as the distribution following the
null hypothesis in the F-test and is applied to the analysis of variance.
(1) F A ¼ V A /V B(A)
(2) F B(A) ¼ V B(A) /V E
(3) F C ¼ V C /V E
(4) F A Â C ¼ V A Â C /V E
– Procedure (6): Determine the alpha statistic, α, and calculate the F-statistics (νA,
νE, and α).
– Procedure (7): A significant difference is determined in comparison with the
control system if the F-ratio is larger than the % point (of the F-distribution).
Table 6.2 lists the calculated results of the analysis of variance. In the microcosm
test method, α ¼ 0.05 is used to determine whether there is a significant difference
(5% is generally adopted as the level of significance in this technique).
When the F-ratio of a point of group and crowd X** is larger than the F-statistic,
it is determined that the addition of the chemical substance has an influence on the
microcosm
**The factor is called the point of group X with a group and the interaction of the
point in time, and the change in the reaction with the point in time differs among
groups. For example, the value in the control system is stable, but, in the addition
system, values may increase or decrease. Therefore, when there is a significant
Table 6.2 Table of branching-type ANOVA (ex. (2)-② means procedure (2)-②)
Factor
Sum of
square
Flexibility
Unbiased
variance
F-ratio
F value 100α%
point*
Group
S A
(2)-②
ν A
(3)-①
V A
(3)-⑨
F A
(4)-①
F(ν A, ν B(A) , α)
Individual
(group)
S B(A)
(2)-③
ν B(A)
(3) - ②
V B(A)
(3) - ⑧
F B(A)
(4) - ②
F(ν B(A), ν E , α)
Time point
S C
(2)-⑤
ν C
(3)-④
V C
(3)-⑪
F C
(4)-③
F(ν C, ν E , α)
groupÂtime point
S A Â C
(2)-⑥
ν A Â C
(3)-⑤
V A Â C
(3)-⑩
F A Â C
(4)-④
F(νν A Â C, ν E , α)
Residual error
S E
(2)-⑧
ν E
(3)-⑥
V E
(3)-⑫
Sum
S T
(2)-⑦
ν T
(3)-⑦
56
K. Kakazu et al.
(2) V A ¼ S A /ν A
(3) V A Â C ¼ S A Â C /ν A Â C
(4) V C ¼ S C /ν C
(5) V E ¼ S E /ν E
– Procedure (5): Calculate an alpha statistic (i.e., level of significance) using the
next expressions (1–4). The following values were obtained according to the
F-distribution. Here, the F-distribution is a consecutive probability distribution
used in statistics and probability theory. It is used as the distribution following the
null hypothesis in the F-test and is applied to the analysis of variance.
(1) F A ¼ V A /V B(A)
(2) F B(A) ¼ V B(A) /V E
(3) F C ¼ V C /V E
(4) F A Â C ¼ V A Â C /V E
– Procedure (6): Determine the alpha statistic, α, and calculate the F-statistics (νA,
νE, and α).
– Procedure (7): A significant difference is determined in comparison with the
control system if the F-ratio is larger than the % point (of the F-distribution).
Table 6.2 lists the calculated results of the analysis of variance. In the microcosm
test method, α ¼ 0.05 is used to determine whether there is a significant difference
(5% is generally adopted as the level of significance in this technique).
When the F-ratio of a point of group and crowd X** is larger than the F-statistic,
it is determined that the addition of the chemical substance has an influence on the
microcosm
**The factor is called the point of group X with a group and the interaction of the
point in time, and the change in the reaction with the point in time differs among
groups. For example, the value in the control system is stable, but, in the addition
system, values may increase or decrease. Therefore, when there is a significant
Table 6.2 Table of branching-type ANOVA (ex. (2)-② means procedure (2)-②)
Factor
Sum of
square
Flexibility
Unbiased
variance
F-ratio
F value 100α%
point*
Group
S A
(2)-②
ν A
(3)-①
V A
(3)-⑨
F A
(4)-①
F(ν A, ν B(A) , α)
Individual
(group)
S B(A)
(2)-③
ν B(A)
(3) - ②
V B(A)
(3) - ⑧
F B(A)
(4) - ②
F(ν B(A), ν E , α)
Time point
S C
(2)-⑤
ν C
(3)-④
V C
(3)-⑪
F C
(4)-③
F(ν C, ν E , α)
groupÂtime point
S A Â C
(2)-⑥
ν A Â C
(3)-⑤
V A Â C
(3)-⑩
F A Â C
(4)-④
F(νν A Â C, ν E , α)
Residual error
S E
(2)-⑧
ν E
(3)-⑥
V E
(3)-⑫
Sum
S T
(2)-⑦
ν T
(3)-⑦
56
K. Kakazu et al.