needed for statistical analyses), a calculation procedure and the results analyzed
using a branching-type ANOVA are shown. For example, the analytical procedure
for the no-effect scenario (0.1 mg/L of added nonylphenol) and the case in which
there were effects (1 mg/L of added nonylphenol) are indicated below. The process
of practically calculating the effects (in this case, the lack of effect) of the 0.1 mg/L
addition of nonylphenol to the system is described. The “addition system” in the
following procedures refers to the addition of 0.1 mg/L of nonylphenol. The formula
is calculated according to the expressions listed above.
By this method, it becomes the number of populations, i ¼ 1, 2 (1 represents the
control system and 2 represents the addition system), the number of experiments,
j ¼ 1, 2, 3, and the time mark, k ¼ 1, 2, 3, 14.
– Procedure (1)
(1) Mean of the control system 14 days after the addition in the first replicate
(i ¼ 1, j ¼ 1):
y 12 ∙ ¼ (0.46 + 0.42 + 0.48 + 0.63 + 0.65 + 0.53 + 0.47 + 0.43 +
0.38 + 0.33 + 0.3 + 0.36 + 0.4 + 0.48) Ä 14 ¼ 0.451
Mean of the control system 14 days after addition in the second replicate
(i ¼ 1, j ¼ 2):
y 12 ∙ ¼ (the sum in the control system 14 days after addition in the second
replicate) Ä 14 ¼ 0.509
As above, calculate in order,
y 13 ∙ (i ¼ 1, j ¼ 3) ¼ 0.594,
y 21 ∙ (i ¼ 2,
j ¼ 1) ¼ 0.410,
y 22 ∙ (i ¼ 2, j ¼ 2) ¼ 0.392,
y 23 ∙ (i ¼ 2, j ¼ 3) ¼ 0.491. (i ¼ 1
represents the control system, i ¼ 2 represents the addition system, and j
represents the repetitions.)
(2) The mean in each population, namely, the mean of the three replicates of the
control system data 14 days after addition:
y 1 ∙ ∙ ¼ (the sum of the first replicate of the control system data 14 days after
addition + the sum of the second replicate of the control system data 14 days
after addition + the sum of the third replicate of the control system data
14 days after addition) Ä (14 Â 3) ¼ 0.518‧‧‧.
y 2 ∙ ∙ ¼ (the sum of the first replicate of the addition system data 14 days
after addition + the sum of the second replicate of the addition system data
14 days after addition + the sum of the third replicate of the addition system
data 14 days after addition) Ä (14 Â 3) ¼ 0.431.
(3) Mean for each time and population:
Control system:
y 1 ∙ 1 ¼ (0.46 + 0.75 + 0.58) Ä 3 ¼ 0.597,
y 1 ∙ 2 ¼ (the sum of the second-day
data of the three replicates of the control system) Ä 3 ¼ 0.559, ‧‧‧‧‧‧,
y 1 ∙ 14
¼ (the sum of the 14th-day data of the three replicates of the control system)
Ä 3 ¼ 0.486.
Addition system:
y 2 ∙ 1 ¼ (0.47 + 0.44 + 0.40) Ä 3 ¼ 0.439,
y 2 ∙ 2 ¼ (the sum of the second-day
data of the three replicates of the addition system) Ä 3 ¼ 0.439,‧‧‧‧‧‧,
y 2 ∙ 14
58
K. Kakazu et al.
using a branching-type ANOVA are shown. For example, the analytical procedure
for the no-effect scenario (0.1 mg/L of added nonylphenol) and the case in which
there were effects (1 mg/L of added nonylphenol) are indicated below. The process
of practically calculating the effects (in this case, the lack of effect) of the 0.1 mg/L
addition of nonylphenol to the system is described. The “addition system” in the
following procedures refers to the addition of 0.1 mg/L of nonylphenol. The formula
is calculated according to the expressions listed above.
By this method, it becomes the number of populations, i ¼ 1, 2 (1 represents the
control system and 2 represents the addition system), the number of experiments,
j ¼ 1, 2, 3, and the time mark, k ¼ 1, 2, 3, 14.
– Procedure (1)
(1) Mean of the control system 14 days after the addition in the first replicate
(i ¼ 1, j ¼ 1):
y 12 ∙ ¼ (0.46 + 0.42 + 0.48 + 0.63 + 0.65 + 0.53 + 0.47 + 0.43 +
0.38 + 0.33 + 0.3 + 0.36 + 0.4 + 0.48) Ä 14 ¼ 0.451
Mean of the control system 14 days after addition in the second replicate
(i ¼ 1, j ¼ 2):
y 12 ∙ ¼ (the sum in the control system 14 days after addition in the second
replicate) Ä 14 ¼ 0.509
As above, calculate in order,
y 13 ∙ (i ¼ 1, j ¼ 3) ¼ 0.594,
y 21 ∙ (i ¼ 2,
j ¼ 1) ¼ 0.410,
y 22 ∙ (i ¼ 2, j ¼ 2) ¼ 0.392,
y 23 ∙ (i ¼ 2, j ¼ 3) ¼ 0.491. (i ¼ 1
represents the control system, i ¼ 2 represents the addition system, and j
represents the repetitions.)
(2) The mean in each population, namely, the mean of the three replicates of the
control system data 14 days after addition:
y 1 ∙ ∙ ¼ (the sum of the first replicate of the control system data 14 days after
addition + the sum of the second replicate of the control system data 14 days
after addition + the sum of the third replicate of the control system data
14 days after addition) Ä (14 Â 3) ¼ 0.518‧‧‧.
y 2 ∙ ∙ ¼ (the sum of the first replicate of the addition system data 14 days
after addition + the sum of the second replicate of the addition system data
14 days after addition + the sum of the third replicate of the addition system
data 14 days after addition) Ä (14 Â 3) ¼ 0.431.
(3) Mean for each time and population:
Control system:
y 1 ∙ 1 ¼ (0.46 + 0.75 + 0.58) Ä 3 ¼ 0.597,
y 1 ∙ 2 ¼ (the sum of the second-day
data of the three replicates of the control system) Ä 3 ¼ 0.559, ‧‧‧‧‧‧,
y 1 ∙ 14
¼ (the sum of the 14th-day data of the three replicates of the control system)
Ä 3 ¼ 0.486.
Addition system:
y 2 ∙ 1 ¼ (0.47 + 0.44 + 0.40) Ä 3 ¼ 0.439,
y 2 ∙ 2 ¼ (the sum of the second-day
data of the three replicates of the addition system) Ä 3 ¼ 0.439,‧‧‧‧‧‧,
y 2 ∙ 14
58
K. Kakazu et al.