Look at the scenario that is presented below and select an appropriate experimen
ID: 2929609 • Letter: L
Question
Look at the scenario that is presented below and select an appropriate experimental design. Use the data to provide a sample ANOVA for your experimental design.
Position (Pj)
Depth from Top of Pool
0 ft
5 ft
10 ft
1
4.90
4.90
4.94
4.91
4.89
4.80
2
4.90
4.89
4.75
4.91
4.89
4.83
3
4.94
4.91
4.86
4.90
4.91
4.83
4
4.93
4.94
4.83
4.91
4.90
4.89
5
4.90
4.94
4.83
4.87
4.90
4.86
You want to determine the effect of both depth and position in a pool on the concentration of chlorine in parts per million. Concentrations are measured at three depths from the surface of the pool (0 ft, 5 ft, and 10 ft). At each depth measurements are taken at five different lateral positions in the pool.
Position (Pj)
Depth from Top of Pool
0 ft
5 ft
10 ft
1
4.90
4.90
4.94
4.91
4.89
4.80
2
4.90
4.89
4.75
4.91
4.89
4.83
3
4.94
4.91
4.86
4.90
4.91
4.83
4
4.93
4.94
4.83
4.91
4.90
4.89
5
4.90
4.94
4.83
4.87
4.90
4.86
Explanation / Answer
Answer:
Look at the scenario that is presented below and select an appropriate experimental design. Use the data to provide a sample ANOVA for your experimental design.
You want to determine the effect of both depth and position in a pool on the concentration of chlorine in parts per million. Concentrations are measured at three depths from the surface of the pool (0 ft, 5 ft, and 10 ft). At each depth measurements are taken at five different lateral positions in the pool.
Two factor ANOVA
Factor 2
Means:
0ft
5ft
10ft
P1
4.905
4.895
4.870
4.890
P2
4.905
4.890
4.790
4.862
Factor 1
P3
4.920
4.910
4.845
4.892
P4
4.920
4.920
4.860
4.900
P5
4.885
4.920
4.845
4.883
4.907
4.907
4.842
4.885
2
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1 Position
0.0050
4
0.00126
1.00
.4374
Factor 2 depth
0.0282
2
0.01408
11.18
.0011
Interaction
0.0058
8
0.00073
0.58
.7802
Error
0.0189
15
0.00126
Total
0.0579
29
Post hoc analysis
p-values for pairwise t-tests for Factor 2
10ft
0ft
5ft
4.842
4.907
4.907
10ft
4.842
0ft
4.907
.0010
5ft
4.907
.0010
1.0000
Tukey simultaneous comparison t-values (d.f. = 15)
10ft
0ft
5ft
4.842
4.907
4.907
10ft
4.842
0ft
4.907
4.09
5ft
4.907
4.09
0.00
critical values for experimentwise error rate:
0.05
2.60
0.01
3.42
To test effect of position, calculated F=1.0, P=0.4374 which is > 0.05 level. Effect of position is not significant.
To test effect of depth, calculated F=11.18, P=0.0011which is < 0.05 level. Effect of depth is significant.
To test effect of interaction, calculated F=0.58, P=0.7802 which is > 0.05 level. Effect of interaction is not significant.
Two factor ANOVA
Factor 2
Means:
0ft
5ft
10ft
P1
4.905
4.895
4.870
4.890
P2
4.905
4.890
4.790
4.862
Factor 1
P3
4.920
4.910
4.845
4.892
P4
4.920
4.920
4.860
4.900
P5
4.885
4.920
4.845
4.883
4.907
4.907
4.842
4.885
2
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1 Position
0.0050
4
0.00126
1.00
.4374
Factor 2 depth
0.0282
2
0.01408
11.18
.0011
Interaction
0.0058
8
0.00073
0.58
.7802
Error
0.0189
15
0.00126
Total
0.0579
29
Post hoc analysis
p-values for pairwise t-tests for Factor 2
10ft
0ft
5ft
4.842
4.907
4.907
10ft
4.842
0ft
4.907
.0010
5ft
4.907
.0010
1.0000
Tukey simultaneous comparison t-values (d.f. = 15)
10ft
0ft
5ft
4.842
4.907
4.907
10ft
4.842
0ft
4.907
4.09
5ft
4.907
4.09
0.00
critical values for experimentwise error rate:
0.05
2.60
0.01
3.42
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