Four different formulations of an industrial glue are being tested. Each of the different formulations were randomly applied to joint parts of five test specimen and the tensile strength of the glue when it is applied to each test specimen is recorded. However, the tensile strength is also related to the application thickness. The data on the strength (in lbs) and thickness (in 0.01 inches) are shown in the following table. Identify the treatment (specify levels), experimental units, concomitant variable, and response variable.

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Four different formulations of an industrial glue are being tested. Each of the different formulations were randomly applied to joint parts of five test specimen and the tensile strength of the glue when it is applied to each test specimen is recorded. However, the tensile strength is also related to the application thickness. The data on the strength (in lbs) and thickness (in 0.01 inches) are shown in the following table. Identify the treatment (specify levels), experimental units, concomitant variable, and response variable.
Formulation
A
A
A
A
A
B
B
B
B
B
Strength
46.5
45.9
49.8
46.1
44.3
48.7
49.0
50.1
48.5
45.5
Thickness
13
14
12
12
14
12
10
11
12
14
Formulation
C
C
C
C
C
D
D
D
D
D
Strength
46.3
47.1
48.9
48.2
50.3
44.7
43.0
51.0
48.1
48.6
Thickness
15
14
11
11
10
16
15
10
12
11
Transcribed Image Text:Formulation A A A A A B B B B B Strength 46.5 45.9 49.8 46.1 44.3 48.7 49.0 50.1 48.5 45.5 Thickness 13 14 12 12 14 12 10 11 12 14 Formulation C C C C C D D D D D Strength 46.3 47.1 48.9 48.2 50.3 44.7 43.0 51.0 48.1 48.6 Thickness 15 14 11 11 10 16 15 10 12 11
jamovi outputs:
ANOVA
ANOVA Thickness
Formulation
Residuals
ANOVA
ANOVA Strength
Formulation
Residuals
ANCOVA
Sum of Squares
4.55
Formulation
Thickness
Residuals
ANCOVA Strength
58.40
Sum of Squares
11.5
78.7
Sum of Squares
1.90
58.24
20.50
df
3
16
df
3
16
df
3
1
15
Mean Square
1.52
3.65
Mean Square
3.85
4.92
Mean Square
0.633
58.240
1.367
0.416
F
0.782
F
0.463
42.615
р
0.744
р
0.521
[3]
р
0.712
<.001
[3]
Transcribed Image Text:jamovi outputs: ANOVA ANOVA Thickness Formulation Residuals ANOVA ANOVA Strength Formulation Residuals ANCOVA Sum of Squares 4.55 Formulation Thickness Residuals ANCOVA Strength 58.40 Sum of Squares 11.5 78.7 Sum of Squares 1.90 58.24 20.50 df 3 16 df 3 16 df 3 1 15 Mean Square 1.52 3.65 Mean Square 3.85 4.92 Mean Square 0.633 58.240 1.367 0.416 F 0.782 F 0.463 42.615 р 0.744 р 0.521 [3] р 0.712 <.001 [3]
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