An engineer wants to assess the relationship between sintering time and the compressive strength of three different metals. The engineer measures the compressive strength of five specimens of each metal type at each sintering time: 100 minutes, 150 minutes, and 200 minutes.

To test the statistical significance of the two factors, and the interaction between them, the engineer uses two-way ANOVA.

The p-values for the type of metal term and the interaction term are less than 0.05, which indicates that both terms have a statistically significant relationship with strength.

There is sufficient evidence to conclude that the type of metal is related to strength. The means table indicates that strength is highest (21.7778) with metal type 2.

However, the significant interaction indicates that the relationship between metal type and strength depends on the value of sinter time. Consequently, the engineer cannot interpret the main effects without considering the interaction effects.

If the engineer uses MetalType 2, SinterTime150 is associated with the highest mean strength (23.6667). However, if the engineer uses MetalType 1, SinterTime 100 is associated with the highest mean strength (21.3333).

To create a graph of the effects that are estimated by a two-way ANOVA model, use a factorial plot.

Factor Information

Factor

Levels

Values

SinterTime

3

100, 150, 200

MetalType

3

1, 2, 3

Analysis of Variance

Source

DF

Adj SS

Adj MS

F-Value

P-Value

SinterTime

2

8.222

4.1111

1.71

0.2094

MetalType

2

20.222

10.1111

4.20

0.0318

SinterTime*MetalType

4

46.222

11.5556

4.80

0.0082

Error

18

43.333

2.4074

Total

26

118.000

Model Summary

S

R-sq

R-sq(adj)

R-sq(pred)

1.55158

63.28%

46.96%

17.37%

Means

Term

Fitted Mean

SE Mean

SinterTime

100

20.3333

0.5172

150

21.4444

0.5172

200

20.2222

0.5172

MetalType

1

19.6667

0.5172

2

21.7778

0.5172

3

20.5556

0.5172

SinterTime*MetalType

100 1

21.3333

0.8958

100 2

20.3333

0.8958

100 3

19.3333

0.8958

150 1

20.3333

0.8958

150 2

23.6667

0.8958

150 3

20.3333

0.8958

200 1

17.3333

0.8958

200 2

21.3333

0.8958

200 3

22.0000

0.8958

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