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# Two-Way ANOVA with Replication

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The effects of developer strength (factor A) and development time (factorB) on the density of photographic plate film were being studied. Two strengths and two development times were used, and four replicates in each of the four cells were used, and four replicates in each of the four cells were evaluated. The results ( with larger being best) are stored in the table below.

At the 0.05 level of significance:
a. Is there an interaction between developer strength and development tie?

b. Is there an effect due to developer strength?

c. Is There an effect due to development time?

d. Plot the mean density for eachh developer strength for each development time.

e. What can you conclude about the effect of developer strength and development time on density?

Strength Time10 Time14
1 0 1
1 5 4
1 2 3
1 4 2
2 4 6
2 7 7
2 6 8
2 5 7

https://brainmass.com/statistics/parametric-tests/two-way-anova-replication-568194

#### Solution Preview

I have answered your questions in the attached MS Word doc, with supporting results in the attached Excel file. I hope that this all helps you understand your material better. Good luck.

The effects of developer strength (factor A) and development time (factorB)
on the density of photographic plate film were being studied. Two strengths and two
development times were used, and four replicates in each of the four cells were used,
and four replicates in each of the four cells were evaluated. The results ( with larger
beaing best) are stored in the table below.

At the 0.05 level of significance:
a. Is there an interaction between developer strength and development tie?

b. Is there an effect due to developer strength?

c. Is There an effect due to development time?

d. Plot the mean density for eachh developer strength for each development ...

#### Solution Summary

The Interaction Effect and any Main Effects of the Developer Strength (2 levels) and Development Time (2 levels) on the resulting Density of Photographic Plate Film are investigated in a Two-Way ANOVA with interaction and a graph of means.

\$2.19

## Two Way ANOVA and Replication

When running an analysis of variance (ANOVA): two-factor with replication (two-way test), you get a p-value for the interaction effect, indicating whether it is statistically significant. If it is significant, you should not try to interpret the main effects at all. Explain why this is the case, giving an example to illustrate your explanation.

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