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# Two-Way ANOVA with Replication

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A student team in a business statistics course performed a factorial experiment to investigate the time required for pain-relief tablets to dissolver in a glass of water. The two factors of interest were brand name (Equate, Kroger, or Alka-Seltzer) and temperature of the water (hot or cold). The experiment consisted of four replicates for each of the six factor combinations. The following data (stored in the Data below show the time a tablet took to dissolve ( in seconds) for the 24 tablets used in the experiment:

At the 0.05 level of significance,
a. Is there an interaction between brand of pain reliever and water temperature?

b. Is there an effect due to brand?

c. Is there an effect due to water temperature?

d. Plot the mean dissolving time for each brand for each water temperature.

e. What is the results of (a) through (d).

Temperature Equate Kroger Alka-Seltzer
Cold 85.87 75.98 100.11
Cold 78.69 87.66 99.65
Cold 76.42 85.71 100.83
Cold 74.43 86.31 94.16
Hot 21.53 24.10 23.80
Hot 26.26 25.83 21.29
Hot 24.95 26.32 20.82
Hot 21.52 22.91 23.21

https://brainmass.com/statistics/parametric-tests/two-way-anova-replication-568201

#### Solution Summary

The effects of the brand of a pain reliever tablet and the water temperature on the amount of time required for the tablet to dissolve completely are investigated. The presence of interaction (it IS present) between these two factors in a two-way factorial ANOVA design is studied and the effect that the presence of interaction has on studying the main effects of the two factors separately is discussed. A graph of the mean "Dissolve Times" is included.

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## 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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