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# Response Variable

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Response variable: personal ratings (how a subject likes or dislikes a particular concentration of a solution on a scale from 1 to 10).

Independent variable 1: concentrations of a solution (5 levels: 5%,10%, 20%, 40%, 80%).

Independent variable 2: two groups of subjects: Group A (sample size 50), Group B(sample size 60).

I need to find out if the response is significantly different between group A and group B when people rate the five different concentrations.

Is ANOVA appropriate here? If yes, what would be df for main effects, interaction, error?
And what test can I use to make pairwise comparisons?

##### Solution Summary

The solution discusses a response variable: personal ratings (how a subject likes or dislikes a particular concentration of a solution on a scale from 1 to 10).

Independent variable 1: concentrations of a solution (5 levels: 5%,10%, 20%, 40%, 80%).

Independent variable 2: two groups of subjects: Group A (sample size 50), Group B(sample size 60).

I need to find out if the response is significantly different between group A and group B when people rate the five different concentrations.

Is ANOVA appropriate here? If yes, what would be df for main effects, interaction, error?
And what test can I use to make pairwise comparisons?

##### Solution Preview

see attachment!

Solution:
You should use the two-way ANOVA test in this problem, since you have provide two factors (one is concentrations of a solution denoted by A, the other is groups of subjects denoted by B. Here I list some basic concept of two-way ANOVA and help you use them to fit this problem.

Stats: Two-Way ANOVA
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The two-way analysis of variance is an extension to the one-way analysis of variance. There are two independent variables (hence the name two-way).
Hypotheses
There are three sets of hypothesis with the two-way ANOVA.
The null hypotheses for each of the sets are given below.
1. The population means of the first factor are equal. This is like the one-way ANOVA for the row factor.
2. The population means of the second factor are equal. This is like the one-way ANOVA for the column factor (this can help you to find out if the response is significantly different between group A and group B when people rate the five different concentrations.)
Factors
The two independent variables in a two-way ANOVA are called factors. The idea is that there are two variables, factors, which affect the dependent ...

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