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Chapter 17 Questions
Complete the following questions. The questions may include pictures or graphics to illustrate or aid in solving the problem. You can check your answer by clicking View Answer. If the question is unclear, confusing, or if you need further clarification, send me an email.
1. 2-Way ANOVA Activity
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2. Recalling the data we analyzed in chapter 16, now let's imagine that not only did subjects receive one of the three anger-inducing treatments, but that these treatments were also administered in two different contexts, before either a statistics final or blind date. Given the following data, perform a two-way analysis of variance. Complete an ANOVA summary table.
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3. Compare the ANOVA summary table for the above two-way analysis with the ANOVA summary table from chapter 16. How did re-envisioning the way the data were modeled (i.e., adding the second factor) affect the ANOVA results?
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In the two-way model, we have more sources of variability which we can explain (i.e., the B and AXB factors). This decreases the variability we cannot explain (i.e.,SSwithin). This increases the likelihood of rejecting the null hypotheses for all three tests in the two-way model.
4. Using the data above, graph the interaction of the two factors. What does this graph tell you about the relationship between anger-inducing technique and context?
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It can be seen that, for the subjects in the final condition (B1), the recollection (A1) and pain (A3) conditions were particularly effective in inducing anger, whereas the insults condition (A2) was much less effective. For the subjects in the date condition (B2), the pain condition (A3) seemed to be most effective in inducing anger (though post-hoc tests would be necessary to determine if this difference was statistically significant). Overall, it can be seen that the pain condition (A3) was most effective in inducing anger, followed by the recollection (A1) and then the insults (A2) conditions. There does not appear to be a difference between the two context conditions (B1 and B2).
5. Explain the formula for the interaction sum of squares. How does the formula itself explain what we are calculating when we are calculating this value?
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The formula for computing the interaction sum of squares, 
, shows that the variability measured here is between the AXB cells after controlling for the particular effects of the levels of A and of B comprising each AXB cell. In other words, this is variability due to the combination of treatments comprising each AXB cell, and not the variability due to A or B. This is accomplished in the formula by subtracting out the A and B means of each AXB cell from the AXB mean.
, shows that the variability measured here is between the AXB cells after controlling for the particular effects of the levels of A and of B comprising each AXB cell. In other words, this is variability due to the combination of treatments comprising each AXB cell, and not the variability due to A or B. This is accomplished in the formula by subtracting out the A and B means of each AXB cell from the AXB mean.