Exam 15: Introduction to the Analysis of Variance

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In the HSD test where k = 3 if the lowest and highest pair comparison is nonsignificant, none of the other comparisons will be significant either.

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Explain how the Q distributions were developed. How does this compare to the t distributions?

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The total variance of a set of data can be completely partitioned into the between-groups variance and the within-groups variance.

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The one-way ANOVA assumes s 12 = s 22 = s 32 = s k 2 .

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A clinical psychologist is interested in comparing the effectiveness of short term relaxation and cognitive-behavioral therapy in treating mild depression. An experiment is conducted in which 15 patients with mild depression are randomly selected and assigned 5 each to a relaxation therapy group, a cognitive/behavioral therapy group, and an attention placebo group. Therapy is administered until the patient is judged no longer depressed or until 10 treatment sessions have elapsed. The following data is obtained. Scores are the number of sessions for each patient. A clinical psychologist is interested in comparing the effectiveness of short term relaxation and cognitive-behavioral therapy in treating mild depression. An experiment is conducted in which 15 patients with mild depression are randomly selected and assigned 5 each to a relaxation therapy group, a cognitive/behavioral therapy group, and an attention placebo group. Therapy is administered until the patient is judged no longer depressed or until 10 treatment sessions have elapsed. The following data is obtained. Scores are the number of sessions for each patient.   Using the Scheffé test with a = 0.05, F <sub>crit</sub> = _________. Using the Scheffé test with a = 0.05, F crit = _________.

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MSwithin is sensitive to the effects of the independent variable.

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The value used in the Scheffé test to evaluate is _________.

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An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory. An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory.   F <sub>obt</sub> = _________. F obt = _________.

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The null hypothesis in the analysis of variance states that µ 1 = µ 2 = µ 3 = u k

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An ANOVA can only be used when n 1 = n 2 = . . . = n k .

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The alternative hypothesis evaluated by F obt in the one-way ANOVA states that _________.

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An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory. An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory.   Using a = 0.05, F <sub>crit</sub> = _________. Using a = 0.05, F crit = _________.

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What is the value of ΣStotal if ΣSbetween = 236 and ΣSwithin = 54?

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An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory. An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory.   Assume you are doing planned comparisons evaluating drug levels 2 and 3 using a = 0.05 and H 1 is nondirectional. What is your conclusion? Assume you are doing planned comparisons evaluating drug levels 2 and 3 using a = 0.05 and H 1 is nondirectional. What is your conclusion?

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The Scheffé test controls for dong multiple comparisons by using F crit from the ANOVA

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Variance ratio is the statistic underlying the F distribution.

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A value of - 1.0 for F obt is never possible if the calculations are done correctly.

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It is possible to have an overall F that is significant and have all the a priori comparisons be nonsignificant.

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Using 2, what is the estimated size of effect? Using <sup>2</sup>, what is the estimated size of effect?

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A clinical psychologist is interested in comparing the effectiveness of short term relaxation and cognitive-behavioral therapy in treating mild depression. An experiment is conducted in which 15 patients with mild depression are randomly selected and assigned 5 each to a relaxation therapy group, a cognitive/behavioral therapy group, and an attention placebo group. Therapy is administered until the patient is judged no longer depressed or until 10 treatment sessions have elapsed. The following data is obtained. Scores are the number of sessions for each patient. A clinical psychologist is interested in comparing the effectiveness of short term relaxation and cognitive-behavioral therapy in treating mild depression. An experiment is conducted in which 15 patients with mild depression are randomly selected and assigned 5 each to a relaxation therapy group, a cognitive/behavioral therapy group, and an attention placebo group. Therapy is administered until the patient is judged no longer depressed or until 10 treatment sessions have elapsed. The following data is obtained. Scores are the number of sessions for each patient.   Estimate the size of the effect. ç <sup>2 </sup>= _________. Estimate the size of the effect. ç 2 = _________.

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