Exam 15: Introduction to the Analysis of Variance

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Define Q crit.

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The F distribution has no negative values.

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For this problem consider the following information from an experiment to compare differences between the length of time a house paint lasts before it begins to fade. The number of subjects are the same in each group. For this problem consider the following information from an experiment to compare differences between the length of time a house paint lasts before it begins to fade. The number of subjects are the same in each group.   , , , Using the HSD test, the value of Q <sub>obt</sub> for the testing the difference between and is _________. , , , Using the HSD test, the value of Q obt for the testing the difference between and is _________.

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Define FScheffé

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If F

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Consider the following data from an independent groups design: a. Is it appropriate to use parametric ANOVA to analyze these results? Why or why not?

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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 the Scheff test with a = 0.05, F <sub>crit</sub> = _________. Using the Scheff test with a = 0.05, F crit = _________.

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A posteriori or post hoc comparisons are the same thing.

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If SS total = 106 and SS within = 24, what is the value of SS between ?

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Give two conditions that should be met before doing a priori comparisons that are not independent.

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The F test for k = 2 is more powerful than the t test.

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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.   The value of F <sub>Scheffé</sub> is _________. The value of F Scheffé is _________.

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Define between-groups variance estimate ( MSbetween ).

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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.   Assume you are comparing cognitive/behavioral therapy with relaxation therapy, using the HSD test. The obtained value of the appropriate statistic is _________. Assume you are comparing cognitive/behavioral therapy with relaxation therapy, using the HSD test. The obtained value of the appropriate statistic is _________.

(Multiple Choice)
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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.   F <sub>obt</sub> = _________. F obt = _________.

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If s 12 = 9, s 22 = 6, s 32 = 8, and n 1 ≠ n 2 ≠ n 3 , then MSwithin equals _________.

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The within-groups variability increases necessarily as the between-groups variability increases.

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List three variables, not including beta, that affect the power of the ANOVA and state what increases in each do to the power of the ANOVA.

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Both the HSD and the Scheffé test use the Studentized Range distributions.

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When doing planned comparisons, the denominator of the t equation changes for each pair of means compared.

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