Exam 15: Introduction to the Analysis of Variance

Assuming that the sample sizes are equal, N = 12 and that k = 3, consider the following data: s 1 = 8.113, s 2 = 8.816, s 3 = 7.258 a. What is the value of s W 2 b. What is the value of ΣS within ?

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 doing post hoc testing between cognitive behavioral therapy and relaxation therapy, using the Scheffé test. Given the following values obtained from the ANOVA: , , , n ₁ = n ₂ = n ₃ = 5, k = 3, df _between = 2, df _within = 12, MS_within = 1.900, the value of SS _{between ( groups i and j)} = _________.

The analysis of variance is used to test for differences between sample means when k ≥ 2.

A dentist wants to know if the flavor of toothpaste affects how often children brush their teeth, and therefore the number of cavities. She makes up 3 flavors of toothpaste, cherry, bubble gum and spinach and observes the following numbers of cavities at a 6-month check-up: a. State H₁ . b. State H₀ . c. What is the value of MS_between ? d. What is the value of MS_within ? e. What is the value of F obt ? f. What is the value of F crit , a = 0.05? g. What do you conclude using a = 0.05?

The appropriate sampling distribution for the HSD test is the Studentized Range distribution.

Define a priori comparisons.

The following data were obtained from an experiment to test the effect of different levels of variable A on heart rate (beats per minute). a. What is the value of MS 1between ? b. What is the value of MS_within ? c. What is the value of F obt ? d. What is the value of F crit , a = 0.01? e. What do you conclude, using a = 0.01?

By doing multiple t tests when there are more than 2 experimental groups we increase the risk of making what kind of mistake?

Using , the estimated size of effect is _________.

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. = _________

If F F crit since the result cannot possibly be significant.

When there are only two groups, then t _obt² = F _obt

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 = .05, what do you conclude?

As the differences between the group means increases, _________.

A major limitation of a two group design is that _________.

The sampling distribution of F is a family of positively skewed curves each with a mean equal to 0.

Is it possible to have a significant result with k = 2 using the t test, but when reanalyzing the data using the F test obtain a nonsignificant result? Explain. (Assume a is the same, the design is the same and you don't make a calculation error.)

A researcher conducts an independent groups experiment and analyzes the data with the t test for independent groups. Assume t _obt = 2.23. Also assume this result is significant at the 0.05 level. Could this data have been analyzed with one-way, independent groups ANOVA? If so, what do you think the value of F _obt would be? Would the result be significant with the ANOVA analysis too? Explain.

What is the value of F _crit for an experiment with k = 3, n 1 = n 2 = n 3 = 10 subjects, and a = 0.01?

If = 46, = 50, = 92 and n 1 = n 2 = n 3 , what is the value of ?