Exam 13: Repeated-Measures and Two-Factor Analysis of Variance

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A two-factor analysis of variance produces an F-ratio for factor A that has df = 3,36.This analysis is comparing three different levels of factor A.

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The following data represent the means for each treatment condition in a two-factor experiment.Note that one mean is not given.What value for the missing mean would result in no AxB interaction? B1 B2 The following data represent the means for each treatment condition in a two-factor experiment.Note that one mean is not given.What value for the missing mean would result in no AxB interaction?  B1 B2

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The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with 2 levels of factor A,3 levels of factor B,and n = 8 participants in each treatment condition. The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with 2 levels of factor A,3 levels of factor B,and n = 8 participants in each treatment condition.     a.Fill in all missing values in the table.(Hint: start with the df column.) b. Compute η² (the percentage of variance accounted for) for each of the main effects and for the interaction. a.Fill in all missing values in the table.(Hint: start with the df column.) b. Compute η² (the percentage of variance accounted for) for each of the main effects and for the interaction.

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The repeated-measures ANOVA is a two-stage process.Which of the following accurately describes what happens during this process?

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For the following data,what is the value of SSB? B1 B2 For the following data,what is the value of SSB?  B1	 B2

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The following data were obtained from a two-factor independent-measures experiment with n = 5 participants in each treatment condition. The following data were obtained from a two-factor independent-measures experiment with n = 5 participants in each treatment condition.     a. State the hypotheses for each of the three separate tests included in the two-factor ANOVA. b. Calculate degrees of freedom and locate the critical region for each of the three tests. c.Calculate the three F-ratios. d.State a conclusion for each test. a. State the hypotheses for each of the three separate tests included in the two-factor ANOVA. b. Calculate degrees of freedom and locate the critical region for each of the three tests. c.Calculate the three F-ratios. d.State a conclusion for each test.

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If the mean and variance are computed for each sample in an independent-measures,two-factor experiment,which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA?

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The F-ratio for a repeated-measures ANOVA has df = 2,16.The research study compared 3 treatments with a sample of n = 8 participants.

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The following table shows the results of a repeated-measures ANOVA.Based on this table,what is the value for n²,the percentage of variance accounted for by the treatments? Source SS df MS Between 22 2 11 F=5.50 Within 58 21 Bet. Sub. 30 7 Error 28 14 2 Total 80 23

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A repeated-measures analysis of variance for a study comparing three treatment conditions with a sample of n = 10 participants,produces an F-ratio of F = 5.40.For this result,which of the following is the correct statistical decision?

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A researcher reports an F-ratio with df = 2,40 from a repeated-measures ANOVA.How many treatment conditions were compared in this experiment?

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For an experiment involving 2 levels of factor A and 3 levels of factor B with a sample of n = 5 in each treatment condition,what is the value for dfwᵢthᵢn?

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A two-factor study with two levels of factor A and three levels of factor B uses a separate group of n = 5 participants in each treatment condition.How many participants are needed for the entire study?

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Because the repeated-measures ANOVA removes variance caused by individual differences,it usually is more likely to detect a treatment effect than the independent-measures ANOVA is.

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The following table shows the results of a two-factor ANOVA.Based on this table,what is the value for  The following table shows the results of a two-factor ANOVA.Based on this table,what is the value for  ² for factor A?   \begin{array} { c c r r l }  \text { Source } & \text { SS } & \text { df } & \text { MS } & \\  \text { Between } & 36 & 3 & & \\ \text { A } & 12 & 1 & 12 & F = 4.00 \\ \text { B } & 3 & 1 & 3 & F = 1.00 \\ \text { AxB } & 21 & 1 & 21 & F = 7.00 \\ \text { Within } & 84 & 28 & 3 & \\ \text { Total } & 120 & 31 & & \end{array}² for factor A? Source SS df MS Between 36 3 A 12 1 12 F=4.00 B 3 1 3 F=1.00 AxB 21 1 21 F=7.00 Within 84 28 3 Total 120 31

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The analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measures ANOVA.

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In the second stage of the repeated-measures ANOVA,individual differences are removed from the denominator of the F-ratio.

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The results of a two-factor analysis of variance produce df = 2,36 for the F-ratio for factor A and df = 2,36 for the F-ratio for factor B.What are the df values for the AxB interaction?

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For a repeated-measures study,df between treatment= 3 and dfₜₒₜₐₗ = 27.This means that there were n = 7 participants in the study.

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A two-factor research study has 2 levels of factor A and three 3 of factor B with n = 8 participants in each treatment condition.For this study,what is the value for df between treatment?

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