Exam 9: Introduction to the Analysis of Variance

Advanced topic: The sum of the squared deviations of each score from the mean of its group plus the sum of the squared deviations of each score's group's mean from the grand mean equals

Forty-five participants (15 per group)were randomly assigned to do a series of math tasks while listening to soft-gentle music,while listening to loud-intense music,or while in silence.The means and estimated population variances for the three groups were: Soft-Gentle: M = 37,S² = 28; Loud-Intense: M = 33,S² = 25; Silence: M = 41,S² = 22.Using the .05 significance level,is there a difference in performance on this kind of math task under these three conditions? a.Use the five steps of hypothesis testing. b.Sketch the distributions involved. c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large. d.Conduct a planned contrast for the Soft-Gentle versus Silence conditions (using the .05 level). e.Conduct Scheffé's test for the groups in (d)and indicate the F cutoff,the F you would use for the comparison,and the hypothesis-testing decision (reject or do not reject). f.Explain the logic of what you did to a person who is familiar with the t test for independent means,but who knows nothing about the analysis of variance.(Be sure your explanation includes the logic of comparing within-groups to between-groups population variance estimates,the logic of how each of these is figured,the F distribution,and the F table.)

The correct order of post hoc comparison procedures following an analysis of variance from the least conservative to the most conservative is

Advanced topic: A health psychologist recorded the number of close inter-personal attachments of 45-year-olds who were in excellent,fair,or poor health.People in the Excellent Health group had 4,3,2,and 3 close attachments; people in the Fair Health group had 3,5,and 8 close attachments; and people in the Poor Health group had 3,1,0,and 2 close attachments.Using the .05 level,is there a significant difference in number of attachments among 45-year-olds having different levels of health? a.Carry out the five steps of hypothesis testing and make a complete analysis of variance table. b.Sketch the distributions involved. c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large. d.Explain the logic of what you did to a person who is familiar with the analysis of variance using the approach in which you figure the variance for each group,but who has not learned anything about the structural model approach.(Be sure to explain dividing the overall deviation from the grand mean,the logic of the different parts of the analysis of variance table,and how all this relates to the logic of the approach in which you figure the variance for each group.)

According to Cohen's conventions,an R² of 14% (.14)is considered a(n)__________ effect size.

Advanced topic: One disadvantage of using the structural model to understand the analysis of variance (as opposed to the method which involves averaging the variances of each group)is that

Advanced topic: A sleep deprivation researcher randomly assigned 18 participants to one of three conditions: 12 hours without sleep,24 hours without sleep,or 36 hours without sleep.Following the manipulation,participants completed a measure of negative mood.Mood scores for each group are listed below.Using the .05 level,was there a significant difference in negative mood depending on length of sleep deprivation? a.Carry out the five steps of hypothesis testing and make a complete analysis of variance table. b.Sketch the distributions involved. c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large. d.Explain the logic of what you did to a person who is familiar with the analysis of variance using the approach in which you figure the variance for each group,but who has not learned anything about the structural model approach.(Be sure to explain dividing the overall deviation from the grand mean,the logic of the different parts of the analysis of variance table,and how all this relates to the logic of the approach in which you figure the variance for each group.)

In a one-way analysis of variance,if the null hypothesis is true,then

In a one-way analysis of variance,"(S²₁ + S²₂ + … + S²_last)/ N_groups" is the formula for __________.(Do not give a symbol.)

In a planned comparison of two particular means,a between-groups population variance estimate,based on the two groups being compared,is divided by a within-groups population variance estimate,based on __________.

If a research article reports that "The mean performance scores for the Normal Sleep,Reduced Sleep,and No Sleep groups were 18.0,16.6,and 15.6,respectively,F (2,36)= 2.95,p < .05," the most accurate conclusion is that

Advanced topic: If you were to use a "signal-noise" analogy to explain the structural model,you could say that "signal" represents

The formula "Σ(M-GM)²/df_Between" is used to compute

A planned comparison involving more than two means,such as the average of two groups versus a third,is called a(n)__________ comparison.

Advanced topic: In a test of recall,three groups of participants were shown a list of words on a screen for a very brief time and later were asked to recall as many of the words as possible.Five participants viewed the list while the experimenter read related words aloud and were able to recall 5,5,5,3,and 6 words from the list.Three participants viewed the list while the experimenter read unrelated words aloud and were able to recall 6,3,and 4 words.The final three participants viewed the list under quiet conditions and were able to recall 7,8,and 3 words.Using the .05 level,was there a significant difference among the three conditions in number of words recalled? a.Carry out the five steps of hypothesis testing and make a complete analysis of variance table. b.Sketch the distributions involved. c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large. d.Explain the logic of what you did to a person who is familiar with the analysis of variance using the approach in which you figure the variance for each group,but who has not learned anything about the structural model approach.(Be sure to explain dividing the overall deviation from the grand mean,the logic of the different parts of the analysis of variance table,and how all this relates to the logic of the approach in which you figure the variance for each group.)

Joe conducts an analysis of variance.If he rejected the null hypothesis,the most likely F value is

An experimenter "fishing for results" once a study is completed is conducting __________.

In an analysis of variance,if the null hypothesis is true,then

based on the following tables. -Advanced topic: df_Within = __________.

In an analysis of variance,if the within-groups variance estimate is about the same as the between-groups variance estimate,then