Exam 9: Introduction to the Analysis of Variance

The Scheffé test requires first figuring the F for the comparison as if a planned comparison is being conducting,then adjusting the F from that comparison by

The F ratio was invented by __________.

based on the following tables. -Advanced topic: Complete the ANOVA summary table,replacing the letters (a)to (i)with the appropriate number.

If a research article reports "F (2,36)= 2.95,p < .05," you know that

In an analysis of variance,you reject the null hypothesis when the F ratio is

A sports psychologist gave a questionnaire about healthy eating habits to randomly selected professional athletes.The results are displayed below.Using the .05 significance level,is there a difference in healthy eating habits among professionals in the three sports? 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 Baseball versus Football players (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.)

In an analysis of variance with a between-groups population variance estimate of 30 and a within-groups estimate of 25,the F ratio is

Rosnow and Rosenthal propose that analyses of variance can often be replaced with __________.

Advanced topic: Thinking of each score in an analysis of variance in terms of its overall deviation being divided into two parts is the core idea of __________.

If a research article does not report the variance estimates,R²

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

To study the effectiveness of possible treatments for insomnia,a sleep researcher conducted a study in which four participants were instructed to count sheep (the Sheep Condition),four were told to concentrate on their breathing (the Breathing Condition),and four were not given any special instructions (the Control Condition).The average number of minutes taken for participants to fall asleep over the next seven days were 39,33,42,and 38 minutes for the Sheep condition; 33,25,31,and 27 minutes for the Breathing condition; and 44,41,38,and 41 for the Control condition.Using the .01 significance level,did the different techniques have different effects? 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.Figure a planned contrast between the means for those in the Sheep Condition versus those in the Breathing Condition using the .05 significance 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.)

In an analysis of variance,if the null hypothesis is false,then the __________- groups estimate of the population variance is much smaller than the __________- groups estimate.

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

In an analysis of variance,if the null hypothesis is false,then the __________- groups estimate of the population variance is larger than if the null hypothesis were true.

In the formula,Σ(M-GM)²/df_Between,"GM" is the

Advanced topic: One advantage 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

based on the following tables. -Advanced topic: SS_Between = __________.(Give a number.)

In general,using the Bonferroni procedure as a post-hoc comparison procedure means that

There are four determinants of the power of a one-way analysis of variance: effect size,sample size,significance level,and the __________.