Exam 9: Introduction to the Analysis of Variance

The results of an analysis of variance would be reported in a research article as

A crucial feature of planned comparisons is that they are

Conducting an analysis of variance involves comparing __________ different estimates of the population variance.(Give a number.)

Because of the assumption that the population variances are equal,when conducting an analysis of variance

Ann conducts a study,and finds that the estimated population variances for the groups are 12.8,16.3,15.1,and 19.9.What is the within-groups estimate of the population variance?

The null hypothesis of an analysis of variance is that the __________ means are equal.

If a research article presented the results of an analysis of variance as,"F (2,38)= 3.60,p < .05," then how many groups were there in the study?

The most serious violation of an assumption for an analysis of variance occurs when

Prior to eating breakfast,25 participants were randomly assigned to eat a large meal,25 to eat a small meal,and 25 to eat nothing.Immediately following the meal,all participants took a memory test.The means and estimated population variances for the three groups on the memory test were: Large: M = 2.1,S² = 1.0; Small: M = 2.5,S² = 1.2; Nothing: M = 2.9,S² = 0.8.Using the .05 significance level,does amount of breakfast eaten affect memory? 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 Large Meal versus Small Meal (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.)

A priori comparisons are also known as __________.

If a researcher conducted six t tests,each at the .05 significance level,the chance that at least one test would reach significance would be about __________,even if the null hypothesis were true.(Give a number.)

When conducting an analysis of variance,one assumption is that each population distribution is __________.

Advanced topic: Each score's deviation from the grand mean represents

A planned comparison comparing two means involves figuring an F ratio in which the denominator

The power of an analysis of variance can be increased by all of the following EXCEPT

R² is never greater than __________.(Give a number.)

Given four populations with equal means and equal variances,an F distribution for situations with samples of 10 scores each could be created by

The cutoff F used to evaluate the significance of the Scheffé test for any particular comparison between two group means is

An analysis of variance differs from a t test for independent means in that an analysis of variance

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