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Mathematics
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Behavioral Sciences STAT
Quiz 12: Understanding the Two-Way Analysis of Variance
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Question 21
Short Answer
How many participants would be required for a complete factorial 4 × 5 between-subjects design with three observations per cell?
Question 22
Essay
For Factor A, you have timed the rate at which three groups of participants can solve puzzles under three conditions of noise: high, medium, and low.In addition, for Factor B the participants have received either no caffeine or a high level of caffeine equivalent to 4 cups of coffee).What kind of design is this called?
Question 23
Essay
Professor Blake has completed an experiment where all subjects were asked to give assessments of three different hypothetical individuals as a function of their age.Prior to making these assessments, half of all subjects were randomly assigned to be first presented with a film designed to promote the challenges of aging whereas the other half purposely did not view this film.What type of research design would this study be and why?
Question 24
Essay
For a two-way ANOVA, state the null and alternative hypotheses for Factor B that has 4 levels.
Question 25
Essay
When you are comparing pairs of cell means for the Tukey HSD Test, which comparisons are confounded and unconfounded?
Question 26
Short Answer
In a 3 x 4 design with four participants per cell, what degrees of freedom would you use in looking up the F
ait
for the interaction effect?
Question 27
Essay
Suppose you have done a two-way ANOVA where the interaction was not significant.How should you next proceed?
Question 28
Essay
When performing the Tukey HSD Test on an interaction, why must we use an adjusted value of k ?
Question 29
Essay
The following table contains the cell means for a study involving two types of dashboard displays and three types of drive seat designs.
Bench Type Seat
Bucket Type Seat
Captain’s Style Seat
Dashboard Display A
20
8
32
Dashboard Display B
6
24
13
\begin{array}{|l|r|r|r}\hline & \text { Bench Type Seat } & \text { Bucket Type Seat } & \text { Captain's Style Seat } \\\hline \text { Dashboard Display A } & 20 & 8 & 32 \\\hline \text { Dashboard Display B } & 6 & 24 & 13 \\\hline\end{array}
Dashboard Display A
Dashboard Display B
Bench Type Seat
20
6
Bucket Type Seat
8
24
Captain’s Style Seat
32
13
a.Graph these means. b.Does this graph indicate the presence of an interaction or not? Explain.
Question 30
Essay
A researcher has done a pilot study where she recruited a small sample of men and women and then assessed their reaction time to a certain stimuli measured in seconds and listed below in the table) after either playing music or not.Calculate and state the main effects for the two factors. Factor A: Playing Music?
Factor B: Gender
Question 31
Essay
In a 2 × 2 design with 40 participants equally distributed across the conditions: a.How many levels of Factor A are there? b.How many participants are in Factor A?
Question 32
Essay
Suppose you perform a 2 x 3 ANOVA on 18 participants equally divided across all cells.Your F
abt
for Factor A is 9.15.This is a significant F
abt
.What is the correct way to report this finding?