Question 1

What does error represent in the analysis of variance?

Accepted Answer

In the context of Analysis of Variance (ANOVA), "error" represents the variation in the data that cannot be explained by the model factors being tested. ANOVA is a statistical method used to compare the means of three or more groups to see if at least one group mean is statistically different from the others. It partitions the total variation in the data into two components: the variation due to the factors being tested (between-group variation) and the variation due to random error (within-group variation).

The error term in ANOVA is associated with the within-group variation, which is the natural variability in the data that occurs within each group. This variability is not due to the experimental treatment or the factors being studied but is instead due to other, uncontrolled or random factors. These could include measurement errors, individual differences among subjects, or other sources of randomness that affect the outcome variable.

The error term is important because it serves as a baseline against which the treatment effects are compared. In ANOVA, the F-statistic is calculated by taking the ratio of the mean square due to the treatment (mean square between) to the mean square due to error (mean square within). A larger F-statistic suggests that the variation between group means is greater than would be expected by chance alone, indicating that the treatment or factor being tested has a significant effect.

In summary, the error in ANOVA represents the unexplained variability within groups that is not attributable to the factors being tested. It is a crucial component of the analysis as it provides a measure of the inherent variability in the data, which is used to determine whether the observed differences between group means are statistically significant.

Question 2

In order to increase the statistical power of her study, Judy decides that she will administer several treatments to each of her subjects. Judy is using __________ research in order to address her question of interest.

Accepted Answer

A)   nonintrinsically repeated measures
B)   intrinsically repeated measures
C)   simple effects
D)   analysis of variance A

Question 3

The F ratio will usually have a value close to 1.0 when the variation between treatment conditions is __________ the variation within the treatment conditions.

Accepted Answer

A)   smaller than
B)   similar to
C)   greater than
D)   eliminated by B

Question 4

In an analysis of variance comparing two groups, the resulting F value is equal to

Accepted Answer

A)   t
B)   Cohen's d
C)    t\sqrt { t }tc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
D)   t2

Question 5

Focused comparisons of more than two conditions are also known as

Accepted Answer

A)   contrasts.
B)   omnibus F tests.
C)   tests of simple effects.
D)   lambda coefficients.

Question 6

Computing a one-way ANOVA, Janet learns that there is a significant difference among the four groups in her study. To reveal precisely which group or groups differ from the rest, she must

Accepted Answer

A)   construct a BESD.
B)   do tests of simple effects.
C)   calculate the effect sizes and corresponding confidence intervals.
D)   compute another ANOVA.

Question 7

Why is the F test considered to be a test that analyzes variances rather than a test that analyzes means?

Accepted Answer

The answer of Why is the F test considered to...

Question 8

How is the "signal-to-noise" analogy applicable to understanding the logic behind F tests?

Accepted Answer

The answer of How is the "signal-to-noise" analogy applicable to...

Question 9

Why are effect sizes not calculated for F ratios that have more than 1 df in the numerator?

Accepted Answer

The answer of Why are effect sizes not calculated for...

Question 10

In John's experiment, there are three different conditions with five subjects per condition. What are the degrees of freedom within-conditions for this experiment?

Accepted Answer

A)   2
B)   14
C)   12
D)   15

Question 11

Variance is also known as

Accepted Answer

A)   the F ratio.
B)   the sum of squares.
C)   the mean square.
D)   the standard deviation.

Question 12

The __________ SS is defined as the sum of squares of deviations from the grand mean for all of the scores.

Accepted Answer

A)   total
B)   between-conditions
C)   within-conditions
D)   grand

Question 13

Designs that require participants to be measured more than once in order to answer the research question are referred to as __________ research.

Accepted Answer

A)   nonintrinsically repeated measures
B)   omnibus statistical procedures
C)   focused statistical procedures
D)   intrinsically repeated measures

Question 14

What is the difference between effect size rs, contrast rs, and alerting rs?

Accepted Answer

The answer of What is the difference between effect size...

Question 15

Error is considered to be the deviation of a score from the

Accepted Answer

A)   grand mean.
B)   mean of the condition.
C)   mean of the row.
D)   mean of the column.

Question 16

What does the "sum of squares" represent? How is this related to the "mean square"?

Accepted Answer

The answer of What does the "sum of squares" represent?...

Question 17

F is intrinsically a __________ test of significance.

Accepted Answer

A)   precise
B)   one-tailed
C)   two-tailed
D)   preferable

Question 18

The F ratio is determined by dividing the __________ mean square by the __________ mean square.

Accepted Answer

A)   total conditions; between-conditions
B)   within-conditions; between-conditions
C)   within-conditions; total conditions
D)   between-conditions; within-conditions

Question 19

A research design in which there are two levels for each of two factors is known as a(n) __________ design.

Accepted Answer

A)   one-way
B)   simple effects
C)   two-way
D)   interaction

Question 20

The __________ SS is defined as the sum of squares of deviations of the individual measurements from their condition means.

Accepted Answer

A)   error
B)   within-conditions
C)   total
D)   between-conditions

Exam 14: Comparisons of More Than Two Conditions