One-Way ANOVA

Question 1

What is the aim of a One-Way ANOVA?

Answer 1

To partition variance to see if the variance due to experimental manipulation is proportionally larger than the rest of the variance (error)

Question 2

What is variance?

Answer 2

The spread of scores around the mean

Question 3

What is error variance?

Answer 3

Random variance AND variance due to unmeasured influences

Question 4

What is treatment variance?

Answer 4

Systematic differences due to the IV

Question 5

How is total variance partitioned in a one-way ANOVA

Answer 5

Into between-groups variance and within-groups variance

Question 6

What is between-groups variance?

Answer 6

Systematic variance due to membership in difference treatment groups

Question 7

What is within-groups variance?

Answer 7

Error variance (averaged from both samples; pooled)

Question 8

What does between-groups variance measure?

Answer 8

The distribution of group means around the grand mean

Question 9

What does within-groups variance measure?

Answer 9

The distribution of individual DV scores around the group mean

Question 10

What is the null hypothesis for a one-way ANOVA?

Answer 10

µj = µ.

Question 11

What is the alternate hypothesis for a one-way ANOVA?

Answer 11

µj ≠ µ.
for at least one group

Question 12

Conceptually, what is the formula for between-groups variance?

Answer 12

The squared sum of the differences between groups means and the grand mean, considering the number of observations in each group

Question 13

Conceptually, what is in the formula for within-groups variance?

Answer 13

The squared sum of the differences between individual scores and the group mean

Question 14

What is the test statistic for one-way ANOVA and how is it calculated

Answer 14

F-ratio = MStreat/MSerror

Question 15

When will the F-ratio be more than 1 (significant)?

Answer 15

When MStreat is bigger than MSerror
When the between-groups variance is bigger than the within-groups variance

Question 16

What does MStreat represent?

Answer 16

The between-groups variance

Question 17

What does MSerror represent?

Answer 17

The within-groups variance

Question 18

What are the steps in a one-way ANOVA?

Answer 18

1. Estimate between-groups variability
2. Estimate within-groups variability
3. Weight each estimate by the number of observations used to generate the estimate (degrees of freedom)
4. Compare the ratio (MStreat/MSerror)

Question 19

What is on the numerator of the F-ratio?

Answer 19

MStreat

Question 20

What is on the denominator of the F-ratio?

Answer 20

MSerror

Question 21

What is the df for MStreat?

Answer 21

no. of groups - 1
(j - 1)

Question 22

What is the df of MSerror?

Answer 22

no. of groups * (no. of scores in each group - 1)
j (n - 1)

Question 23

Conceptually, what is the structural model of a one-way ANOVA?

Answer 23

An individual DV score is:
The grand mean
The effect of being in the jth group (between-groups variability)
Error for i person in the jth group (within-groups variability)

Question 24

What is the long range average of a statistic?

Answer 24

The expected value of a statistic

Question 25

What are the expected mean squares?

Answer 25

The expected value of MStreat and MSerror

Question 26

What is the expected mean square of MSerror?

Answer 26

The population variance

Question 27

What is the long range average of MStreat?

Answer 27

The population variance plus the long-range average of the variance between sample means considering the number of observations in each group

Question 28

What is the expected mean square of MStreat when the group means don’t vary?

Answer 28

The population variance/ MSerror