1 One-way Anova

Question 1

What are limitations and advantages of independent/paired sample t-tests?

Answer 1

They are limited to two groups/conditions. But you can make directional inferences.

Question 2

What are advantage and limitations of ANOVA?

Answer 2

You can compare scores across 2+ groups/conditions. But no directional inferences are possible.

Question 3

What does contrast analysis allow you to do (that is not possible with t-test and ANOVA)?

Answer 3

Ask focussed questions and make directional inferences with more than 2 groups/conditions

Question 4

What is J in ANOVA?

Answer 4

Number of levels of IV

Question 5

What is n_j in ANOVA?

Answer 5

Number of subjects in j^th group

Question 6

What is a person’s score comprised of according to the ANOVA model?

Answer 6

A person’s score = overall mean + any systematic group effect + individual error

Question 7

What is the formula for the ANOVA Model?

Answer 7

Question 8

In the ANOVA model, what is Y_ij?

Answer 8

Score on DV for the i^th person in the j^th group

Question 9

In the ANOVA model, what is µ?

Answer 9

The grand mean

Question 10

In ANOVA model, what is alpha_j?

Answer 10

The effect parameter for group j

Question 11

In the ANOVA model, what is ε_ij?

Answer 11

Random error for the i^th person in the j^th group

Question 12

Why does the sum of all the effect parameters for group j equal zero?

Why does Σα_j = 0?

Answer 12

Because the effect parameter for j is the mean of j - the grand mean. Add all these deviation scores together and you get zero.

αj = µ_{j -} µ

Question 13

What does an omnibus F-test in ANOVA ask?

Answer 13

Are there systematic effects across groups

Question 14

How does α_j change depending on whether there are systematic effects across groups?

Answer 14

If there are no systematic effects then all α_j = 0

If there are systematic effects then not all α_j = 0

Question 15

What is an F ratio the ratio of?

Answer 15

The ratio of between groups variablity to within groups variability

Question 16

What is the formula for between-groups sums of squares?

Answer 16

Question 17

What is the formula for within-groups sums of squares?

Answer 17

Question 18

In ANOVA, what is between-groups degrees of freedom?

Answer 18

The number of groups minus 1

dfB = J-1

Question 19

In ANOVA, what is within-groups degrees of freedom?

Answer 19

Number of groups multiplied by number of participants in each group minus 1

dfW = J(n-1)

Question 20

In ANOVA, what is the total degrees of freedom?

Answer 20

Total number of participants minus 1

dfT = N-1

Question 21

If you cut the error term from the ANOVA model, what does that imply?

Answer 21

That all members of each group scored the same - unlikely for psychological data

Question 22

What are the four assumptions about error in the ANOVA model?

Answer 22

1. Errors are independent (i.e. individual rather than systematic variance)
2. Errors are normally distributed
3. Errors have a mean of zero
4. Homogeneity of variance (homoscedasticity)

Question 23

What has happened if F < 1?

Answer 23

The error variance (MSW) is greater than the effect variance (MSB) - so no effect found.

Question 24

What four things should be mentioned in a one-way ANOVA conclusion?

Answer 24

1. Mean and SD for each group
2. What the DV and IV are
3. Statistical significance
4. Report observed F (with dfs) and relevant p value

Question 25

What is the DER?

Answer 25

Decision-wise type I error rate. The type I error rate for each test in an experiment.

Question 26

What is the EER?

Answer 26

The experiment-wise type I error rate. The overall error rate of the experiment, which may consists of several tests.