Lecture 3: Independent One-Way ANOVA

Question 1

What is an ANOVA?

Answer 1

An analysis of variance

Question 2

When is an ANOVA used?

Answer 2

It is used when we have 1 IV with more than 2 levels.

Question 3

What do ANOVAs test?

Answer 3

Whether the population means under the different levels of the IV are different based on sample means.

Question 4

How is an ANOVA an extension of a t-test?

Answer 4

f= t^2

Question 5

How do you calculate the f ratio?

Answer 5

The variance between IV levels/ Variance within IV levels

Question 6

What does an f value close to 0 tell us?

Answer 6

That there is a small difference between IV levels relative to within IV levels

Question 7

What does an f ratio further from 0 tell us?

Answer 7

That there is a large difference between IV levels relative to within IV levels

Question 8

When p is < .05 what do we do?

Answer 8

Reject the null hypothesis (i.e., heterogeniety)

Question 9

What contributes to variance BETWEEN IV levels?

Answer 9

• Manipulation of IV
• Individual difference
• Experimental error (random and constant)

Question 10

What contributes to variance WITHIN IV levels?

Answer 10

• Individual differences
• Experimental error (random)

Question 11

How do we partition variance?

Answer 11

1. Calculate means for each IV level
2. Calculate grand mean: sum of IV level means/ no. of IV levels
3. Calculate IV level variance: sum of squared differences between individual values and the corresponding IV level means
4. Calculate between IV level variance: sum of squared differences between each IV level mean and the grand mean

Question 12

What are the one-way ANOVA assumptions?

Answer 12

• Normality
• Homogeneity of variance
• Equivalent sample size
• Independence of observations

Question 13

What is the normality assumption in accordance to One-Way ANOVAs?

Answer 13

DV should be normally distributed, under each level of the IV

Question 14

What is homogeneity of variance, in accordance to one-way ANOVAs?

Answer 14

Variance in DV, under each IV level, should be roughly equivalent

Question 15

What is equivalent sample size, in accordance to one-way ANOVAs?

Answer 15

Sample size under each IV level should be roughly equivalent

Question 16

What is independence of observations, in accordance to one-way ANOVAs?

Answer 16

Scores under each level of the IV should be independent.

Question 17

Which statistic will correct for homogeneity of variance, if the assumption is violated?

Answer 17

Welch’s F

Question 18

Which test does SPSS use to check homogeneity of variance?

Answer 18

Levene’s test.

Question 19

If data violates all the one-way ANOVA assumptions, which non-parametric equivalent should be used?

Answer 19

Kruskal-Wallis test, although less powerful and proposes a greater risk of Type II error

Question 20

How do you report the F statistic?

Answer 20

F(df^m, df^r) = F-value, p(italicised) = p-value

Question 21

When do you use a Welch’s F test?

Answer 21

When Levene’s is significant

Question 22

What happens to the degrees of freedom in a Welch’s F test?

Answer 22

Gets adjusted as a ‘penalty’.

Question 23

Should you report degrees of freedom as a decimal?

Answer 23

No.

Question 24

What is the Model Sum of Squares?

Answer 24

Sum of squared differences between IV level means and grand means (i.e., between IV level variance)

Question 25

What is the Residual Sum of Squares?

Answer 25

The sum of squared differences between individual values and corresponding IV level mean (i.e., within IV level variance)

Question 26

What is the equation for the Mean Square for Model?

Answer 26

SSm / dfM

Question 27

What is the equation for Mean Square for Residual?

Answer 27

SSr / dfR

Question 28

How do you calculate the dof between IV levels?

Answer 28

df(model) = K-1

k= number of IV levels

Question 29

How do you calculate dof within IV levels?

Answer 29

df(residual) = N-k

n= total sample size
k= number of IV levels

Question 30

How do you calculate dof for an independent one-way ANOVA?

Answer 30

number of measurements - number of parameters estimated

Question 31

What is a posthoc test?

Answer 31

A secondary analysis used to assess which IV level mean pairs differ

Question 32

When should a posthoc test be used?

Answer 32

When the F-value IS significant

Question 33

What are the 3 corrections, and which one do we usually use?

Answer 33

Bonferroni, Least Significant Difference (LSD), Tukey Honestly Significant Difference (HSD). HSD is the one we usually use

Question 34

How can bonferroni be classified, and what are the error risks does it pose?

Answer 34

It is classified as “very conservative”, for Type I risk, it poses a very low risk, whereas poses a very high Type II error risk.

Question 35

How can Least Significant Difference be classified, and what are the error risks it poses?

Answer 35

It is classified as “liberal”, and poses a high Type I error risk, whereas has a low Type II error risk

Question 36

How can Tukey Honestly Significant Difference be classified and what are the error risks it poses?

Answer 36

It is classified as “reasonably conservative”, and poses a low Type I error risk, whereas a high Type II error risk.

Question 37

Which error are we happy to risk over the other?

Answer 37

We are happy to risk Type II error over Type I error.

Question 38

What is partial ETA squared?

Answer 38

How much variance in the DV is explained by the manipulation of the IV overall

Question 39

How can partial ETA squared values be classified?

Answer 39

Small = > .01
Medium = > .06
Large = > .14

Question 40

What is the equation for partial ETA squared?

Answer 40

SSm / SSm + SSr