Introduction & Further ANOVA (1)

Question 1

What is a one-way analysis of variance (ANOVA) used to determine?

Answer 1

Whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

Question 2

What is the aim of an ANOVA?

Answer 2

To test the null hypothesis (that each of our conditions’ means are equal).

Question 3

What is the null hypothesis for an ANOVA with k groups?

Answer 3

H0: μ1 = μ2 = ⋯ = μk

Question 4

What kinds of variance are compared with ANOVAs?

Answer 4

Both within-group and across-group variance.

Question 5

What does an ANOVA reveal, in simple terms?

Answer 5

Whether the variance across groups is greater than the variance within groups.

Question 6

On what is the within-group estimate of population variance based?

Answer 6

The variance within each experimental condition.

Question 7

Of which concept is the within-group estimate of population variance independent?

Answer 7

It is independent of the truth or falsity of the null hypothesis (H0).

Question 8

On what is the between-group estimate of population variance based?

Answer 8

On the variance between each condition’s mean.

Question 9

On which concept is the between-group estimate of population variance dependent?

Answer 9

It is dependent on the truth or falsity of the null hypothesis (H0).

Question 10

What should be the case in terms of population variance if the null hypothesis (H0) is true?

Answer 10

The between-group population variance estimate should approximately equal the within-group population variance estimate.

Question 11

What should be the case in terms of population variance if the null hypothesis (H0) is false?

Answer 11

The between-group population variance estimate should be greater than the within-group population variance estimate.

Question 12

What should the ratio between the within-group population variance estimate and the between-group population variance estimate be if the null hypothesis (H0) is true and there is no difference between the means of each of our conditions?

Answer 12

Approximately 1.

Question 13

What allows us to test the null hypothesis (H0) that that each of our conditions’ means are equal?

Answer 13

Comparing the within-group population variance estimate with the between-group population variance estimate.

Question 14

What should the ratio between the within-group population variance estimate and the between-group population variance estimate be if the null hypothesis (H0) is false and there is a significant difference between the means of each of our conditions?

Answer 14

Above 1 (this would be the F-ratio).

Question 15

What increases the value of F, making the data more likely to be significant?

Answer 15

Increasing the separation between group means.

Question 16

What is the formula for the F statistic?

Answer 16

F = variance of group means/ mean of the within-group variances

Question 17

What would happen to the F statistic if we were to increase within-group variance?

Answer 17

It would decrease the F statistic, making our data less likely to be significant.

Question 18

How can the total sum of squares (SStotal) be calculated, in simple terms?

Answer 18

By comparing each datapoint with the grand mean (the mean of each condition’s mean).

Question 19

How can the total sum of squares (SStotal) be calculated, in practice?

Answer 19

By subtracting the grand mean from each datapoint individually, and squaring each of these values, before adding them all together.

Question 20

How can the within-group sum of squares (SSwithin) be calculated, in simple terms?

Answer 20

By comparing each datapoint of a condition with the mean of their condition.

Question 21

How can the within-group sum of squares (SSwithin) be calculated, in practice?

Answer 21

By subtracting the condition’s mean from each of the condition’s datapoints individually, and squaring each of these values, before adding them all together.