Factorial ANOVA

Question 1

What are factorial designs?

Answer 1

Designs with one dependent variable and two or more independent variables

Question 2

Why are designs with more than 3 factors unusual

?

Answer 2

• Complicated to interpret
• Require a large n
• Take too long per participant

Question 3

What 2 things do factorial ANOVA designs tell us?

Answer 3

• How IVs individually affect the DV

- How IVs combine to affect the DV

Question 4

What are the main effects?

Answer 4

• Summarise data of the individual IVs
• Most straightforward results
• However can be misleading

Question 5

What are interactions?

Answer 5

How two or more IVs combine to affect the DV

Question 6

What assumptions are made for factorial ANOVA?

Answer 6

• interval/ratio scale
• normal distribution
• homogeneity of variance
• sphericity of covariance

Question 7

What action should be taken if assumptions are violated?

Answer 7

No non-parametric alternatives so proceed with caution and report that assumptions have been violated

Question 8

How many F-values are provided by two-way and three-way factorial ANOVA?

Answer 8

two-way = 3 F values
three-way = 7 F values

Question 9

How are the degrees of freedom in two way factorial ANOVA calculated?

Answer 9

For conditions A and B
df (A) = ncA -1
df(B) = ncB -1
df(A*B) = df(A)*df(B)
df(total) = N - 1
df (error) = df(total) - df(A) - df(B) - df(A*B)

Question 10

How are the results of factorial ANOVA reported?

Answer 10

F (error df, between groups df) = F-value p = p-value

Question 11

when do we use factorial ANOVA

Answer 11

when we have two independent variables

Question 12

when f-value increases, how does p-value change?

Answer 12

as f-value increases, p-value decreases

Question 13

what do we look for when we say that we have a significant main effect or interaction in an ANOVA (or any other parametric inferential statistics, including t-test)?

Answer 13

1) a test statistic above the critical value (in Excel)

2) a p-value or significance below the alpha level of 0.05 (in SPSS)

Question 14

When doing ANOVA, what extra step do we need for between-subject tests?

Answer 14

we need to use a coding variable when we are planning between-subject analyses. (we also need to do this for independent samples t-tests)
be careful that we need to use a coding variable for each independent variable if we r doing between subjects factorial ANOVA

Question 15

The Levene’s test of homogeneity of variance is nonsignificant as its p-value is ___(greater/lower) than the alpha level of 0.05. It is therefore ___(appropriate/ inappropriate) to proceed with the between subjects factorial ANOVA

Answer 15

greater; appropriate

for both ANOVA and Mauchly’s test, we want the nonsignificant results if we are to proceed with our analyses as normal

Question 16

if the p-value form SPSS is 0.000, how do we report that?

Answer 16

p<0.001

this is an exception in reporting p-value. in any other cases, report p-value as shown in the SPSS output table

Question 17

what is familywise error?

Answer 17

it’s the chance of getting a single false-positive significant result in amongst all the comparisons being made

Question 18

how do we determine the bonferroni threshold

Answer 18

to determine the bonferroni threshold, one must divide the standard alpha level 0.05 by the number of comparisons being controlled for. This helps to ensure that familywise error remains at the standard alpha level of 0.05

Question 19

how to read the ANOVA output table ofr tests of within subjects effects

Answer 19

If the Mauchly’s test is nonsignificant or unavailable, look at the Sphericity Assumed row for both the main effect/interaction and its error term.
If the Mauchly’s test is significant, look at the Greenhouse Geisser row for both the main effect / interaction and its error term.