Introduction to ANOVA

Question 1

What problems arise when multiple pairwise t-tests are used?

Answer 1

• computationally inefficient

- increases probability of type 1 error, known as ‘familywise error’

Question 2

What is ANOVA?

Answer 2

ANalysis Of VAriance

- Statistical test designed for factors with more than two levels

Question 3

What is one-way ANOVA?

Answer 3

One independent variable with more than two conditions

Question 4

What is factorial ANOVA?

Answer 4

more than one independent variable

Question 5

How is the F statistic calculated?

Answer 5

between groups variance (deviation of group means from grand/overall means)/ within-groups variance (deviation within each group from group mean)

Question 6

Ideally, what should the between groups variance and within groups variance consist of?

Answer 6

between groups - treatment or condition effect plus measurement error
within groups - only measurement error

Question 7

What are the 2 degrees of freedom in the F statistic?

Answer 7

• df of number of conditions

- df of number of participants in each condition

Question 8

What are the assumptions of one-way ANOVA?

Answer 8

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

Question 9

How is between-subjects ANOVA used and how do you calculate the df?

Answer 9

• Compare different groups
• df(tot) = total number of measurements (N) - 1
• df (bet) = number of grups (nc) - 1

Question 10

How is between subjects ANOVA reported?

Answer 10

F(dfbet, dftot) = F-value, p = (p-value)

Question 11

When is within-subjects ANOVA used? What additional assumption must be made?

Answer 11

To compare observations from the same group

Sphericity, or the variances of the differences between conditions should be equal

Question 12

How do you calculate the degrees of freedom for within-subjects ANOVA?

Answer 12

df (tot) = total measurements (N) -1
df (bet sub) = number of participants (np) -1
df (treat) = number of treatment conditions (nc) - 1

Question 13

How is the F statistic for within subjects ANOVA calculated?

Answer 13

= between groups variance (treatment + error)/ within groups variance (error)

Question 14

How is df (error) calculated?

Answer 14

= df(tot) - df(between sub) - df (treat)

Question 15

How would you conduct t-tests without a specific hypothesis if the F value is significant?

Answer 15

• accepted post hoc tests such as Tukey’s HSD

- controls for familywise error

Question 16

when do we use one-way ANOVA?

Answer 16

when there is one independent variable with more than two level

Question 17

how to calculate the critical F value in excel?

Answer 17

=F.INV( )

The significant value changes from FALSE to TRUE depending on whether our computed F value exceeds the critical value.

Question 18

what is F critical value?

Answer 18

it represents how much the variability among the means exceeds that expected due to chance. An F-statistic greater than the critical value is equivalent to a p-value less than alpha and both mean that you reject the null hypothesis

Question 19

what does it mean to have the Levene’s test non-significant (i.e. with a p value greater than 0.05)?

Answer 19

the data variance is equal across groups.

Question 20

how to report f value?

Answer 20

F(treatment or between-group df, within-groups (or error) df) = F-value (2 decimal place), p= p-value (3 decimal place)

Question 21

why do we say the Bonferroni test is more conservative than the Turkey test?

Answer 21

The bonderroni test systematically produces larger p-values

Question 22

can we chose one-tailed or two-tailed test in ANOVA?

Answer 22

No. ANOVA is always one-tailed. (i.e. the results are never directional). they merely tell us that there is a difference between one of our conditions and the other

Question 23

what does the mauchy’s test of sphericity of covariance in SPSS output do?

Answer 23

this is testing the null hypothesis that our data possess sphericity of covariance. we want the p-value (under Sig.) to be non-significant (greater than 0.05) to proceed with ANOVA

Question 24

what is a Kruskal-Wallis test?

Answer 24

it’s a between-subject ANOVA alternative that compare the sums of the groups’ ranks. If one group’s summed ranks value is much higher than the other groups’, the test returns a significant result.

Question 25

how to report the results of Kruskal-Wallis test?

Answer 25

A K-W test found a/no significant difference between the groups, X^2(chi-squared)=… (2 decimal), p=… (3 decimal)

Question 26

what is a Friedman test?

Answer 26

a within-subjects ANOVA alternative that compares the sums of treatment conditions’ ranks.
If one treatment condition’s summed ranks value is much higher than the other treatment conditions’, the test returns a significant result.