Analysis of Variance 2

Question 1

What is the simple measure of effect size for ANOVA?

Answer 1

The η2 (eta-squared) statistic is conventional

Question 2

How do you calculate η2 (eta-squared)?

Answer 2

By dividing SSb by SStot

Question 3

In ANOVA, what does MSb/MSw represent?

Answer 3

The test-statistic (F)

Question 4

How do you calculate etaSquared in R?

Answer 4

etSquared(x)

x = variable comtaining the groups

Question 5

How do you add effect size to your stat block for ANOVA’s?

Answer 5

Question 6

What is the main problem with ANOVA’s?

Answer 6

They can tell us whether there is a difference, but it doesn’t tell us which group is better

Question 7

What can we do to determine which group is better when ANOVA’s tell us that one group is but doesn’t specify which one?

Answer 7

1) This can be solved with descriptive statistics (e.g. boxplot())
2) Or can be done by doing t-tests for every pair of groups

Question 8

What is the problem with doing t-tests for every pair of groups in an ANOVA?

Answer 8

As groups get larger more chance of running into the type 1 error rate (5%), you’re likely to get one if running 20 test

Question 9

What can we do to solve the problem of doing t-tests for every pair of groups in an ANOVA?

Answer 9

This can be solved with the family-wise Type 1 error rate

Family wise is the probability of obtaining at least one Type 1 error among multiple tests

You need to “adjust” the raw p-values using a family-wise correction method

Question 10

What is the Bonferroni correction?

Answer 10

A way of obtaining the family-wise Type 1 error rate.

Question 11

What is the weakness of the Bonferroni correction?

Answer 11

Very conservative

meaning you lose a ‘lot’ of power relative to more sophisticated methods

Question 12

What is the Holm correction?

Answer 12

A method to adjust the ‘family-wise’ correction method.

(recommended method to use)

Question 13

How do you do the Holm correction in R?

Answer 13

posthocPairwiseT( x = model1)

model1 = variable containing ANOVA variables

Question 14

Do you need to make a family-wise correction when analysing lots of t-tests as a part of an ANOVA?

Answer 14

Yes, very important.

Question 15

What is a post hoc test?

Answer 15

A test that you conduct after you’ve done your ANOVA and for which you don’t have any particular hypothesis (e.g. pairwise t-tests run with no particular plan in mind)

Question 16

What is a multiple test correction?

Answer 16

A method used to control your overall (e.g. family-wise) Type 1 error rate (e.g. Bonferroni, Holm)

When you’re running post hoc tests, you usually need to apply a multiple test correction

Question 17

If you have a specific hypothesis in mind (you are not doing a post hoc test by have a hypothesis) do you need to run a multiple test correction?

Answer 17

No

Question 18

What are the assumptions made in ANOVA tests?

Answer 18

1) Population distributions are normal (test using QQ plots and Shapiro-Wilk tests)

2) Homogeneity of variance across all groups (test with Levene’s test)

3) Independence of data

Question 19

What is the Levene test?

Answer 19

Used to check whether the different groups have the same standard deviation

Question 20

What is the R command for the Levene test?

Answer 20

leveneTest( model1 )

model1 = variable containing ANOVAs.

Question 21

In a Levene test, a significant result means that the groups have…

Answer 21

unequal variance

therefore your assumptions are violated