10. Comparisons among categories: Analysis of variance

Question 1

When do we use ANOVA?

Answer 1

to analyses variance of categorical data

Question 2

How do you construct a (one way) ANOVA table

Answer 2

y:
Treatment
Error
Total

x:
Sums of squares
D.f
Mean squares
F-ratio
p-value

Question 3

How can you calculate variance and variation explained by data (R^2) from an ANOVA table?

Answer 3

Variance:
Total Sums of squares / Total d.f

R^2:
Treatment Sums of squares / Total Sums of Squares

Question 4

How do you calculate the sum of squares total?

Answer 4

sum of (group treatment - mean)^2 and (units treatment - mean)^2

Question 5

How do you calculate the sums of squares of treatment?

Answer 5

companion of means within groups

sum of (group size(group mean - total mean)^2)

Question 6

How do you calculate the sums of squares of error

Answer 6

Difference between total and treatments

Question 7

How do you calculate mean squares

Answer 7

sums of squares over d.f

Question 8

How do you calculate the f-ratio?

Answer 8

MS-treatment/MS-error

H0: we expect this to be close to 1

H1: expect to exceed 1

Question 9

What does R^2 inform us of?

Answer 9

the biological relevance

Question 10

Why do we use planned comparisons?

Answer 10

as ANOVA only identifies significant differences
- not which means are different

Question 11

How do we do a planned comparison?

Answer 11

same as two-sample t-test but SE is calculated differently

to calc SE we use the pooled error variance (MS-error) and the error of df

Question 12

What is a rule of thumb for a planned comparison?

Answer 12

if t-statistic is twice SE, we can conclude there is a statically significant difference between the means