Week 11 - ANOVA

Question 1

What is a one-way ANOVA?

Answer 1

It is an analysis of variance on more than two groups
It is like an extension of an independent t-test
Seeing if the means are different for more than two groups

Question 2

How does a one-way ANOVA use the F ratio?

Answer 2

Uses it to determine if the group means are significantly different

Question 3

Probably a question What should you use ANOVA instead of running multiple independent t-tests?

Answer 3

The experimental wise error = 1 - (0.95)^n meaning that doing multiple t-tests inflates the type one error rate

Question 4

What are the hypotheses for ANOVA?

Answer 4

𝐻0: 𝜇1 = 𝜇2 = 𝜇𝑘
𝐻𝐴: 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝜇𝑠 𝑎𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡
k is the number of groups

Question 5

What are the assumptions for a one-way ANOVA?

Answer 5

Normality of the outcome variable
Homogeneity of variance
Outcome is continuous (scale)
The error is independent

Question 6

What are the types of variables in a one way ANOVA?

Answer 6

Dependent variable - quantitative
Independent variable - categorical

Question 7

How does ANOVA work?

Answer 7

Divides data into two sources of variation
Variability among measurements within a group (variation among sampling units within a categorical level) - called residual variation
Variability between groups (group variation among means of categorical levels) - called group variation

Question 8

What is the F statistic that is used in ANOVA?

Answer 8

F = variance among groups/variation within groups
F = group variation/residual variation
If there is no difference between Y bar a, Y bar c, Y bar d, and Y bar d, then the F ratio is close to 1 (within variation is equal to among variation)

Question 9

Is there direction for a one-way ANOVA?

Answer 9

No

Question 10

What are the dfs for ANOVA and what are they used for?

Answer 10

Fcrit (df group, df error)
They are used for the Fcrit

Df group = # of groups - 1
Df error = total observed - # of groups

Question 11

What are post hoc tests used for?

Answer 11

They are used to determine which groups are different

Question 12

When do you reject the null hypothesis when running an ANOVA?

Answer 12

Fcrit < Fobserved
p < 0.05

Question 13

What is repeated measures ANOVA?

Answer 13

Extension of a paired t-test
Comparing participants across 3 or more points in time (instead of 2)
Can also be comparing related groups

Question 14

What does the repeated measures ANOVA consider about subjects?

Answer 14

Considers that subjects are the same over time
This leads to a reduction in the SS error term
This leads to a larger F statistic

Question 15

What are the hypotheses for repeated measures ANOVA?

Answer 15

𝐻0: 𝜇1 = 𝜇2 = 𝜇3
𝐻𝐴: 𝜇1 ≠ 𝜇2 ≠ 𝜇3
HA: 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝜇′𝑠 𝑎𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡

Question 16

What are the dfs for repeated measures ANOVA?

Answer 16

Df time = total # of groups - 1
Df error = (observed - 1)(# of groups - 1)

Question 17

What are the assumptions for repeated measures ANOVA?

Answer 17

The outcome is scale
The data is paired
The participants are independent
Normality
Sphericity: where the variance between the various combinations of groups are equal

Question 18

When do you reject the null hypothesis for repeated measures ANOVA?

Answer 18

Fcrit < alpha
p < alpha