Chapter 11 part a: GLM1

Question 1

ANOVA

Answer 1

• Linear model to compare several means

Question 2

Predictor with 2 categories

• b

Answer 2

• represents the difference between the mean of 2 categories

- is the difference statistically different?

Question 3

Predictor with more than 2 categories

• b

Answer 3

• we have to create dummy variables so that b compares differences between two means
• each dummy variable will have 2 categories

Question 4

ANOVA vs Regression

Answer 4

• we use ANOVA to test fit of regression line
• ANOVA: special case of linear model (regression)
• Equation: Same
  Outcome=model+error

Question 5

Important in ANOVA:

Answer 5

• baseline category sample size must be fairly large so b retains reliability

Question 6

ANOVA Equation

Answer 6

Outcome = bo + b1Dummy1 +b2Dummy2

• bo: mean of base category
• b1: difference between control mean and 1st group to compare to mean
• b2: difference between control mean and 2nd group to compare to mean

Question 7

ANOVA: F significant

Answer 7

• using group means to predict is better than using overall mean

Question 8

Logic of F-ratio

Answer 8

• if group means are the same: our model is poor [F small]
• if group means are different: our model is good [F large]
• F: whether group means are different

Question 9

Logic of ANOVA

Answer 9

• Simplest Model: Grand Mean of outcome: No effect
• Intercepts and parameters describe the model
• Parameters: shape of fitted Model
  —> the bigger the coefficients (b): the greater the deviations between model & grand mean
• Experimental research: b represents the difference between group means
• If the difference between groups is large enough then our model is better than grand mean

Question 10

Total Sum of Squares [SST]

Answer 10

• total amount of variation

- SST=sum(obs. data-grand mean)^2

Question 11

Grand Variance

Answer 11

• variances between all scores regardless of experimental condition
• grand variance (s^2)=SST/(N-1)
• SST=grand variance x (N-1)

Question 12

Model Sum of Squares [SSM]

Answer 12

• variation explained by the regression model
• SSM=sum[nk(group mean-grand mean)^2]
• dfM= k-1

Question 13

Residual Sum of Squares [SSR]

Answer 13

• variation that can NOT be explained by our model
• variation caused by extraneous factors

—> SSR= SST-SSM
—> SSR=sum(xk- group mean)^2
—> SSR= SSR1+ SSR2+ SSR3...
—> SSR=sum[sk^2 (nk-1)]
        - variance of each group x (nk-1)
—> dfR= dfT-dfM
—> dfR= N-k

Question 14

dfT

Answer 14

N-1

Question 15

dfM

Answer 15

k-1

Question 16

dfR

Answer 16

N-k

Question 17

ANOVA

Answer 17

• Omnibus test: whether explained variance is larger than unexplained variance
• significant F: means of categories are not equal (several scenarios possible)
  —> manipulation has had some effect but what the effect is: Does NOT say

Question 18

Mean Squares

- why do we need them?

Answer 18

• SS are biased

- MS eliminate their biases

Question 19

Model Mean Square

Answer 19

• SSM/dfM

- systematic variation

Question 20

Residual Mean of Squares

Answer 20

• MSR=SSR/dfR

- unsystematic variation

Question 21

F-ratio

Answer 21

• how well the model is against how bad it is
• F= MSM/MSR
• F>1: if model good but check its significance

Question 22

Assumptions of One-WAy ANOVA

Answer 22

• Linearity
• Normality
• Homoscedasticity: check using Levene’s and correct using Brown or Welch
  ~ F(bf): SSR=sum[sk^2 (1-nk/N)]
  ~ both techniques control for Type 1
  ~ Welch: best except when very large variance
• Independence of Errors

Question 23

Is ANOVA robust?

Answer 23

• controls somewhat for Type 1
• controls for skew, kurtosis, non-normality for 2tailed
• less control for 1 tail
• leptokurtic: type 1 error too low
• platykurtic: type 2 too high

Question 24

ANOVA Robust to Normality?

Answer 24

• Yes, when group sizes are equal

- When group sizes are unequal: F and power may be affected

Question 25

ANOVA robust to heteroscedasticity?

Answer 25

• Yes, when sample sizes are equal

- No, when sample sizes are unequal