Stat Ch 5

Front 1

Model (df)

Back 1

K-1

Front 2

Error (df)

Back 2

n-K

Front 3

Total (df)

Back 3

n-1

Front 4

Model (SS)

Back 4

∑(ȳk - ȳ)^2

Front 5

Error (SS)

Back 5

∑( y - ȳk)^2

Front 6

Total (SS)

Back 6

∑( y - ȳ)^2

Front 7

MSGroups

Back 7

MS = SS/df

Front 8

MSE

Back 8

MS = SS/df

Front 9

F

Back 9

MSGroups/MSE

Front 10

Sig F

Back 10

tail

Front 11

Assumptions for ANOVA

Back 11

Linearity
Independence
Normality
Equal Variance

Front 12

Equal Variance

Back 12

The error for each group should have the same variance. Can use the residual plot:
y - ȳk
vs
ȳk

Front 13

Equal Variance rule of thumb:

Back 13

Smax/Smin < 2

Front 14

Normality

Back 14

The error for each group should be normally distributed. Can evaluate using the quantile plot for the residuals
y - ȳk

Front 15

Independence

Back 15

Sampling should be done in an independent manner

Front 16

Linearity

Back 16

If the sampling has a trend or not.

Front 17

Total Model

Back 17

y = µk + ∊

Front 18

Group means are estimated by...?

Back 18

ûk = ȳk

Front 19

Predicted values are...?

Back 19

ŷ = µk

Front 20

Residuals are also known as...?

Back 20

Errors

Front 21

Residual equation

Back 21

∊ = y - µk

Front 22

Group effects ∝k model

Back 22

∝k = µk - µ

Front 23

Alternate way of writing the group effect model

Back 23

y = µ + ∝k + ∊

Front 24

One-Way ANOVA F-Test

Back 24

whole purpose is to test if the means are equal within groups.

Front 25

ANOVA Theorem (Generalizing to the Population)

Back 25

If our sample was chosen randomly from the population, we are justified in applying our statistical results to the population. Otherwise, we are not (based on statistics alone).

Front 26

ANOVA Theorem (Inferring Causation)

Back 26

When we perform a randomized experiment and find a significant difference between groups, we can say the explanatory variable (treatments) caused the difference. If it is observational or if it isn't randomized, we can't say the explanatory variable caused the difference (based on statistics alone).

Front 27

Levene's test for H0:

Back 27

all groups have the same variance (homoscedasticity)

Front 28

Levene's test...

Back 28

Gives a good way for testing the equal variance assumption in ANOVA (more definite than residual plots or Smax/Smin).
Sometimes this is a useful test on its own - i.e. for quality control (less variance is more consistency).

Front 29

Pairwise Error Rates (definition)

Back 29

When computing multiple comparisons:
1. Individual error rate
2. Family-wise error rate

Front 30

Individual error rate

Back 30

The probability of making a Type 1 error when focused on one of the comparisons.

Front 31

Family-wise error rate

Back 31

The probability of making at least one Type 1 error in a series of comparisons, when all the null hypotheses are true.

Front 32

Pairwise Confidence Intervals

Back 32

If an ANOVA test concludes that we have a significant difference in means between at least 2 groups, then we can compute confidence intervals for the difference of means between any two of the groups. If we focus on individual error, we get Fisher LSD confidence intervals. More conservative is the Tukey HSD and even more conservative is the Bonferonni approach.