General Statistical Facts

Question 1

Assumptions of Independent ANOVAs

Answer 1

• Independence of data points
• Homogeneity/equality of variance = Levene’s (pass if p>0.05 - if fail = Welch’s correction
• Normality of residuals = Shapiro-Wilk’s

Question 2

Assumptions of a Repeated Measures ANOVA

Answer 2

• Independence of data points = Durbin-Watson
• Spherical – homogeneity/equality of difference between groups = Mauchy’s (pass if p>0.05) - if fail – Greenhouse Geisser correction
• Normality of residuals = Shapiro-Wilk’s

Question 3

Assumptions of Multiple Linear Regression

Answer 3

• Linear relationship
• Independence of data points
• No autocorrelation occurring = Durbin-Watson
• No multicolineraity occurring = VIF < 10
• Homoscedastic relationship = look at scatterplot of residuals
• Normal distribution of residuals = Shapiro-Wilks

Question 4

Assumptions of Simple Linear Regression

Answer 4

• Linear relationship
• Independence of data points
• No autocorrelation occurring = Durbin-Watson
• Homoscedastic relationship = look at scatterplot of residuals
• Normal distribution of residuals = Shapiro-Wilks

Question 5

Standardised Residuals

Answer 5

A measure of the strength between the observed and expected values
If more than 5% are >2, may indicate a poor model
Should not get >3

Question 6

Cook’s Distance

Answer 6

A measure of the overall influence of a date point on the overall model
>1 = cause for concern

Question 7

Leverage Value

Answer 7

The influence of the data point on the predicted values (slope) - how far the data point is from the centre of gravity
0 (no influence) - 1 (complete influence)

Question 8

Standardised DFFit

Answer 8

How the fit of the model would change if the data point were to be removed
>1 = substantial influence

Question 9

Standardised DFBeta

Answer 9

How the slope of the model (expected data points) would change if the data point were to be removed
>1 = substantial influence

Question 10

Simple linear regression has the same output as…

Answer 10

Unpaired t-test

SLR - one of the variables is categorical using dummy variables

Question 11

Multiple linear regression has the same output as…

Answer 11

One-Way ANOVA - when MLR uses dummy variables!

Question 12

Helmert

Answer 12

Orthogonal

Each category except the last is compared to the mean of the subsequent ones

Question 13

Difference

Answer 13

Orthogonal

Each category except the first is compared to the mean of the previous categories

Question 14

Deviation

Answer 14

Non-Orthogonal - need to perform post-hoc tests
Each category except the first (or last) is compared to the overall experimental effect
ie. 2 vs. 1, 2, 3, 4

Question 15

Simple

Answer 15

Non-Orthogonal - need to perform post-hoc tests
Each category is compared to the first (or last) category
Similar to Dunnet’s post-hoc

Question 16

Repeated

Answer 16

Non-Orthogonal - need to perform post-hoc tests

Each category is compared to the previous category

Question 17

Polynomial

Answer 17

Tests for trends in the data

Only makes sense to perform on ANOVAs where there is a logical order to the group

Question 18

Tukey

Answer 18

Equal sample sizes - good trade off between type 1 + 2 errors

Question 19

Bonferoni

Answer 19

Conservative - lacks power
Conserve type 1 error rate at the expense of the type 2 error rate
Use for repeated measures simple effect analysis

Question 20

Gabriels

Answer 20

Slightly different sample sizes

Question 21

Hochberg’s GT2

Answer 21

Very different sample sizes

Question 22

Games-Howell

Answer 22

Any doubt about the equality of variance assumption

Question 23

Standardised effect sizes

Answer 23

Small
R=.1
d= .2

Medium
R=.3
d=.5

Large
R=.5
D=.8

Question 24

Simpson’s Paradox

Answer 24

A trend appears in several different groups of data but disappears/reverses when there groups are combined

There is an apparent paradox between treatment outcomes and overall outcome due to hidden confounding variables