WEEK 1: ONE-WAY ANOVA & GENERAL LINEAR MODEL

What is the general linear model (GLM)?

flexible statistical approach that can be used to test any hypothesis where the outcome is numeric

How can all GLM models be expressed?

outcome = (model) + error

What are three (3) examples of GLM?

• ANOVA

• Multiple regression

• ANCOVA

What does ANOVA stand for?

analysis of variance

What is a one-way ANOVA?

single categorical independent variable (IV)

What is a two-way ANOVA?

two categorical IVs

What is a factorial ANOVA?

general term for an arbitrary number of categorical IVs

What is a factor?

independent variable

What are levels?

conditions within a factor/IV

What hypotheses do one-factor ANOVAs test?

hypotheses about mean group differences in situations where we have two or more groups

When are one-factor ANOVAs most useful?

at least 2 factors/IVs OR 1 factor that contains 3 or more levels

What does ANOVA test for?

difference across all levels of the factor

What is variance?

variability in differences between individual scores and the mean

What is dispersion?

the extent to which a distribution is squeezed or stretched

What is the GLM equation?

Y_ij = μ + A_i + S(A)_ij

Why is sums of squares used?

some variance is positive and some is negative, so by adding them all up we would lose information as they may cancel each other out

What are degrees of freedom?

number of parameters that are freely estimated in the model

How are degrees of freedom calculated for a one-way ANOVA?

• df_A = number of groups in factor - 1

• df_S(A) = number of participants - number of groups

What is the F statistic?

the ratio of variance due to differences between groups to variance within groups

What can be derived from the F statistic?

p-value

What are post-hoc tests?

used in ANOVA to identify which specific levels have differences

What are the assumptions of the GLM?

1. observations are independent and identically distributed

2. homogenity of variances

3. normality of residuals

What is homogenity of variances?

the variance across all levels of the factor (between-subject ANOVA) are the same

How do we check for homogenity of variances?

Levene’s test

How do we know if Levene’s test has been violated?

significant value, red text, violin plots have unequal vertical spread

Why can Levene’s test not be used for large sample sizes?

it can become overly sensitive

What is normality of residuals?

the residuals (error) are normally distributed

How do we check for normality of residuals?

do a QQplot of residuals, dots shouls fall along the line

What if GLM assumptions aren’t met?

1. carry out ANOVA anyway

2. transform the dependent ot use other suitable models

3. use a non-parametric test which doesn’t require the data to conform to these assumptions

What are the risks of carrying out ANOVA if assumptions aren’t met?

reduces power, increases risk of type ii error

What non-parametric test can be used in place of a one-way ANOVA?

Kruskal-Wallis test

What is the risk of using a non-parametric test?

lose a lot of power