Topics include Bayesian Factor, Linear Regression, Multiple Regression, and more. Notes are detailed and organised, and perfect for exam prep. I earned an overall 75% on this module.
General Linear models: One Factor ANOVA
ANOVA: compares amount of variance within groups (error) to the variance between groups (group
differences)
● One-way ANOVA: single categorical predictor
● Two-way (two factor) ANOVA: two categorical predictors
○ Does handedness and time of day predict reaction times?
■ 2 (left and right) x 2 (A.M and P.M)
Assumptions:
1. Independent observations: are all observations for different people?
2. Equal variance test —> Levene’s test
3. Normally distributed —> qq plot
One-Factor ANOVA: tests hypotheses about mean group differences in situations where we have 2 or
more groups
● Alternative hypothesis: there is a difference between the groups mean test scores
○ H1 : µ1≠ µ2 ≠ µ3
● Null Hypothesis: there is no difference between the groups mean test scores
○ H0 : µ1 = µ2 = µ3
GLM: measures within and between group variance that generalizes to situations with more than one
factor
○
○ ^Yij = μ+Aiμ+Ai
■ Model predicted value or “fitted value"
■ ^ represents an estimate of the value
Sum of Squares: calculates amount of variance associated with each component of the model
● Achieved by squaring each number in decomp matrix column and adding them up
● Divide by the degrees of freedom → Mean Square
, ○ Rationale: sum of squares between group variance will be much larger for small number
of participants in many groups than that for large number of participants in a small
number of groups
Degrees of freedom: number of independent values for a term
● dfA = number of groups -1
● Degrees of freedom for error: dfS(A)= number of participants - number of groups
● Degrees of freedom for overall mean
● dfµ= 1 because there is only 1 mean value
● dfY = total number of data points
F statistic: ratio of variance due to differences between groups to variance within groups
● How big is the difference between variance for the effect relative to the variance of the error?
● If F is large, grouping variable explains a lot of variation relative to sampling error
○ Not much difference between the groups
● If F is small, group variable explains little of variation relative to sampling error
Case study: A group of 12 runners wanted to know whether what they ate in the morning before their run
impacted their speed.
● 3 groups of 4, where each group ate either banana, toast, or porridge
● 4 people in each 3 groups so 12 GLM equations
○ 1 overall mean
○ 3 group effects
○ 12 error terms
● Procedure
○ Make decomp matrix
○ Calculate mean squares
○ Calculate degrees of freedom: dfeffect= 2; dferror= 9
○ Find mean squares → sum of squares/ degrees of freedom
○ Find F statistic
○ Find P value
● ezANOVA (dat, wid=id, dv=time, between= food, detailed= TRUE)
○ Writeup: There was a significant effect of food on running time; F(1,2) = 12.97, p = .002,
ges= 0.74.
Two Way ANOVA
Two-factor ANOVA: test hypotheses about mean differences in situations where we have more than one factor
● Main effect of A: There is no overall difference between levels of A
● Main effect of B: There is no overall difference between levels of B
, ● Interaction between A and B: The difference between levels of A does not depend on level of B
(same as saying: The difference between levels of B does not depend on level of A).
GLM equation
● Interaction= measures the extent to which observed effect of one factor depends on the other
factor
○ is the mean score for each “cell” (combination of the levels of the factor)
○ add up to 0 across each factor (rows and columns)
Degrees of freedom
● Main effects: dfA / dfB = number of levels -1
● Error: dfS(AB)= number of participants - (levels A x levels B)
● Interaction dfAB = dfA x dfB
Case Study: How Personality type (introvert vs extrovert) and Type of Motivation (Praise/Blame) affect
performance of a task
● Possible outcomes
1. Effect on motivation, no effect on personality
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller hannahkim2001. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £25.49. You're not tied to anything after your purchase.
