Analysis of Variance (ANOVA)

If we have >2 independent groups, can we do a bunch of t-tests?

No, each test will increase the amount of error

When do we use ANOVA

3 or more conditions or groups are compared

What are factors/levels

nominal/ordinal IVs

What are the assumptions with ANOVA

randomization

normal distribution

equal variances

Since ANOVAs assume data is normally distributed, what kind of test is this

parametric test

What are 2 facts that are important to keep in mind when using an ANOVA

determines differences among means > chance

based on F statistic

When is a one-way ANOVA used

When there is 1 DV (continuous) and 1 IV (factor), typically with 3 or more levels

What is a null hypothesis

There will be no statistical significant difference

What is an alternative hypothesis

you expects groups 1 and 2 will be the same, but different from groups 3 and 4 (which are the same)

H_A: (µ₁=µ₂) ≠ (µ₃=µ₄)

What is Sum of Squares

total variability within a data set

what are between-group effects

spread of group means around the grand mean

What are within-group effects

spread of scores within each group around the group mean

What value do we want F to exceed to indicate that the change is greater than error

1.0

What is F

ratio between the group (between-groups) variance and the error variance

MSb=

mean square between (between-groups variance)

MSe=

mean square within (within-groups/error variance)

F=

MSb/MSe

if F >/= the critical value…

you will reject the null (significant difference)

What is the p value

<0.05 probability

What does the p-value represent

the probability of Type I error

What is eta

gives us an effect size estimate

What is the MSD

mean differences to compare to a minimum significant difference

What is the requirement to characterize a small effect size

eta n² = .01

What is the requirement to characterize a medium effect size

eta n² = .06

What is the requirement to characterize a large effect size

eta n² = .14

When should a two-way ANOVA be used

when there is 1 DV (continuous) and 2 IV factors , typically with 3 or more levels

define main effect

effect of each IV on the DV

define interaction effect

the effect of the interaction of the IV on the DVs

What is the difference between Fa, Fb, and Fab

an F ratio can be found for each factor and for the interaction between them

When there is no interaction effects, what to we use to interpret results

look at the outcome of the F-test for each IV (main effect)

When there is an interaction effects but main effect are not significant, what to we use to interpret results

the interaction of the IVs is meaningful, but not on their own

When there is an interaction effects and the main effects are significant, what to we use to interpret results

exam each IV to see which one has the greatest effect

Is there an interaction effect when the graphed lines are parallel?

no

Is there an interaction effect when the graphed lines are cross?

yes

What type of trends can we have

linear, quadratic, cubic, etc

What is the point of trend analysis

helps us determine direction of the change

what are the limitations to using trend analysis

space of intervals

number of data points

avoid extrapolation

How often will we see pure trends

very rarely

How can nonlinear trends impact our F ratio

we use a linear equation for comparison, which can make F look much smaller

What are type I errors

When a true null hypothesis is incorrectly rejected (saying there is an effect when there truly isn’t)

What are type II errors

When a false null hypothesis is accepted (saying there was no effect when there was one)