RMC. W4 Flashcards
ANOVA designs
• One way design (one-way ANOVA) = 3 conditions with one factor
• Factorial design = 2 factors + when you combine these factors, there are 4 possible conditions (2x2 design because there are 2 factors with 2 conditions
- Could also have a factorial ANOVA with 3 factors > the third factor would go into a third-dimensional space + would have 8 possible combinations of each factor (2x2x2 = 8 conditions)
Using participant data to put together ANOVA forms:
○ you could have between-participants > different people for every condition of the experiment
- E.g. in a 2x2 ANOVA, you would have 4 different groups of people
○ Could also have within-participants > the same people in every condition
- E.g. in the 2x2, you would get 4 different datapoints from the same group of participants
○ There is also a mixed design: is when there are one set of people using one set of conditions while another group of people use another set of conditions > at least one factor would be between participants and at least one factor is within participants.
> Common design for this is pre-intervention + post-intervention design
Multi-way ANOVA
- Factorial ANOVA is sometimes called multi-way ANOVA
- Multi-way ANOVA = Number of ‘ways’ = number of IVs (factors) > is the number of independent variables or factors that we’re investigating.
§ A one-way ANOVA has one IV
§ A two-way ANOVA has two Ivs
§ A three-way ANOVA has three IVs - Importantly, there is only one single DV no matter how many ‘ways’, factors or IV’s that there are in each ANOVA
Describing ANOVA
- Terms can be used interchangeably: Factors = IVs = treatments
- Levels of a treatment = number of groups on one factor > amount of conditions for one factor
- number of conditions = all combinations of all factors > you work out the combinations of the factors by all possible ways in which the number of factors you’ve got can be combined.
§ E.g. if you have a 2x3 ANOVA, the numbers 2 and 3 tell us that there are 2 numbers aka 2 factors, each individual number (2x3) also tells us how many levels there are to each of those factors so for first factor (2) there are 2 levels and second factor 3, has 3 levels > can workout total amount of conditions by doing 2x3=6
§ 2x4 ANOVA = 2 factors. First factor has 2 levels, second factor has 4. There are 2x4 conditions so 8 conditions in total
Where does variance come from? One-way ANOVA
• E.g. note-taking in laptop condition, laptop + review then pen-paper (3 conditions)
• Error is always a source of variance > This is due to the differences between different people’s scores, naturally occurring differences.
- Then we have the effect of the variable which is due to the different conditions if they have an effect on peoples performance > this is called the main effect
Sources of variance: two-way ANOVA
• If we add factors to the previous example so each condition + review and each condition w/o review then this gives us a 2x3 design with 6 overall conditions
• Because there are two factors, there are 2 main effects so the effect of how we take our notes (3 conditions) and also is there an effect from reviewing notes before performing (2 conditions)
• In this design, we’ve got more sources of variance because each factor adds sources of variance and interactions.
○ we have error, which is due to the different people ask before > the error is how much people’s individual marks vary from the mean or from each other.
○ we have the variation due to the main effect of note taking. > how much the mean marks for 3 different kinds of note-taking differ
○ We have the variation due to the main effect of review > how much the mean marks for groups that reviewed vary from the groups that didn’t review.
○ we have the variation that is due to the interaction of note taking and review. (so variation from how the two factors work together aka interact > how much the mean marks for the different combinations of notetaking and review differ from each other.
Source of variance: three-way ANOVA - 2x2x3
• Same factors as before but an additional one now, is choice
• So 2x2x3 > 2 = review/no review, 2 = choice/no choice, 3 = laptop, laptop review or pen + paper
• In this design we have 3 main effects > so the main effect of note-taking (3 conditions), main effect of review (2 cond) and main effect of choice (2 cond)
• 4 possible interactions: note-taking x review, note-taking x choice, review x choice and note-taking x review x choice.
• In this design, we have even more variance
○ Error
○ Main effect of note-taking
○ Main effect of review
○ Main effect of choice
○ 4 interactions > note-taking x review, note-taking x choice, review x choice and note-taking x review x choice.
Factors and interactions
- The more factors we have the more interactions we are going to get that we have to interpret and make sense of.
- 2 factors = 1 interaction, 3 factors = 4 interactions, 4 factors = a lot of interactions :)
- each additional factor adds more possible unique combinations of factors that are interactions that we might have to try and understand.
Working out the number of interactions in an ANOVA
• You can work out the number of interactions in an ANOVA essentially by looking at the way in which factors can interact.
○ Every factor can interact with every other factor on its own in a number of two way interactions.
○ then every factor can interact with all other factors in all possible unique combinations.
- E.g. In three-way ANOVAs (regardless of the levels on each factor) there are always 4 interactions >Factor 1 interacts with factor 2, Factor 1 interacts with factor 3, Factor 2 interacts with factor 3 + All three factors interact with each other.
Formula for calculating the number of interactions
• Formula = 2k– k – 1 > (K = number of factors)
• E.g. in a three-way ANOVA, there are 3 factors
○ 2³– 3 – 1 = 1
○ 2 x 2 x 2 = 8
○ 8 - 3 = 5
○ 5 - 1 = 4 > number of interactions
- This formula can be used to workout big ANOVA’s but simple designs are best
What are interactions?
• An interaction is any variation in the scores which is not due to error or main effects
• They can be represented graphically by plotting the means for each combination of our factors against the dependent variable.
• Rule of thumb when looking at graphs for interaction is that if there are Parallel lines = no interaction and if there is Not parallel lines = interaction > to check properly an analysis of variance would be needed but the graph lines can indicate if there is an interaction
1. E.g. DV is performance out of 5, one factor = task difficulty (easy topic, difficult topic), second factor = motivation (low motivation + high motivation)
○ No interaction because the lines of the graph are parallel (refer to ON)
- Interactions could have no significant effect, a significant effect (there could be an interaction or not, but there is a main effect) or a cross-over effect (main effects alone here were not that useful but the interaction was_
Interpret ANOVA results in Onenote
Interpret ANOVA results in Onenote
