(6) Three-way factorial ANOVAs - overcoming limitations

What is meant by a three-way interaction?

A three-way interaction occurs when the two-way interaction between two variables changes depending on the level of a third variable.

How many two-way interactions and main effects are in a three-way ANOVA?

A three-way ANOVA has three main effects (one for each IV) and three two-way interactions, plus one three-way interaction.

when looking at a plots for a three way interaction what do they look like if they are sig interaction

they will look different from each other in the 2nd level

What should you do if a three-way interaction is not significant?

Move down the hierarchy: interpret the two-way interactions, and if those are not significant, interpret the main effects.

What are the limitations of ANOVA in psychological research?

Assumptions are often violated (normality, homogeneity, sphericity); sensitive to outliers, skew, measurement error; - - NHST (Null hypothesis significance testing ) logic is limited and can be unintuitive.

how can you overcome the limitations of an ANOVA

• non parametric tests or robust ANOVA

What steps are taken in a robust ANOVA?

• Use trimmed means to reduce influence of extreme values (remove data from each end of the distribution)

• run bootstrapping procedures to estimate parameters across many resampled datasets.

  • treat sample like mini population

  • take a random sample from within the sample

  • run analysis on mini sample

  • take average of parameter estimate

What are limitations of null hypothesis significance testing (NHST)?

p-values depend heavily on sample size; p>.05 does not confirm the null; p<.05 does not prove the alternative; the threshold is arbitrary and often misleading.

• you only assume that you haven’t found evidence of it not being there- not the same as it actually existing

What is Bayesian inference and how does it differ from NHST?

• entirely different from ANOVA

• beliefs about the effect prior to collecting the data and then adjust the beliefs

• testing the alternative hypothesis

• the bayes factor is a ration of support for null hypothesis vs alternative hypothesis (need to do 1/B for actual value)