anova - independent groups Flashcards
(16 cards)
what is the problem with running multiple t-tests?
if each test has an alpha of 5% the overall likelihood of error becomes (just under) 15% which is too high
could reduce alpha to 1.6666% so that combined error is still 5% but still reduces our power
what does ANOVA stand for?
ANalysis Of VAriance
what is ANOVA?
extension of t-test
allows us to test whether 3 (or more) population means are the same, without reducing power
what are the assumptions of ANOVA?
scores were sampled randomly and are independent
roughly normal distribution
roughly equal number of participants in the groups (improved power if exactly the same)
roughly equal variance for each condition
true for all versions of the test
what is the basis of ANOVA?
way to compare multiple conditions in a single, powerful test
invented by Fisher (so test statistic = F)
compares amount of variance explained by our experiment with the variance that is unexplained
what is explained variance in between-groups ANOVA?
variance between groups
what is unexplained variance in between-groups ANOVA?
variance within a group
how are degrees of freedom affected in a between-groups ANOVA?
degrees of freedom associated with both variance values (degrees of freedom between conditions, residual degrees of freedom)
ANOVA critical values require two degrees of freedom values, one for each aspect of variance, so must report both
how do you know which conditions differ in ANOVA?
run multiple comparisons
some of these are “planned comparisons” some are “post-hoc” tests
correct for multiple comparisons - many options but easiest to understand is “Bonferroni correction”
what is Bonferroni correction?
essentially to divide alpha (criterion) by number of tests
uses a t-test and then divides alpha by some value based on number of tests
very strict - very safe but not very powerful
what are the different versions of ANOVA?
one-way or one factor ANOVA
multi-factor ANOVA
MANOVA
ANCOVA
what is one-way or one factor ANOVA?
one variable but varying on multiple levels
what is multi-factor ANOVA?
often referred to as e.g. 2x3 ANOVA
multiple things manipulating
what is MANOVA?
Multivariate ANalysis Of VAriance
extension of ANOVA for multiple DVs
multiple things measuring
what is ANCOVA?
ANalysis of COVAriance
extension of ANOVA to handle continuous variables (e.g. correlations)
what are post-hoc tests?
only run (or report) post-hoc tests if main test found significant result
great many voices, heavily debated area
