LECTURE 5 one way anova Flashcards
why use anova
test whether all group means are equal when there is more than two levels to your independent variable or more than one independent variable
why cant you use t tests to look at one factor with three levels
inflates change of getting a type 1 error (say sig but not)
anova allows change of 5% to remain at a 5% level -
in t test prob of type 1 error is 1-0.95xno.levels
what is an omnibus test
tests for an effect across all means but doesnt say where the difference lies
how does an anova work
takes the F ratio of variance of participants performance that is due to the systematic differences caused by the IV compared to variance due to chance
f= variance by systematic exp manipulation / variance expected by chance
what are the sources of variability
systematic differences/experimental effects
individual differences
experimental error
sources are additive to make up the total variance
define systematic difference variability
difference conditions cause differences between samples
define individual difference variability
differences in level of ability between the participants cause the difference in the samples
define experimental error variability
unpredicatble changes due to extraneous variables ie the device used to measure the data
sources of variability in between group (independent measure)
systematic differences
individual differences
experimental error
effect of the experiment SSm
sources of variability in within group (independent measure)
individual differences and experimental error
(NOT SYSTEMATIC DIFFERENCES AS NOT COMPARING AGAINST DIFF CONDITION BUT LOOK AT VARIANCE IN SAME CONDITION)
residual error SSr
f ratio in independent measures to account for all sources of variability
F RATIO =
sys. diff + indiv diff + exp error (SSM - between group variability)
/ indiv diff + exp error (SSr - within group variability)
how to calculate total sum of square SSt
SSm (group means from grand mean) + SSr (individual data from individual group means) - SSt (all data from grand mean)
how to calculate Mean squared error
MSm = SSm (group means from grand mean) / dfm MSr = SSr (within group variability/individual data from individual group means)/ dfr
How to calculate F Ratio
F = MSm (SSm/dfm) / MSr (SSr/dfr)
what does homogeniety of variances test
that variance in each condition is equal - levene stat
if means not the same (sig diff) then run kruskal wallis
how is df worked out in between groups
df = k - 1 where k = no. conditions
how is df worked out in within groups
df = n - k where n = no. subjects
how to report one way anova
f (df between, df within) = __, p = __, MSE = ___, n2=___
what is effect size
measure of magnitude of the observed effect independent of sample size - compare effects across studies ie meta analysis
degree null is believed to be false - indexed by discrepency between null and alt hyp (index own method for working out ie cohens d)
what is cohens d effect size
diff between means of null and alt hyp / STDV
small 0.2, medium 0.5, large 0.8
how can you estimate effect size
look at previous research
pilot study
estimate by reference to cohens d
what is anova effect size
eta squares (n2) explained variability / total variability (sum of between and within group variability)
effect size is the proportion of variance accounted for by between group variability
what is power
the probability of accepting an effect when there is one ie occurance of type 1 (0.5) or type 2 (0.2) error
what effects power
alpha
sample size
effect size
use of power
decide sample size
look at power test has
Need for one way between subjects anova
1 IV
3+ levels
