ANOVA Flashcards
what are two causes of difference in dependant variables?
- the manipulation of the independent variables
2. error, meaning that there is no true difference, just the difference we measure was due to random chance
what is ANOVA? when is a one-way ANOVA used?
an analysis of variance test
tests significance of differences
only in a between subjects experiment
what is the null hypothesis? why can’t we accept it? what are the 2 types of errors?
H0 says that there is no actual difference between the means and any difference observed is just due to sampling error
we can’t acccept it because there is always uncertainty, we can only fail to reject it
type1: reject h0 even tho it is true
type2: failing to reject h0 even tho it is false
what is the sum of squares?
the sum of the squared residuals, an unscaled measure of variability
what are SSeffect, SStotal and SSerror?
effect = total-error
effect is the variability caused by group membership, the larger the number is the more likely it is we can reject H0
total is variability between samples A and B, the higher this number the more likely we can reject H0
error is the variability within samples. not due to manipulation of the IV and thus is regarded as a source of error. the higher this number the less likely we can reject H0
what is the F-ratio?
F = MSeffect/MSerror
the number we need to reject h0. the higher the F-ratio, the better - will become large if the effect is larger than the error
the critical value is the threshold the F ratio must exceed to reject H0 at a preset confidence level
what are the assumptions of ANOVA?
the samples are independant and identically distributed(iid)
- this means that each random variable is distributed according to the same probability distribution (like the d6 graph)
- all of the random variables are mutually independent (probabilities of one don’t affect the other)
the residuals are normally distirbuted
the groups have equal variance, or homogeneous variance
how are the degrees of freedom calculated?
dferror = n participants - m groups
degrees of freedom within groups
this is the number of way you can arrange the residuals and still have them sum to zero for each group
dfeffect = m groups - 1
degrees of freedom between groups
this is the number of ways we can arrange their deviations away from the mean so that their average always sum to zero
what are the mean squares?
MS = SS/df
scaled sums of squares by their degrees of freedom
when is anova not appropriate?
when data is not normally distributed
when data is not continuous
when using rank data
outliers that violate the assumption of homogeneity of variances are particularly troublesome
why might you fail to reject the H0
the effect was small
there weren’t enough participants to gain statistical power
random chance
or it is true
what does it mean to reject the h0 at the 0.05 confidence level
it means that 1/20 times when you think you rejected h0 it was actually true
