week 10 Flashcards
dependent anova
why will unsystematic error variance shrink
due to size of systematic error variance
all error in an independent group design is
random
assumptions of dependent ANOVA
- INDEPENDENT RANDOM SAMPLING
- NORMALITY
- CIRCULARITY OF THE VARIANCE
sum of squares for treatment is the same as
independent anova
treatment variance
difference between group means
unsystematic error variance
variability within each group
systematic error variance
variance that is unique to each block/participant
SSerror
SStotal-SStreatment-SSblock
sum of squares for treatment
sum of squared deviations of the treatment mean about the grand mean
sum of squares for block
sum of squared deviations of the block mean about the grand mean
DF treatment
k-1
DF blocks
b-1
DF unsystematic error
(k-1)(b-1)
when will the dependent anova be more powerful than independent anova
if subject variance that is removed reduces the unsystematic error term to a sufficient degree
what is the primary difference between independent and dependent anova
partitioning of error variance into systematic and unsystematic error variance
What happens to the F ratio as the treatment variance increases?
It increases
- further it gets from 1 = more likely it is statistically significant
Why do we want to undertake additional error control?
To increase the power of our analysis
if you are trying to increase size of f-ratio what should you do
decrease magnitude of error term
what is simplist way to control error
arrange data into blocks
as unsystematic error shrinks f ratio becomes
larger
What is the circularity of the variance/covariance assumption?
- variance of difference between any two treatment groups, is equal to variance of the difference between any other two
- most typically tested using Machly’s test of sphericity
Why is the sum of squares for the error term different in dependent ANOVA from independent?
The unsystematic error term of the independent groups ANOVA has been partitioned into systematic sources of error and unsystematic sources of error
- since it was partitioned further it changes
What does a non-significant F-ratio for the blocks effect suggest
a non-significant F-ratio for the blocks effect does NOT suggest that you should run the analysis without removing systematic error
- it is possible that the removal of non-significant block or subject variance will have a sufficient impact on the unsystematic error term as the justify the lower df in error
What is a non-significant F-ratio
F ratio of 1.00
- recall that our goal in testing the omnibus F-ratio is to evaluate whether or not F is significantly larger than 1
is the df for the error term smaller in dependent of independent groups ANOVA
Df for the error term is markedly less than the df for the independent groups ANOVA
- this is a direct parallel to the dependent groups ANOVA is the subject variance that is removed reduces the unsystematic error term to a sufficient degree as to compensate for the reduction in power associated with a lower df
when should you calculate a partial eta square
if we want to evaluate the percentage of variance that is accounted for by the treatment effect, after controlling for the subject variance that you removed from your design - you should calculate partial eta-square
in a dependent group ANOVA what does the partial eta square tell you
The percentage of variability that is due to the treatment, after controlling for SYSTEMATIC error
what can block variance be described as
systematic error variance
What does unsystematic error variance refer to in a dependent groups ANOVA?
The variability within each group
What does systematic error variance refer to in a dependent groups ANOVA?
the variability unique to each subject
the reason to undertake additional error control is to
increase the power of our analysis
systematic error variance in a dependent anova
variability that is unique to each subject/block
better control of error =
greater power in ANOVA
in independent group anova the error term is partitioned into error and – term for the dependent anova
error and block
arranging data into blocks allows you to
remove subject variance from your unsystematic error variance
