Module 1
One way within subjects
Repeated measures
Design
1 independent variable X with k levels
1 quantative variable Y
N subjects for each level of X
if K=2 then Anova=paired t-test
Univariate/mixed model
Multivariate/manova
SPSS
assumptions
normaility
SPSS
GLM repeated measures
assumptions
normality
click to edit
Pretends every level is different person
X=fixed N=random
GLM univariate
if X has multiple levels: F=MS(X)/MS(X*person)
if X has one level: F=MS(X)/MS(residual)
sphericity
Y is normally distributed in each k
if k is transformed into k(k-1)/2 then they all have same variance
compound symmetry
all k have same variance and all pairs (k(k-1)/2) have same correlation
no issue if k=2
Mauchley test
assumes normality (not robust)
power may be insufficient
Not reliable so always assume no sphericity
consequences
Overestimation of F
over or underestimates SE
Correcting
epsiolon-adjustment
multivariate method #
doesn't assume spericity
df numerator and df denumarator of F * epsilon
Greenhouse Geigser is recomended (but underadjusts a bit)
can also correct pairwise comparisons and contrasts
only for overall F
Method
transform k repeated measure into...
Their average
k-1 orthogonal contrasts
contrast = weighted sum of repeated measures
only usfull if more BS factors
centered
weights in each column add up to 0
Orthogonal
cross product of two columns is 0
normalization
coefficient devided by square of SS per contrast
SS=1
Separate row for each repeated measure
N*k records
Thinks this is a two way BS design
Doesn't test sphericity
More type 1&2 errors
1 row per person
With and without epsilon adjustment
Factors
fixed factors
random factors
conditions?
Participants?
Used to make predictions about population
Mixed anova
Fixed and random factors
Acually 2 way BS Anova
1 fixed and 1 random io 2 fixed factors
Look at difference score between conditions
d
Assumptions
Dependent (Y) is quantitative (nr)
Dependent groups
Example
every subject gets 3 different treatments
Difference scores normally distributed
Sphericity
all difference scores have same variance
Machlys test
unreliable
assume violation
epsilon correction
NOT ADVISED #
Increased type 1 error
More power if sample is small/sphericity
More power is sample is large/no sphericity