HC 01: One-way within subject design ANOVA
WS design
● Amount of repeated measures of a quantitative outcome of the same persons
● Under amount of conditions or time points
● Blocked/mixed
● Can be combined with repeated measures in the case of between subjects
experiment = split-plot
● Basically paired t-test when comparing 2 conditions and with BS this is unpaired t-
test (or 1-way WS/BS ANOVA)
Example:
Xavier, a superhero, can rescue people out of 3 different situations; natural disaster, alien
invasion or fire. The dependent variable is in this case the amount of people he rescued
under 3 different conditions. Since at all times we talk about the same superhero, we call this
a WS design.
WS vs BS: advantages and drawbacks
● Advantages
a. Much smaller amount of persons needed
b. Each person is his/her own control
● Drawbacks
a. Not feasible in case of irreversible treatment effect
b. Carry over effects (wash out period is needed)
,With BS you compare different superheroes to each other and they can differ in how skilled
they are, so they differ in how well they can cope with the threat situation. A WS design can
partly explain this this error variance that could not be explained in the case of BS, since the
same superhero is measured under 3 conditions.
● Y = how many people this Xavier was able to rescue under the 3 conditions, person
10, so Y1,10, Y2, 10 and Y3, 10.
● U = effect of constant factors
● Pi i = how skilled Xavier is as a superhero
● T j = effect of the scenario with 3 conditions from which he needs to save people
● PiT ij = performance change among
● E ij = faces the same effect twice and his performance differs and this variance
cannot be explained by the other factors included
● Fixed factor is in this case the scenario (alien etc.)
, ● Random factor is the superhero (person), since you want to generalize findings to
also other superheroes with amount of levels depending on how many people have
to be rescued.
● Random + fixed = mixed design
Calculations Univariate method
● SS total = score of person under each condition - grand mean
● SS condition = mean condition - grand mean
● SS person = person mean - grand mean
● SS error = what is left
● Dividing by degrees of freedom gives the mean squares, but take into account that
we have one observation per cell (person x condition) > interaction + error cannot be
separated and MS(residual) is a mix of interaction and error + person is random and
not fixed
, Sphericity assumption (only univariate)
Besides that the Y is a quantitative variable, threat conditions are independent from each
other and the samples are dependent on each other. Sphericity is an extra assumption =
each pairwise difference has same variance, so same standard error (SD/wortel n).
Almost the same as compound symmetry = same variance in each condition, same
correlation in all pairs of conditions.
Mauchly’s test tests H0 = each pairwise difference has same variance, so when p<0,05 then
this assumption is not met, however:
● Not robust against violations of normality assumption
● Little power with small sample size, so bigger chance on type II error
● Always met when the condition has only 2 levels
Univariate (long) data format with GLM Univariate
● Assumes sphericity, gives no check or correction, because SPSS sees it as a BS
design, since person is seen as a sort of second factor in our design, while in fact we
are measuring the same superhero under three conditions.
> Ignoring that the data is correlated, because we measure the SAME person under different
conditions and therefore the MS error is too large > F-value should be lower > p-value
should be smaller
WS design
● Amount of repeated measures of a quantitative outcome of the same persons
● Under amount of conditions or time points
● Blocked/mixed
● Can be combined with repeated measures in the case of between subjects
experiment = split-plot
● Basically paired t-test when comparing 2 conditions and with BS this is unpaired t-
test (or 1-way WS/BS ANOVA)
Example:
Xavier, a superhero, can rescue people out of 3 different situations; natural disaster, alien
invasion or fire. The dependent variable is in this case the amount of people he rescued
under 3 different conditions. Since at all times we talk about the same superhero, we call this
a WS design.
WS vs BS: advantages and drawbacks
● Advantages
a. Much smaller amount of persons needed
b. Each person is his/her own control
● Drawbacks
a. Not feasible in case of irreversible treatment effect
b. Carry over effects (wash out period is needed)
,With BS you compare different superheroes to each other and they can differ in how skilled
they are, so they differ in how well they can cope with the threat situation. A WS design can
partly explain this this error variance that could not be explained in the case of BS, since the
same superhero is measured under 3 conditions.
● Y = how many people this Xavier was able to rescue under the 3 conditions, person
10, so Y1,10, Y2, 10 and Y3, 10.
● U = effect of constant factors
● Pi i = how skilled Xavier is as a superhero
● T j = effect of the scenario with 3 conditions from which he needs to save people
● PiT ij = performance change among
● E ij = faces the same effect twice and his performance differs and this variance
cannot be explained by the other factors included
● Fixed factor is in this case the scenario (alien etc.)
, ● Random factor is the superhero (person), since you want to generalize findings to
also other superheroes with amount of levels depending on how many people have
to be rescued.
● Random + fixed = mixed design
Calculations Univariate method
● SS total = score of person under each condition - grand mean
● SS condition = mean condition - grand mean
● SS person = person mean - grand mean
● SS error = what is left
● Dividing by degrees of freedom gives the mean squares, but take into account that
we have one observation per cell (person x condition) > interaction + error cannot be
separated and MS(residual) is a mix of interaction and error + person is random and
not fixed
, Sphericity assumption (only univariate)
Besides that the Y is a quantitative variable, threat conditions are independent from each
other and the samples are dependent on each other. Sphericity is an extra assumption =
each pairwise difference has same variance, so same standard error (SD/wortel n).
Almost the same as compound symmetry = same variance in each condition, same
correlation in all pairs of conditions.
Mauchly’s test tests H0 = each pairwise difference has same variance, so when p<0,05 then
this assumption is not met, however:
● Not robust against violations of normality assumption
● Little power with small sample size, so bigger chance on type II error
● Always met when the condition has only 2 levels
Univariate (long) data format with GLM Univariate
● Assumes sphericity, gives no check or correction, because SPSS sees it as a BS
design, since person is seen as a sort of second factor in our design, while in fact we
are measuring the same superhero under three conditions.
> Ignoring that the data is correlated, because we measure the SAME person under different
conditions and therefore the MS error is too large > F-value should be lower > p-value
should be smaller
