Outline:
problem of individual differences
the goal of withinsubject designs
withinsubject ttest
an example
problem of individual differences
People differ. On any given measure some people will score high
and some people will score low and lots of people will score in between.
This is due to their basic abilities and history of experiences.
The problem arises when you have great individual differences on your dependent measure. This can be a problem of inability to see an effect of your IV due to the noise of individual differences.
The basic formula for hypothesis testing statistics:
differences between groups caused by IV
variability within the groups
The bottom part of the equation (variability within groups) is composed
of two parts:
1. due to measurement error on any given day
2. due to individual differences
differences between groups caused by IV
measurement error + individual differences
If individual differences are large, then the overall ration will
be low. This means even for important effects you may not be able
to pick them up in your stats because of large individual differences.
the goal of withinsubject designs
The goal of withinsubjects variables is to remove individual differences
from the bottom part of the equation. Consider the example in the
handout.
• high individual differences in reading speed
• 7 of 8 subjects were slower on more complex piece
The individual differences means that if you do this as a betweensubjects design you do not find any difference between the two conditions.
But you know something is going on because 7 of 8 went in the same direction. You want to pick this up and that is the goal of withinsubjects designs: To allow you to find the effect in spite of great variability among subjects.
withinsubject ttest
The way we go about doing this in a ttest is to compare each subject
to his/herself in pretty much the way we did by eyeballing the effect.
For each subject you compute a difference score.
di = Xi1  Xi2This difference score ignores the range of scores for that subject  it equates subjects who started high and subjects who started low by looking to see if they changed.
It is then possible to compute a mean of these difference scores:
Md = SUMi (di)
What we then ask with the withinsubjects ttest is: Is the
average difference score large compared to the variability in the difference
scores?
t = Md / SEMd
= Md / (sd / sqrt N)
Since in computing the difference scores we ignored the starting
range of that person’s scores, we have effectively removed individual differences
from this equation.
differences between groups caused by IV
measurement error (without individual differences)
an example
Effect of Text Complexity on Reading Speed of 4th Graders.
Students read two stories of equal length that vary in complexity of the the writing. The DV is the number of minutes it takes the students to read the stories.
Text Complexity















































Assume a between subjects design
t = (M_{1}  M_{2}) / sqrt (s_{1}^{2}/n_{1} + s_{2}^{2}/n_{2})
= (14.06  15.80) / sqrt(6.24^{2}/8 + 6.31^{2}/8)
t (14) =  0.55 p > .20
Assume a within subjects design
Text Complexity
















































t = Md / SEMd
= Md / (sd / sqrt N)
t =  1.74 / (1.62 / sqrt 8)
t (7) =  3.038, p < .02