What formula would be used for a within-participants design in statistics?
The basic formula for hypothesis testing statistics: & differences between groups & variability within the groups
The bottom part of the equation (variability within groups) is composed of two parts: 1.& due to measurement error 2.& due to individual differences & differences between groups & 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 within-subject designs The goal of within-subjects variables is to remove individual differences from the bottom part of the equation.& Consider the example. within-subject t-test For each item you compute a difference score. di = Xi1 - Xi2 This difference score ignores the range of scores for that item -- it equates items which started high and items which 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 within-subjects t-test is:& Is the average difference score large compared to the variability in the difference scores? & t = Md / SEMd& = Md / (sd / sqrt N) Example: Text Complexity Student simple complex d 1 10.4& & & 14.3 -3.9 2 16.9 & 20.4 -3.5 3 & 6.7 & & 7.5 -0.8 4 25.9 26.8 -0.9 5 12.4 14.6 -2.2 6 18.5 20.3 -1.8 7 13.5 12.3 1.2 8 & & & & & & & 8.2 10.2 -2.0 . . . . M 14.06 15.80 -1.74 SD & & & 6.24 & 6.31 & 1.62 & Within-subjects t-test t = Md / SEMd & = Md / (sd / sqrt N) & t& =& - 1.74 / (1.62 / sqrt 8) t (7)& =& - 3.038, p < .02