In a one-way repeated-measures ANOVA, we are testing for differences between the means of three or more related groups (in this case, the three successive tasks) with the same participants (in this case, the eight participants).
The degrees of freedom between persons are calculated as follows:
df_between = k - 1
where k is the number of groups (in this case, the number of participants), and -1 represents the constraint that the overall mean must be calculated from the group means.
Since there are eight participants in this study, the degrees of freedom between persons for a one-way repeated-measures ANOVA would be:
df_between = 8 - 1 = 7
Therefore, there are 7 degrees of freedom between persons in this study.