I ran a controlled experiment and am now trying to explain the conditions I investigated. In one condition, the chance that the subjects in my study got some additional information Z for a specific item was 20%. I first wrote
Z was provided at a random chance of 20%.
My institute employs an English native speaker for proofreading our writing. She told me to replace "at a random chance of 20%" with "in a random 20% of cases". However, I think this is not exactly what I am trying to express, but I cannot ask her at the weekend and have a very close deadline for this text.
The problem with her suggestion is that (please correct me if I am misunderstanding this) it means that the subjects got Z for exactly 20% of the items. What I am trying to say is: For each combination of subject and item, the chance that Z was provided was 20%. So some subjects actually got Z for less than 20% of the items, whereas others got it for more than 20%. Based on this answer, I came up with this sentence now:
In each observation, the chance that Z was provided was 20%.
Does this express what I am trying to say?