Scientist: To study the comparative effectiveness of two experimental medications for athlete's foot, a representative sample of people with athlete's foot were randomly assigned to one of two groups.
Scientist
To study a new med for athlete's foot, we split up a representative sample of people suffering from that condition into group 1 and 2.
Group 1 received only M. Group 2 received only N.
The only people whose athlete's foot was cured were those were were given M.
Reporter
So you're saying, "If you didn't have your athlete's foot cured, then you didn't receive M (i.e. you did receive N).
Evaluate
Since the scientist's final claim and the reporter's claim are both conditionals (the only / if), we should be highly suspicious that we're being tested on some Necessary vs. Sufficient error, i.e. a conditional logic mistake, an illegal reversal or negation.
The trigger "the only" is a sufficient / Left side indicator (by contrast, the much more common triggers "only" and "only if" are necessary / Right side indicators).
So the scientist's final claim looks like this:
Your AF was cured → You took M You didn't take M → Your AF wasn't cured
The trigger "If" is a sufficient / Left side indicator. So the reporter's claim looks like this:
Your AF wasn't cured → You didn't take M
We can see that the reporter's interpretation is an illegal reversal of what the scientist said. In conversational terms, the scientist is telling us that if you were in group N, you definitely didn't get your athlete's foot cured. If you were in group M, maybe you did. At least some people in group M had their athlete's foot cured. But it doesn't have to be all. Consider this example data:
100 ppl with athlete's foot, divided into M and N M: 10 cured, 40 not cured N: 50 not cured
It's true to say, . But it's not true to say (as the reporter does), . After all, there were 40 people whose AF wasn't cured but were given M.
Goal
We can describe the reporter's reasoning error in formal terms, by saying she confused necessary and sufficient conditions.
Or we can describe it in conversational terms, saying that she fails to consider that some of the people who were given M might have not had their athlete's foot cured.