Phase II trials are pre-test post-test designs. They can yield useful causal inferences if for example we know that a current chemotherapy never reduces tumours more than X percent, and a new drug results in a reduction greater than X percent in some participants (see https://www.bmj.com/rapid-response/2011/11/01/all-or-none-studies). This is the strongest case because we have decent knowledge of natural history (i.e. what would in all likelihood have been the response in a randomized concurrent control group). Outcomes with a more variable natural history, or that cannot be measured 'objectively', will always prompt the question of what would have happened had the same participants, or a randomly chosen subset, been exposed to the control condition. So my opinion is that the knowledge value of your inference is heavily conditioned by how much is already known about the outcome variable in a 'natural' no-intervention condition or to quote from the above reference, "quality of evidence is not an absolute notion solely based on methodological criteria. Its assessment must be adjusted with clinical knowledge of the condition under study."

I'd strongly endorse Mark R Speechley 's answer to this - but would emphasise that the particular example he gives, where you might confidently infer a treatment effect - is not the usual case. Most phenomena we study are highly variable and subject to multiple influences and so before and after designs cannot be used to infer with any confidence that differences between t 1 and t2 represent any treatment effect. However, you give little detail and it is hard to grasp exactly what you are proposing - what's the treatment and if you have no pre-treatment assessment how could you infer change? Are the 'tasks' what generate your assessment data?

Thank you both for the answer!

I would like to clear my study design to Peter Donald Griffiths :

Participants underwent a meditation training. Functional MRI was used to assess brain activity before and after the training.

During the scan, participants were required to perform some tasks: specifically, at time point 1 (before) just to rest, at time point 2 (after) to meditate and then to perform an attentional task (chosen because of the similarities with meditation). Now, as you could notice, there is not a task that was performed at both time points, but tasks at time point 2 might be considered similar. Would you infer any training effect? Maybe you can do that by exploring and making comparisons with literature.

Thank you again

Strikes me that the problem you have in making an inference is that any 'effect' from the second task could be influenced by the first, making it difficult to make confident inferences - but in a more tentative manner you could compare before and after effects between the two and consider the difference in effect (difference in difference) as a potential estimate of the treatment effect. If the order of the tasks had been randomised you could probably be quite confident in the inference. Take a look at difference in difference designs and related analysis and see if anything matches what you have.

Thank you again