One often sees researchers attributing a change in the dependent variable to their experimental manipulation, semingly without considering whether this change in DV occurs between or within groups.
For instance, in the classical Bargh et al. (1996) paper on behavioural priming, subjects in an experimental group were shown word primes recalling stereotypes of old age (e.g. "forgetful"), while subjects in a controlg group were shown neutral words. Everyone's walking speed as they left the experiment was measured, and because the first group's was slower, it was concluded that priming people with words relating to a certain concept (in this case: old age) makes them unconsciously take on characteristics of that concept (in this case: walking more slowly).
The question that comes to my mind is, however: how do we know that the mean difference in walking speed is not just due to pre-existing (baseline) differences between the groups? How can we be sure it is due to the IV manipulation (different word primes)?
To me, believable evidence for this claim would be if they had measured everyone's speed pre&post-experiment, and then found an interaction showing that, while controls' speed stayed the same pre-to-post, that of the old-age-primed group had decreased. Without such an interaction (involving the use of a mixed between-within model), is the authors' between-groups-only inference statistically correct?