Attributing change in DV to IV manipulation: between-groups (control group) vs mixed-model (pre&post measure) 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&amp;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?
There's a short straightforward answer, and a more nuanced answer.

The short answer is that people were randomly assigned to the two groups. Any baseline differences between people will be equally likely to affect both groups. Will there still be differences? Absolutely. This is why researchers use statistical inference to rule out the possibility that baseline differences are responsible for the observed difference.

The more nuanced answer is that we can't be certain that the observed differences aren't due to these random baseline differences. In any experiment, there will always be noise that causes differences in the groups. When researchers use statistical inference, they aren't able to say with certainty that the effect was due to the manipulation. They are merely assessing the probability that random noise could account for the data. If the probability that random noise can explain the data is very low, then researchers claim that the manipulation had an effect. However, this is a probabilistic inference and sometimes the researchers will be wrong and the difference really is due to noise. Within-subject designs help remove some of this noise, but not all of it, because people change over time, even over the short timescale of a social priming experiment.