Many studies report that a speed-accuracy trade-off (SATO) did not occur in the data since there is a positive correlation between RTs and error rates. In other words, people took longer to respond for the trials that were more difficult, i.e. the same that elicited more errors on average, rather than trading speed for accuracy or vice-versa, a participant behaviour seen as undesirable. The absence of a SATO is then strongly indicative of a participant having given their best during the task, i.e. correctly following the usual instructions to give fast but accurate responses. A certain level of skill is then said to characterise a particular SATO curve, and this parameter of the curve can change as people become better at the task.
However, rarely if ever have I seen papers that DO report a SATO, i.e. a negative correlation betewen RTs and error rates, or, in other words, participants that remained at a relatively constant level of skill but simply moved "up and down" their SATO curve. Clearly this is not a sign of "good data", but still, what is the correct analysis to perform in such situations, assuming that you can't just proceed to do analyses on RTs and error rates the way you normally do (in the absence of a SATO)?
Also, the above two paragraphs refer to the cases where a RT-errors correlation exists and is positive (1st para) or negative (2nd para). But what if there isn't a significant correlation at all?
A good paper discussing this phenomenon is Pachella's 1974 paper "The Interpretation of Reaction Time in Information Processing Research". However, I don't believe it addresses my questions above.