Influenced by Helmholtz’s (1850) technique for assessing nerve conduction velocity, Donders (1868) introduced the so-called subtraction method to infer the speed of higher mental processes from reaction time (RT). Donders devised three basic tasks to measure the durations of cognitive processes: the A-task (or simple RT), the B-task (or choice RT) and the C-task (or go/nogo task). He argued that the go/nogo task is identical to the simple RT task except that it requires the additional process of stimulus discrimination. Similarly, the go/nogo and the choice RT tasks are identical, except that the latter includes the additional process of response selection. Thus, subtracting mean RT of the simple RT task from the go/nogo task yields an estimate of the duration of stimulus discrimination, whereas subtracting RT for the go/nogo task from that of the choice task yields an estimate of the duration of response selection.

Donders’s method is based on three assumptions. First, it is assumed that in these tasks the mental processes of stimulus detection, stimulus identification, response selection and response execution are arranged sequentially in the sense that the output of one serves as the input to the next. Second, it is assumed that only one process can be active at each moment in time between stimulus input and response output. Thus, each process or processing stage is assumed to be functionally distinct and to consume a certain duration, denoted as the stage duration. According to this serial processing model, RT is equal to the sum of all the stage durations (the serial processing assumption). Third, it is assumed that a mental process can be added or omitted without affecting the duration of the other processes, the so-called assumption of pure insertion. Especially the first and the second assumption have been supported and tentatively accepted by many researchers, whereas the third assumption has been severely criticized.

Using these three assumptions, Donders estimated the durations of various processes by subtracting the RT for one task from the RT for another more complex task; that is, the more complex task was assumed to require an extra mental process compared to the less complex task. He reasoned that the difference in RT between the tasks provides an estimate of the duration of this extra process. A drawback of this method is that the estimation procedure involves three unknowns (the durations of stimulus identification, response selection and the residual processes like stimulus detection and motor processing) and three independent functions relating mean RT to mean stage durations for each task. Thus, from a mathematical point of view this system of equations is completely determined and therefore untestable. Consequently, Donders’ estimation procedure provides no internal checks on the validity of its assumptions.2

Külpe (1893) noted that various laboratories reported inconsistent duration estimates, which often differed substantially from each other. Külpe suggested that this inconsistency was most likely caused by violations of the assumption of pure insertion.3 Relying on introspective reports, Külpe argued that changing from a simpler to a more complex task may not only insert an extra processing stage but also affect other stages, both qualitatively and quantitatively. Additional discussion of these historical concerns can be found in, for instance, Luce (1986, pp. 212–215), Welford (1980) and Woodworth (1938).

Although early RT researchers criticized the subtraction method, we doubt that these criticisms are empirically strong enough to rule out any possibility of applying this method. The subtraction method would clearly be a very powerful tool in RT research if its assumptions could be verified. Hence, it is easy to see why some more contemporary RT researchers have developed rigorous distributional tests to check the validity of the assumption of pure insertion. For example, Ashby (1982) and Ashby and Townsend (1980) applied such tests with success to memory scanning tasks, where the tasks compared are alike except with respect to the number of items to be memorized. It seems quite plausible that pure insertion may hold in this task, because there is no obvious qualitative change in a memory scanning task when the number of memory set items is increased. However, such a qualitative difference is clearly much more likely with the three tasks devised by Donders.

Curiously, only a few different tests of the validity of pure insertion involving the original RT tasks have been reported in the literature to our knowledge. The first test was performed by Taylor (1966). He basically extended the original three tasks by developing a modified choice RT task in which participants did not need to identify the stimulus but nevertheless were required to select a response to its nonappearance at a more or less expected time. This additional task, termed the “selection” task, was held to require response selection but not stimulus identification. Because there were four tasks but only three unknown stage durations to estimate, one degree of freedom was left. This enabled a comparison between the observed and predicted stage durations (i.e., of the sum of stimulus identification and response selection). Taylor reported a nonsignificant difference between the observed and the predicted durations and concluded that the assumption of pure insertion was supported.