Motivation(s) from control: response-effect contingency and confirmation of sensorimotor predictions reinforce different levels of selection

Abstract

Humans and other animals live in dynamic environments. To reliably manipulate the environment and attain their goals they would benefit from a constant modification of motor-responding based on responses' current effect on the current environment. It is argued that this is exactly what is achieved by a mechanism that reinforces responses which have led to accurate sensorimotor predictions. We further show that evaluations of a response's effectiveness can occur simultaneously, driven by at least two different processes, each relying on different statistical properties of the feedback and affecting a different level of responding. Specifically, we show the continuous effect of (a) a sensorimotor process sensitive only to the conditional probability of effects given that the agent acted on the environment (i.e., action-effects) and of (b) a more abstract judgement or inference that is also sensitive to the conditional probabilities of occurrence of feedback given no action by the agent (i.e., inaction-effects). The latter process seems to guide action selection (e.g., should I act?) while the former the manner of the action's execution. This study is the first to show that different evaluation processes of a response’s effectiveness influence different levels of responding.

Introduction

Notwithstanding substantial scientific attention, how humans establish a Sense of Agency (SOA)—whether detecting which events were affected by their actions (Chambon and Haggard 2013) or predicting which events will be so affected (Gozli 2019) is an open question with multiple implications.

An accurate SOA allows us to predict and evaluate the consequences of our actions and to behave in an effective manner to achieve our goals (e.g., grabbing a piece of chocolate). Reinforcing behavior that effectively controls the environment, regardless of any desirable outcomes, can serve as a strategy for maintaining a biological advantage (Skinner 1965). Consistent with this claim, some have argued that executing control over the environment is itself reinforcing (Eitam et al. 2013; Higgins 2011, 2019; Hull 1943; Wen 2019; White 1959), possibly through similar neural pathways as “actual” tangible rewards (Redgrave et al. 2008; Redgrave and Gurney 2006).

Empirical work has accumulated to show that responses that lead to predictable, value-free perceptual changes (i.e., action-effects) are reinforced, both in human infants as young as 2 months old (Hauf et al. 2004; Watanabe and Taga 2006, 2011; Zaadnoordijk et al. 2018, 2016) and adults (Bakbani-Elkayam et al. 2019; Eder et al. 2017; Eitam et al. 2013; Hemed et al. 2019; Karsh and Eitam 2015a; Karsh et al. 2016, 2020; Penton et al. 2018; Tanaka et al. 2021).

Given that previous work strongly suggests that SOA, indicating control over the environment might serve as a reinforcer, the current work moves beyond to determine what is the statistical evidence by which this process determines when to reinforce a response.

Note that unpacking the function by which this process operates is uniquely important to our basic understanding of reward processes. This is because that differing from other primary reinforcers, reinforcement from effectiveness is solely computational. What we mean is that unlike any other known primary reinforces, it lacks any robust hedonic or experiential aspect such as sweetness, sexual pleasure, or pain (cf., Haggard 2005). This lack of a hedonic component accompanied by reinforcing capacities is, among other things, strong evidence for the dissociation between reinforcement and hedonic experience.

The statistics of reinforcement from effectiveness

A model that explains how effective actions are reinforced, must first account for how the brain, mind, or person recognizes that an action is effective in changing the environment and which of these can be shown to lead to reinforcement. Most modern accounts of the SOA state that there are two distinct (although possibly interconnected) types of SOA—conceptual and sensorimotor (also known as explicit and implicit, or judgment of Agency vs. feeling of agency; Moore et al. 2009b; Saito et al. 2015; Synofzik et al. 2008; Wen and Haggard 2020; Wen et al. 2015; for a recent review see Wen 2019).

The sensorimotor SOA is assumed to be generated by an internal model that relies solely on sensorimotor input (‘Comparator’; Blakemore et al. 1998; Carruthers 2012; Haggard and Eitam 2015; Wolpert et al. 1995). Arguably, the following sequence is activated once a motor program is produced: a forward model predicts the action’s effect on the environment and then a comparator component compares the sensorimotor prediction to the perceived action-effect. If the comparison yields little to no prediction error, agency over the specific action effect is felt or judged. It should be kept in mind that the 'comparator' itself only provides a sensory prediction error following an action. The comparator itself does not entail knowledge about the control an action gives one over the environment. However, as we elaborate below, this sensorimotor prediction can serve in the evaluation of the effectiveness of an action—and drive its reinforcement.

Regardless of how the comparator can be used to estimate control, in recent years doubts emerged regarding the sensorimotor modularity of the comparator, or at least about the sensorimotor modularity of the measures hypothesized, sometimes tacitly, to be driven by its working such as intentional binding (Haggard et al. 2002) and sensory attenuation (Blakemore et al. 1998). These doubts are driven by multiple demonstrations that these behavioral measures are biased by high-level knowledge and cognitions that should not be available to the Comparator (Aarts et al. 2012; Barlas and Obhi 2014; Berberian et al. 2012; Buehner 2015; Christensen et al. 2019; Desantis et al. 2011, 2012; Dogge et al. 2012; Gentsch et al. 2015; Haering and Kiesel 2012; Lynn et al. 2014; Moore et al. 2009a, b; Pfister et al. 2014; Preston and Newport 2010; Takahata et al. 2012).

Unlike sensorimotor driven SOA, conceptually driven SOA has not been associated with a single mechanism. Given this, a reasonable assumption is that judgements of own agency are similar to other subjective judgements of causality; or more generally, of whether events co-occur (Gozli 2019; Wegner and Wheatley 1999).

Judgements of causality and co-occurrence

The co-occurrence of events has been termed contingency, and describes the difference between the conditional probability of an event (E; e.g., reward) given a condition (R; e.g., instrumental response) and the conditional probability of that event barring the condition (“Contingency”; APA dictionary, VandenBos 2007). Contingency in this sense ranges between perfect positive contingency (1; when the reward appears only following the response) and perfect negative contingency (− 1; when the reward is given only in the absence of the response). One of the term's main applications in psychological science is in the study of the effect of contingency on behavior and judgements of causality.

For example, the ΔP rule (‘Delta-P’; [P(E|R) − P(E| E|¬R)]; Rescorla 1967). In the context of instrumental behavior, positive values of Delta-P describe a positive association between a response and reward, were found to lead to higher response frequencies while smaller (negative) values of Delta-P led to reduced response frequencies. This pattern has been established for non-human animals responding to gain food or water (e.g, Hammond 1980) and for humans responding to secondary reinforcers (e.g., monetary gains; Liljeholm et al. 2011; Shanks and Dickinson 1991; Vallée-Tourangeau et al. 2005).

Even more pertinent to our current case is that the value of Delta-P has been found to correlate with judgements of causality (including self-causality; Liljeholm et al. 2011; O’Callaghan et al. 2019; Shanks and Dickinson 1991; Vaghi et al. 2019; Van Hamme and Wasserman 1994; Wasserman et al. 1983) and action-selection or operant learning (Elsner and Hommel 2004; Hammond 1980; Liljeholm et al. 2011; Shanks and Dickinson 1991).

Given the above, Delta-P seems to be a very reasonable candidate for capturing the functional relationship between environmental events and people’s conceptual judgements of SOA or effectiveness (Moore et al. 2009a). These judgements, as was shown for desired outcomes, should affect action selection (frequency of responding) if SOA indeed is reinforcing on that level of response selection.

Another important outcome of utilizing Delta-P as a functional description of the conceptual SOA is that it also leads to an interesting prediction of dissociation between the statistics that underlie the conceptual and sensorimotor SOA’s. Specifically, committing to the above functional relation constrains the candidate algorithms (or mental mechanisms) and effectively rules out the operation of a sensorimotor mechanism such as the comparator described above (De Houwer and Moors 2015). This is because the comparator’s prediction-effect-comparison sequence described above is initiated if and only if a motor-program is sent to production (i.e., a forward model). As this does not occur in the case of inaction such a mechanism is incapable of tallying perceptual changes that follow inaction as it does not generate a prediction when no motor program is sent to production (for more on inactions, see the “General discussion”). Thus, the functional relationship between the environmental input and sensorimotor SOA must be different.

As we elaborate below, based both on our own work (Eitam et al. 2013; Hemed et al. 2020; Karsh and Eitam 2015a; Karsh et al. 2016, 2020) and others’ previous work (Penton et al. 2018; Tanaka et al. 2021; Watanabe and Taga 2011) we argue that only the sensorimotor predictability of the effects influences the sensorimotor SOA.

More formally, in terms of contingency, if it indeed relies on an efference copy the functional relationship between sensorimotor SOA and the environmental input should follow the strength of the conditional probability of the occurrence of an effect only given a motor response (i.e., a sensorimotor prediction) or P(E|R). Accordingly, the reinforcing effects of sensorimotor driven SOA, if such exist, should follow only P(E|R) and not contingency or Delta-P (which is [P(E|R) − P(E|¬R)]).

While our previous conceptual and empirical work strongly suggests that sensorimotor SOA is modular and hence should influence (reinforce) mostly the execution of motor programs and not the selection of actions; as another model of SOA suggests that sensorimotor SOA may influence the more abstract level of action selection by indirectly affecting the postdictive or conceptual SOA (Synofzik et al. 2008) or by some other hedonic phenomenal experience feeding into the conceptual SOA (e.g., 'fluency'; Chambon and Haggard 2012).

The current study was designed to empirically test whether the contribution of the different sources of SOA to response selection and execution can be dissociated based on the above functional relationships.

The current study

In the current study, participants performed a task previously shown to reliably capture reinforcement from effectiveness on reaction time (presumably due to sensorimotor SOA; Hemed et al. 2019; Karsh et al. 2016) which we modified to also capture the potential effect of reinforcement on response frequency. The task is a variant of a choice reaction-time task introduced by Eitam and colleagues (Eitam et al. 2013), where participants' viewed on each trial an imperative cue and were asked to respond with the correct spatially-mapped key. Pending experimental condition, responses to imperative cues lead to either no visual change, to a value-free action-effects, or a similar yet lagged action effect. In that study, the responses of participants in the immediate action-effect condition were the quickest, while participants in the no-feedback or lagged action-effects conditions were (equally) slower. Although response speed was highest with immediate action-effects, there was no difference in accuracy between immediate, lagged or no action-effects conditions. It is important to keep in mind that both participants in the immediate and lagged action-effects conditions receive performance feedback (as they must respond correctly to receive action-effects), still lagged action-effects resulted in response speed that was as slow as that of the no-feedback condition. This comes to show that the facilitation in response speed displayed in the task is not due to receiving performance feedback. In addition, another experiment in the above study had participants on all conditions also view a score counter, showing a sum that increased with correct responses; yet only participants that received immediate action-effects were faster to respond. Reaction time facilitation due to neutral own-action 'effects' was recently replicated by our group (Karsh et al. 2016; Experiment 1a) as well as others (Tanaka et al. 2021).

Further studies provided additional evidence that the facilitation of response speed due to immediate action-effects does not depend on performance feedback, but most likely on sensorimotor SOA driving reinforcement of actions. In these studies (Karsh et al. 2016, Experiments 2a–2b), participants performed the same task, but the location of the action-effect was either spatially predictable or spatially unpredictable, surrounding the imperative cue. Spatially unpredictable action-effects led to response times that were as slow as those on the no action-effects condition. This again shows that performance feedback is not what facilitates response time in the task, as participants receiving spatially perturbed action-effects had to press the correct key to receive the action-effects, but still were slower compared with the participants in the spatially predictable condition. A replication of the above comparison between spatially predictable and unpredictable action-effects was recently obtained (Hemed et al. 2020).

Finally, additional evidence ruling out the possibility that response time change in our task is due to performance feedback comes from a different task. In this task, participants viewed an imperative cue at the center of the screen and were required to pick a key at random on each trial, such that there are no correct or incorrect responses. Still, response time decreased if responding to the cue resulted in immediate action-effects, compared with lagged or no action-effect (Karsh and Eitam 2015a; Karsh et al. 2016, Experiment 1b).

Given these findings, it is very likely that the facilitation in response time in the task used here is due to changes in sensorimotor SOA, as found in previous studies utilizing implicit measures of agency for spatial and temporal perturbation (e.g., Barlas and Kopp 2018).

Findings from explicit reports and judgements of agency from our previous studies also support the argument that changes in response time comes from changes in sensorimotor SOA (Eitam et al. 2013; Karsh et al. 2016). In conditions in which the action-effects are lagged or spatially-perturbed participants’ subjective judgements of agency (i.e., conceptual SOA) are the same whether receiving immediate, spatially predictable or lagged action-effects. Relatedly, participants usually maintain similar levels of response frequency regardless of temporal action-effect delay (in a free-choice rather than cued task; Karsh and Eitam 2015a). The latter shows that conceptual SOA as termed above, might be mostly insensitive to spatial and temporal features of feedback, when judging causality on the person or deliberate-level. It should be noted that while delays could reduce response frequency (Karsh et al. 2021), it is not fully clear how delays actually impact conceptual SOA (Wen 2019; see “General discussion”).

Such a dissociation fits the differentiation between a conceptual vs. sensorimotor SOA as well as their differential influence on levels of the response selection and execution process. In the current study, we focus on this dissociation.

To systematically test this ostensibly different sensitivity we manipulated the presence of action-effects and inaction-effects (i.e., effects occurring in the absence of a preceding action), using either a free operant procedure (Experiments 1 and 2a–2b) or a cued Go/No-Go task (Experiments 3a–3b). Given the above we predicted the following:

• (a) action-effects trigger the sequence that generates a sensorimotor SOA and consequently credits (i.e., reinforces) the effective motor-programs.

• (b) This form of reinforcement is argued to operate on a non-conceptual level; therefore, (b1) it will be sensitive to the conditional probability P(E|R) rather than to Delta-P, that also involves P(E|¬R) and (b2) as this form of SOA credits a specific motor program it will affect only the very specific manner of execution here measured as response speed and not the ‘volitional aspects’ of the response (Brass and Haggard 2008), here measured as response frequency.

• (c) A conceptual, regularity-detecting, mechanism of SOA will consider both action and inaction-effects and hence will be captured by Delta-P. The conceptual mechanism is argued to be detached from the motor-system (Wen and Haggard 2020; but see Synofzik et al. 2008), so it can modulate actions through inputting to action-selection processes—the “whether and what to do” measured here as response frequency.

The study consists of five experiments that test the same hypotheses using different experimental designs. To facilitate understanding of the findings, the pattern of results across experiments is also depicted as a forest plot (see Fig. 7, “General discussion”).

Experiment 1

Methods

Participants

We recruited 65 students from Tel-Hai Academic College, to participate for either course credit or ~ 6$. 68% of them were female, ages 19–33 (M = 24.89, SD = 2.39).

Previous studies (Eitam et al. 2013; Karsh et al. 2016, 2020) found that contingent, immediate action-effects lead to the facilitation of response speed compared with a condition in which responses are never followed by action-effects. The most basic finding comes from a two-samples t-test comparing the no action-effects condition and the immediate action-effects condition (Bakbani-Elkayam et al. 2019; Eitam et al. 2013; Karsh et al. 2016, 2020). The standardized effect size for this comparison ranged between Cohen’s d of 0.5 and 1.2, we estimate the population standardized effect size at 0.8. Yet here differing from previous studies, participants were instructed to select at random whether to respond or not on each trial. Thus, due to the novelty of the task, no power analysis was conducted before the collection of the data, as this experiment served as sort of a pilot for the current study.

Experiment 1 included four conditions. However, in terms of power, we refer only to the two conditions that are most similar to those from previous studies. In the current study, these are the action-effects present, inaction-effects present condition and the action-effects absent, inaction-effects absent condition. Given that and with roughly 15 participants per group (given random assignment), we had a statistical post hoc power (1 − β) of ~ 0.7 for detecting a Cohen’s d of ~ 0.8. Such an effect-size is consistent with those found in previous studies. However, we should note that we did not opt for an effect size that is based on an ANOVA, for several reasons. First, previous comparisons between the two conditions described above (action-effects vs. no-action effects), provide us with a benchmark for pair-wise comparisons between the action-effects present, inaction-effects absent condition and all others. Second, ANOVAs performed in previous studies were irrelevant as they were performed as a one-way analysis of differences in response time between several experimental conditions (e.g., immediate action-effects, action-effects with short or long temporal lags and no-action effects; Eitam et al. 2013). This sort of evidence would be meaningless as for a two-way analysis with an interaction. Finally, predicting a specific effect size based on an ANOVA would be uninformative when testing the difference between the baseline condition and the action-effects absent, inaction-effects present condition. Unrelated to the discussion above, we had no prediction about the effect size of the differences in response frequency, given the lack of previous evidence.

Design and task

Throughout the study, we manipulated the presence and absence of action-effects and inaction-effects, yielding four experimental conditions (see Fig. 1A)—(a) action-effects present, inaction-effects present, (b) action-effects present, inaction-effects absent, (c) action-effects absent, inaction-effects present and (d) (a) action-effects absent, inaction-effects absent. In Experiment 1, participants were randomly assigned to one of these experimental conditions, manipulated between subjects.

Fig. 1

Method and predictions. A The four conditions and the feedback scheme they received. B A depiction of an exemplar trial (dashed line not shown to the participant and is included for illustration only). C The visual appearance of trials with no effects (left panel) or with action-/inaction-effects (right panel). D Idealized predicted pattern of results. We predict that response speed (left plot) will be facilitated by the presence of action-effects (green and blue vs. orange and grey bars) but will not be affected by whether inaction-effects are present or absent (green and orange vs. blue and grey bars). In contrast, response frequency (left plot) is predicted to be facilitated by the presence of action-effects compared with their absence (green and blue vs. orange and grey bars) and reduced by the presence of inaction-effects (green and orange vs. blue and grey bars)

The task used was a four-alternative choice reaction time task, where on each trial an imperative cue appeared in one of four locations (with a 0.25 probability for the cue to appear in any of the four locations). The cue moved down on the screen for 950 ms (the response window; see Fig. 1B and C), followed by an ITI of 1150 ms, and only then the next cue appeared (on previous studies a response window of 850 ms and an ITI of 700 ms was used, similar to Experiments 2–3 in the current study). Participants were instructed to voluntarily decide whether to respond to the cue or withhold their response when the cue appeared, and to take care to respond on 70% of the trials. No feedback was given to the participants about their actual response frequency during the experiment. The instructions did not mention the possibility of action- or inaction-effects at any point on any of the experiments.

Participants in the two action-effects present conditions received feedback if they responded correctly during the response window. For subjects in the inaction-effects present conditions, there was an 80% chance of receiving feedback if they did not respond. A correct response meant pressing the spatially mapped key, either ‘S’, ‘D’, ‘K’ or ‘L’ (e.g., ‘S’ and ‘K’ for the depictions in Fig. 1B and C, respectively). Only the first response was recorded, so participants were not able to correct their response if they first responded using an incorrect key. Feedback consisted of the cue turning white for 100 ms and vanishing for the remainder of the response window (a ‘flash’). Regardless of response time and of whether feedback was given or not, the duration of the response window and ITI were kept constant. Trials were deemed as No-Response trials if no response (either correct or incorrect) was detected until a timepoint late in the response window (randomly sampled from a uniform distribution between 600 and 700 ms from cue onset). There was no special alert (e.g., error message) given an incorrect response, late, or no response. Based on our experience with the task, we predicted that very few trials will be slower than 600 ms—the typical mean RT in the task is within 400–500 ms with a standard deviation of 30–60 ms (Eitam et al. 2013; Karsh et al. 2016).

Procedure and apparatus

Participants signed an informed consent form, entered a soundproof dimly lit room, and were asked to decide on each trial whether to respond or withhold their response while maintaining a 70% response frequency across the experiment. They were further instructed that if they do choose to respond then they should do so as quickly and accurately as possible. They performed ten practice trials (during which the experimenter gave verbal feedback on their performance) followed by 240 task trials. The experiment ended with a self-report questionnaire, followed by a demographics questionnaire and debriefing.

The experiment was programmed in PsychoPy 2 v.1.84 (Peirce 2007). Stimuli were presented on a Samsung Syncmaster 943BM monitor with the refresh rate set to 60 Hz. Responses were collected with a standard PC keyboard.

Results

Data were pre-processed with Stata (StataCorp 2015). Statistical analyses were carried out in R through RPy2 (Gautier 2021, 2018), mainly using afex (Singmann et al. 2015) and BayesFactor (Morey et al. 2018). Plots were generated using Python’s Seaborn (Waskom 2018).

Data preprocessing

Note that percentages of trials filtered by each screening criterion overlap, as a trial can be classified as invalid based on more than one criterion such as when a response is both slow and incorrect. Similarly, a participant can be an outlier both in terms of response speed and response frequency. The screening criteria were based on previous studies (Eitam et al. 2013; Hemed et al. 2019; Karsh et al. 2016). Crucially screening did not change the qualitative pattern of results—for a side-by-side comparison of the analyses repeated on both filtered and unfiltered data see Supplementary Materials.

No-Response trials (18.71% of raw data; trials with no response or a response that is slower than the random timepoint described above) were not analyzed. Response trials were further labeled as valid or invalid based on several criteria. A total of six outlier (± 2SD) participants, in either Response-Frequency (three participants, 4.6%) or Response-Time (four participants, ~ 6.2%) were filtered out (9.23% of N = 65). Out of the remaining subjects (90.77% of raw data), incorrect responses (~ 3.6%; not the correct key was pressed), fast responses (0.02%; below 200 ms), and slow responses (4.27%; above 700 ms) were also filtered out. All filtration of invalid Response trials resulted in the loss of 16.25% of the raw data.

Data analyses

We defined response speed as the mean response time (RT) elapsing from the presentation of the imperative cue until a keypress and response frequency (RF) as the percent trials in which the participant responded (rather than withholding her response or responding later than the timepoint described above) out of the total number of experimental-block trials. For testing our two main hypotheses, we ran a between-subject 2 × 2 ANOVA—action-effects (present, absent) × inaction-effects (present, absent). We ran the ANOVA for predicting RT and RF, separately. As post hoc tests we compared the action-effects present, inaction-effects absent condition to all other between-subject conditions. We selected this condition as the baseline for comparison given previous studies used a variation of the same task. Due to unequal variances (here and on Experiment 3a), the independent-samples t test was corrected using the Welch–Satterthwaite correction for degrees of freedom. The 95% CI for the Cohen’s d reported on the t tests were calculated using the ‘effsize’ R package (Torchiano and Torchiano 2020), for the between-subject and within-subject designs as recommended by Cohen (1988) and Gibbons et al. (1993), respectively. Additionally, the frequentist analyses were supplemented by comparable Bayesian t tests, which are crucial given our null hypothesis that inaction-effects do not influence RT. For the Bayesian tests, we selected an uninformed prior (Cauchy χ₀ = 0, γ = 0.707) and sampled 10,000 observations from the posterior distribution on each analysis. Note that all of the individual contrasts specified below are also plotted as standardized effect sizes in Fig. 7 in the “General discussion”. For group descriptive statistics of response and frequency, see Fig. 2A and B below, for response accuracy see supplementary materials.

Fig. 2

Experiment 1. Response speed increases with the presence of action-effect but is insensitive to the presence or absence of inaction-effects (A–C). Response frequency on the other hand, is weakly facilitated by the presence of action-effects and inhibited by the presence of inaction-effects (B–D). A and B Individual and group means of response time (A) and response frequency (B). Error bars indicate 95% CI of estimated marginal means. Dashed lines indicate the grand average. C and D) Bayesian Estimation of the contrasts between the action-effects present, inaction-effects absent condition, and all other conditions. Horizontal lines indicate 95% HDI

First, we analyzed RT data (see Fig. 2A and C). As predicted, presence of action-effects facilitated RT (with a large effect size) [F(1, 55) = 21.35, p < 0.0001, Partial-η² = 0.280], while neither inaction-effects [F(1, 55) = 0.19, p = 0.660, Partial-η² = 0.003], nor the interaction term [F(1, 55) = 0.21, p = 0.650, Partial-η² = 0.004] had any significant effect on RT. We continued by comparing the baseline condition (action-effects present, inaction-effects absent) to all other conditions. For the key comparison, and in accordance with our expectations, there was no difference in RT between the two action-effects present conditions [Two-tail—t(28) = 0.02, p = 0.983, Cohen's d = 0.01, 95% CI (− 0.74, 0.76), BF 1:0 = 0.34].¹ Compared to baseline, RT was significantly slower on the action-effects absent conditions—regardless of whether inaction-effects were present [Upper-tail—t(19) = 2.96, p = 0.004, Cohen's d = 1.21, 95% CI (0.32, 2.10), BF 1:0 = 15.75] or inaction-effects were absent [Upper-tail—t(30) = 3.79, p < 0.001, Cohen's d = 1.28, 95% CI (0.50, 2.06), BF 1:0 = 66.73].

Regarding RF (response-frequency; see Fig. 2B and D, an identical two-way between-subject ANOVA found an insignificant influence on response frequency by action-effects [F(1, 55) = 2.96, p = 0.090, Partial-η² = 0.050], with a significant influence of inaction-effects [F(1, 55) = 7.69, p = 0.008, Partial-η² = 0.120] and no interaction between the two [F(1, 55) = 1.16, p = 0.290, Partial-η² = 0.020]. Subsequently we compared the action-effects present, inaction-effects absent baseline condition to all others. Compared with the action-effects present, inaction-effects present condition we found that response frequency was nominally higher on the baseline condition, with an insignificant difference (Bayesian: insensitive result) [Lower-tail—t(28) = − 1.43, p = 0.082, Cohen's d = − 0.52, 95% CI (− 1.28, 0.24), BF 1:0 = 1.31]. We found that response frequency was significantly higher on the baseline condition compared with the action-effects absent, inaction-effects present condition [Lower-tail—t(16) = − 2.61, p = 0.010, Cohen's d = − 1.11, 95% CI (− 1.99, − 0.23), BF 1:0 = 10.05], but not significantly different than the condition in which both action-effects and inaction-effects were absent [Lower-tail—t(31) = − 0.53, p = 0.299, Cohen's d = − 0.18, 95% CI (− 0.9, 0.53), BF 1:0 = 0.50].

Experiment 2a

The results of Experiment 1 supported the notion that action-effects facilitate response speed, but inaction-effects do not. Crucially, the Bayesian analysis supported the null hypothesis for no difference between both conditions in which action-effects were present (see Fig. 2C). Regarding our hypothesis that a calculation that considers both action-effects and inaction-effects could facilitate response frequency, we found support for influence from inaction-effects, but the pattern is not as clear as with response speed. The pattern may not match our prediction that both action-effects and inaction-effects influence response frequency; regarding response frequency, the pattern we found is that inaction-effects robustly reduce response frequency, and that action-effects facilitates response frequency but to a lesser degree (see the ANOVA analysis above). Most importantly for our theoretical purposes, the data do clearly show that differing from response speed—inaction effects are influential for response frequency (sometimes exclusively so; see Fig. 7 for comparison of all effect sizes on the study).

There were two specific caveats that we wanted to address in the following experiments. The first being that participants did not receive feedback regarding their response frequency and responded on a greater proportion of trials than they were requested to (> 80%, instead of ~ 70%). Therefore, in Experiment 2a, we aimed to better control the ratio of required Response and No-Response trials. The second concern was that inaction-effects (No-response trials on inaction-effects present conditions) appeared at random timing but also relatively late in the response window. The lateness of the inaction-effects could have helped participants differentiate between own-action effects and spontaneously occurring, inaction-effects, and possibly for that reason inaction-effects did not influence response speed. However, that would not explain why we found evidence for an influence of inaction-effects on response frequency.

Finally, it could also be the case that inaction-effects would have affected RT if they were less delayed and such a finding would seriously challenge our explanation of our basic finding here and in previous studies (Eitam et al. 2013)—facilitation of RT. This is because our current explanation is that RT is facilitated by reinforcement of a specific motor program that is credited—using the comparator’s (sensorimotor SOA) output as its input—with causing the perceptual effect. If it would have been consistently found that RT is facilitated in inaction-effects present conditions this explanation would be falsified.

As such in Experiment 2a we sought to equate the timing of action- and inaction-effects by titrating inaction-effects to participants’ response speed. Finally, given the large individual differences found in Experiment 1, we opted for using a more sensitive, repeated-measures design.

Methods

Participants

Twenty-five naïve students from the University of Haifa were recruited, 88% female, ages 21–29 (M = 24.4, SD = 0.42). As we had no experience with the current task in a within-subject design, we estimated that the effect would be like the one found on between-subject designs in previous studies (Cohen’s d = 0.8) when comparing conditions similar to the inaction-effects absent conditions in the current study. The sample allowed us to detect a similar effect in a within-subject design with a power of ~ 0.98.

Design and task

The experiment included the same four experimental conditions as in Experiment 1 (see Fig. 1), but for Experiment 2 we used a within-subject design, and each condition was blocked (the block order was random for each participant to cancel out order effects). Each block was 200-trials long (4 cue locations × 50 repetitions, in random order).

As in Experiment 1, if no response was given up to a certain timepoint, the trial was considered a No-Response trial. Here, the timepoint was set initially to 500 ms. However, following the first correct response, the timepoint was recalculated on each additional trial to be the 75th percentile plus 1 standard deviation of all previous correct response times. This gave participants sufficient time to respond, without arbitrarily truncating the RTs distribution’s right tail and significantly blurred the difference in timing of action- and inaction-effects. On the inaction-effect present conditions, the probability of an inaction-effect was 1 and not 0.8 as in Experiment 1. Additionally, participants were instructed to respond on 50% of the trials, the ITI was 700 ms and the number of repetitions for each cue location was equal.

Procedure and apparatus

The instructions were read to the participants who then proceeded to complete four experimental blocks, separated by self-paced breaks. During the break, participants were notified of their cumulative response frequency by an on-screen message and were reminded to maintain a 50% response frequency. The equipment was identical to Experiment 1 except those stimuli were now presented on a BENQ XL2420T screen.

Results

Data pre-processing

No-Response trials (53.47% of raw data; trials in which participants did not respond or responded later than the timepoint described above) were not analyzed. We filtered out 7 (28% of N = 25) participants, all of who had less than 20 valid trials on at least one experimental condition which precluded calculating a reliable estimate of their RT (Simmons et al. 2011). One of these was also an outlier (± 2SD) in both response speed and frequency. For the remaining subjects (72% of raw data), we filtered incorrect responses (~ 4.89%), and fast responses (0.4%; below 200 ms). Filtration of invalid response trials (both complete participants and individual trials) resulted in a loss of 31.59% of the data. Applying these filters did not modify the pattern of results (see Supplementary Materials section).

Data analyses

We used a repeated-measures ANOVA and paired t tests, in line with Experiment 2a’s design. First, we analyzed RT data (plotted in Fig. 2A and C). For the ANOVA, we used the Greenhouse–Geisser correction for sphericity (here and in the following within-subject experiments). A two-way within-subject ANOVA matched our prediction regarding response speed—we found a significant effect for action-effects [F(1, 17) = 6.4, p = 0.020, Partial-η² = 0.270] but no influence of inaction-effects [F(1, 17) = 0.62, p = 0.440, Partial-η² = 0.040] or an interaction [F(1, 17) = 1.30, p = 0.270, Partial-η² = 0.070]. We followed by comparing the baseline condition (action-effects present, inaction-effects absent) to all other conditions. As predicted, we found no difference between the baseline condition or the action-effects present, inaction-effects present condition [Two-tail—t(17) = 0.12, p = 0.904, Cohen's d = 0.02, 95% CI (− 0.35, 0.40), BF 1:0 = 0.24]. In contrast with our prediction, in this experiment we did not find that RTs were faster in this condition compared with action-effects absent, inaction-effects present [Upper-tail—t(17) = 0.93, p = 0.182, Cohen's d = 0.17, 95% CI (− 0.200, 0.54), BF 1:0 = 0.57]. Finally, we found the predicted slower RT on the condition where both action-effects and inaction-effects were absent compared [Upper-tail—t(17) = 2.50, p = 0.011, Cohen's d = 0.39, 95% CI (0.06, 0.73), BF 1:0 = 5.31].

A two-way repeated-measures ANOVA was used to the test effect of action-effects and inaction-effects on response frequency (see Fig. 3B–D). It showed that the effect of action-effects on response frequency is significant [F(1, 17) = 14.96, p = 0.001, Partial-η² = 0.470], but the effect of inaction-effects was not [F(1, 17) = 0.12, p = 0.730, Partial-η² = 0.007] and neither was the interaction [F(1, 17) = 2.86, p = 0.110, Partial-η² = 0.140]. We continued by comparing the action-effects present, inaction-effects absent condition to all others. We found that response frequency was nominally lower when both action-effect and inaction-effects were present, but the comparison was not significant and insensitive by Bayesian terms [Lower-tail—t(17) = − 1.47, p = 0.080, Cohen's d = − 0.52, 95% CI (− 1.28, 0.24), BF 1:0 = 1.10]. As predicted, we found lower response frequency when only inaction-effects were present [Lower-tail—t(17) = − 2.93, p = 0.005, Cohen's d = − 0.94, 95% CI (− 1.73, − 0.16), BF 1:0 = 11.08] or when both action- or inaction-effects were absent [Lower-tail—t(17) =  − 3.73, p = 0.001, Cohen's d = − 1.27, 95% CI (− 2.2, − 0.34), BF 1:0 = 47.64].

Fig. 3

Experiment 2a. Response speed increases with the presence of action-effect but is practically insensitive to the presence or absence of inaction-effects (A–C). Response frequency is facilitated by the presence of action-effects, and nominally lowered by the presence of inaction-effects (a non-significant interaction; B–D). A and B Individual and group means of response time (A) and response frequency (B). Error bars indicate 95% CI of estimated marginal means. Dashed lines indicate the grand average. C and D Bayesian Estimation of the contrasts between the action-effects present, inaction-effects absent condition, and all other conditions. Horizontal lines indicate 95% HDI

Experiment 2b

The results of Experiment 2a were similar to those of Experiment 1 while controlling for the difference in the timing of the inaction-effects and variance in response frequency. An unexpected finding in Experiment 2a was that the action-effects absent, inaction-effects present condition was as fast as the baseline, action effects only, condition. If found to be robust this finding would falsify our theoretical position that the facilitation of response speed stems from a sensorimotor process based on an efferent copy (i.e., Comparator), as such a process must be indifferent to events that are not preceded by an action. Crucially, an inspection of the forest plot depicted in Fig. 7 shows that this result is an oddball suggesting that it is a statistical fluke.

In Experiment 2b, we aimed to replicate Experiment 2a while timing inaction-effects more in line with that used in Experiment 1 (i.e., a random timepoint not titrated to the participant). Additionally, we increased experimental control by instructing subjects not to balance their response frequency across blocks (see below). Experiment 2b served another purpose that is not directly related to the current work and hence these parts are discussed only in the Supplementary materials section. Experiment 2b was similar to Experiment 2a but included two additional between-subject conditions in which instead of value-free feedback participants received feedback indicating attainment of either negligible or substantial sums of money. We did so initially to allow a comparison of value-free feedback to studies in which a similar free-operant procedure with tangible outcomes was used (O’Callaghan et al. 2019; Shanks and Dickinson 1991; Vaghi et al. 2019). As this discussion is not directly relevant to the model underlying ‘pure’ effectiveness, which is the focus of the current study, only the value-free feedback is presented in the main text, with the additional between-subject conditions appearing in the Supplementary materials. Experiment 2b was pre-registered on OSF (Hemed et al. 2017).²

Methods

Participants

Forty-One naïve students from the University of Haifa were recruited. 77% of which were female, ages 23–27 (M = 24.43, SD = 3.85). We did not conduct an a-priori power analysis, but the current sample (41) and design allows to detect of an effect size of ~ 0.4 (as found on the action-effects present, inaction-effects absent vs. action-effects absent, inaction-effects absent contrast of Experiment 2a, for the RT data) with a power of ~ 0.85. We indicate the effect size found on Experiment 2a as this was the first time we used the current task in a within-subject design.

Task, procedure, and apparatus

Excluding the monetary-gain conditions mentioned above, Experiment 2b was identical to Experiment 2a save for two further changes. First, the timepoint for determining if the current trial is a No-Response trial was sampled from a pre-generated normal distribution of 200 values (μ = 650 ms, σ = 40; based on the results of Experiment 2a and designed to ensure that the timing of inaction-effects was (a) not late in the trial and (b) would not truncate the response window). Second, between blocks participants were informed of the percentage of trials in which they responded during the recent block (rather than the cumulative percentage as in Experiment 3) and were reminded to maintain a rate of 50% throughout the coming block. The purpose of this modification was to ensure that participants would not try to balance their responses across blocks but would treat each block independently. As in Experiment 2a, block order was randomized for each participant to avoid order effects.

Results

Data preprocessing

No-Response trials (45.41% of raw data) were not analyzed. We filtered out in total five outliers (12.2% of N = 41) which were either extreme (± 2 SD) in RF (three participants, 4.3%) and in RT (two participants, 5.38%) or had less than 50% of correct responses on Response-Trials (one participant, ~ 1.1%; which was also one of the RT-outlier participants). Out of the remaining subjects (87.8% of raw data) we filtered out incorrect responses (~ 5.55%), fast (0.02%; below 200 ms) and slow responses (0.07%; above 700 ms). Filtration (both complete participants and individual response-trials) resulted in the loss of ~ 17% of the data.

Data analyses

We used a repeated-measures ANOVA and paired t-tests, as in Experiment 2a. First, we analyzed RT data (plotted in Fig. 4A–C). A two-way within-subject ANOVA matched our predictions—showing significant effect of action-effects [F(1, 35) = 11.60, p = 0.002, Partial-η² = 0.250] and no influence of inaction-effects [F(1, 35) = 2.75, p = 0.11, Partial-η² = 0.070] or the interaction term [F(1, 35) = 0.35, p = 0.56, Partial-η² = 0.010]. We followed by comparing the baseline condition (action-effects present, inaction-effects absent) to all other conditions. As predicted, we found no difference between the action-effects present, inaction-effects absent condition or the action-effects present, inaction-effects present condition [Two-tail—t(35) = 1.33, p = 0.191, Cohen's d = 0.19, 95% CI (− 0.1, 0.49), BF 1:0 = 0.40]. In line with our prediction, we found faster RT for the action-effects present, inaction-effects absent condition, compared with the action-effects absent, inaction-effects present condition [Upper-tail—t(35) = 3.40, p = 0.001, Cohen's d = 0.51, 95% CI (0.19, 0.82), BF 1:0 = 39.700] and the action-effects absent, inaction-effects absent condition t [Upper-tail—t(35) = 3.02, p = 0.002, Cohen's d = 0.29, 95% CI (0.09, 0.49), BF 1:0 = 16.32].

Fig. 4

Experiment 2b. Response speed increases with the presence of action-effect but is insensitive to the presence or absence of inaction-effects (A–C). Response frequency, on the other hand, is not influenced by the presence of action-effects and lowered by the presence of inaction-effects (B–D). A and B Individual and group means of response time (A) and response frequency (B). Error bars indicate 95% CI of estimated marginal means. Dashed lines indicate the grand average. C and D Bayesian estimation of the contrasts between the action-effects present, inaction-effects absent condition, and all other conditions. Horizontal lines indicate 95% HDI

We used a two-way repeated-measures ANOVA to analyze the RF data (see Fig. 4B–D). We found no effect of action-effects on response frequency [F(1, 35) = 0.05, p = 0.82, Partial-η² = 0.002], a significant effect of inaction-effects [F(1, 35) = 5.07, p = 0.03, Partial-η² = 0.130] and no interaction [F(1, 35) = 0.12, p = 0.73, Partial-η² = 0.004]. We compared the action-effects present, inaction-effects absent condition to all other conditions and found that as predicted, response frequency was significantly lower when both action-effect and inaction-effects were present (yet Bayesian analysis shows that the current data is insensitive) [Lower-tail—t(35) = − 1.87, p = 0.035, Cohen's d = − 0.41, 95% CI (− 0.86, 0.04), BF 1:0 = 1.65]. We also found lower response frequency for the contrast with action-effects absent, inaction-effects present [Lower-tail—t(35) = − 1.96, p = 0.029, Cohen's d = − 0.46, 95% CI (− 0.96, 0.03), BF 1:0 = 1.90]. In contrast with our predictions, we found no significant difference between the baseline condition and the action-effects absent, inaction-effects absent condition [Lower-tail—t(35) = − 0.43, p = 0.336, Cohen's d = − 0.10, 95% CI (− 0.57, 0.37), BF 1:0 = 0.26].

Experiment 3a

In Experiments 1 and 2a–2b, in line with our hypothesis, we found that action-effects decreased response speed, but inaction-effects did not (and there was no interaction between the two). Another, seemingly stable pattern, is an asymmetry between the robust reduction of response frequency by inaction-effects and the weaker influence (at best) action-effects have on facilitating response frequency. This pattern for response frequency was not predicted based on previous work on ‘Delta-P’ (e.g., Vaghi et al. 2019) as well as our work on control feedback (Karsh and Eitam 2015a, b). In Experiment 3a, we aimed at replicating the facilitating effect of action effects using a more controlled, cued task rather than a free operant procedure, given the noisiness of the response frequency measure.

Methods

Participants

One hundred and twenty-one students at the University of Haifa were recruited, 66% were females, ages 18–39 (M = 24.96, SD = 3.47). None of them participated in our previous experiments. We did not conduct a-priori power analysis, but about 30 participants per group would allow us to detect a Cohen’s d of 0.8 with a statistical power (1 − β) of ~ 0.92 (for the RT data contrast of action-effects present, inaction-effects absent vs. action-effects absent, inaction-effects absent; see Experiment 1 “Participants”).

Task

The trials on Experiment 3a were identical to Experiments 2a–2b, except that each trial was preceded by a 500 ms Respond/Do not respond auditory cue (a 440 or 196 HZ tone, respectively), followed by a 200 ms ISI and only then by the imperative cue and the response window.

Participants were randomly allocated to one of the experimental conditions (manipulated between subjects) and performed only this condition throughout all experimental blocks (three blocks, each consisting of 120 trials, 50% Respond cue trials, 30 repetitions of each cue location in random order). A commission error (responding on a Do not respond cue trial or an omission error (no response on a Respond cue) trial did not lead to action-effects or inaction-effects, regardless of the experimental condition. Additionally, given the auditory cue, we had substantial control regarding whether a participant would respond to a cue or forgo the trial. Therefore, we titrated the timing of inaction-effects to the participants’ response speed, set to the median of all correct responses on previous Response trials, including the practice block (see below).

Procedure and apparatus

Participants were familiarized with the auditory cues and completed a short training block (32 trials) during which the experimenter gave them vocal feedback on their performance, but they did not receive any action-effects or inaction-effects regardless of the experimental condition. They then completed the three experimental blocks (120 trials each), separated by self-paced breaks. Following the task they completed a debriefing questionnaire and the SOA scale (Tapal et al. 2017). Responses were collected using a response box (Empirisoft, DirectIN High-Speed Button-Box). Sounds were played through standard PC speakers.

Results

Data preprocessing

No-response trials (50.82% of the raw data; trials in which participants did not respond, regardless of the auditory cue or the response accuracy) were not analyzed. We filtered out eight (6.61% of N = 121) outlier (± 2SD) participants in either Response Frequency (five participants, ~ 4.1%) or Response-Time (three participants, ~ 2.5%) or had less than 50% of correct responses on Response Trials (three participants, ~ 2.5%). Out of the remaining subjects (93.39% of raw data) we removed incorrect responses (~ 1.8%), fast (0.44%; below 200 ms) and slow responses (0.5%; above 700 ms). Filtration of invalid Response trials (both complete participants and individual trials) resulted in loss of 8.83% of the raw data.

Data analyses

Like Experiment 1 we used the Welch–Satterthwaite correction for degrees of freedom for independent samples t test. First, we analyzed RT data (see Fig. 5A–C). As predicted, a two-way between-subject ANOVA showed that action-effects significantly influenced RT [F(1, 109) = 7.3, p = 0.008, Partial-η² = 0.060], but inaction-effects did not [F(1, 109) = 0.24, p = 0.62, Partial-η² = 0.002] and neither did the interaction [F(1, 109) = 0.57, p = 0.45, Partial-η² = 0.005]. We continued to compare the action-effect present, inaction-effects absent condition to all other conditions. In line with our predictions, we found no difference in RT when both action-effects and inaction-effects were present [Two-tail—t(56) = − 0.20, p = 0.842, Cohen's d = − 0.05, 95% CI (− 0.58, 0.47), BF 1:0 = 0.27]. Additionally, as predicted RT was significantly slower on the action-effects absent, inaction-effects present condition compared with the baseline condition [Upper-tail—t(54.48) = 2.27, p = 0.014, Cohen's d = 0.60, 95% CI (0.06, 1.14), BF 1:0 = 4.28], but only nominally slower on the action-effects absent, inaction-effects absent [Upper-tail—t(52.63) = 1.35, p = 0.092, Cohen's d = 0.36, 95% CI (− 0.18, 0.9), BF 1:0 = 1.02].

Fig. 5

Experiment 3a. Response speed increases with the presence of action-effect but is practically insensitive to the presence or absence of inaction-effects (A–C). Response frequency was not influenced by the presence of either action-effects or inaction-effects, or their interaction (B–D). A and B Individual and group means of response time (A) and response frequency (B). Error bars indicate 95% CI of estimated marginal means. Dashed lines indicate the grand average. C and D Bayesian Estimation of the contrasts between the action-effects present, inaction-effects absent condition, and all other conditions. Horizontal lines indicate 95% HDI

Second, we analyzed RF data (see Fig. 5B–D). A two-way between-subject ANOVA did not find a significant effect of action-effects [F(1, 109) = 0.01, p = 0.92, Partial-η² = 0.000], inaction-effects [F(1, 109) = 0.58, p = 0.45, Partial-η² = 0.005] or the interaction term [F(1, 109) = 2.38, p = 0.13, Partial-η² = 0.020]. We continued to compare the action-effect present, inaction-effects absent condition to all others. In contrast with our prediction, we found that when both action-effects and inaction-effects were present, response frequency was significantly higher [Lower-tail—t(38) = − 1.96, p = 0.029, Cohen's d = − 0.52, 95% CI (− 1.05, 0.02), BF 1:0 = 2.500]. Additionally, we did not find the predicted lower response frequency when action-effects were absent, regardless of whether inaction-effects were present [Lower-tail—t(52) = 0.50, p = 0.689, Cohen's d = 0.13, 95% CI (− 0.4, 0.66), BF 1:0 = 0.19] or absent [Lower-tail—t(53) = 1.17, p = 0.876, Cohen's d = 0.31, 95% CI (− 0.23, 0.85), BF 1:0 = 0.14], both with Bayesian support for the null hypothesis.

Experiment 3b

In Experiment 3a, the pattern of response speed found in Experiments 1 and 2a–2b was replicated. However, the pattern of results for the response frequency measure was in contrast with the one predicted nor was it consistent with the unpredicted pattern that was found in the other experiments in this study. It is possible that the tightly controlled nature of the task (using auditory cues, rather than free operant procedure) minimized the (albeit, limited) ability of action-effects and inaction-effects to influence response frequency, even though participants still displayed a similar pattern of RT to that seen in all previous experiments.

Our interim conclusion regarding the facilitating effect of value-free effects on response frequency is weak as it is highly sensitive to participants’ interpretation of the task, their interpretation of the relevance and informativeness of the perceptual effects in relation to the task’s goals, their interest in the task and so on. In hindsight, this volatility is consistent with the theoretical framework suggested by us elsewhere (Karsh and Eitam 2015b) which specifies that action-selection (e.g., how and how much to respond) depends on participants’ current high-level cognitions of which Delta-P is only a small and potentially not key determinant.

The volatility of the effect of own-action effects on response frequency is very different from the robustness of the effect of (predictable and immediate) own action effects on response time which also attests to the modular nature of the mechanism producing them.

This current experiment aimed to alleviate a concern raised by a previous reviewer of the paper³ that in Experiment 3a participants were able to fully disambiguate action-effects and inaction-effects using the auditory cues they received; thus they could have disregarded the inaction-effects occurring on No-Response trials as irrelevant to their behavior (although their timing was titrated, see Experiment 2a), and that is allegedly, the reason inaction-effects did not influence response speed. Note that this alternative explanation is not likely given that we observed a similar pattern of response speed when using a free-response task (Experiments 1 and 2a–2b) and a cued-response task (Experiment 3a). Yet to alleviate this concern, we aimed to dissociate the auditory cues and action-effects, hypothesizing that we would still find the pattern of results for response speed that we found in previous studies, and the same (with less certainty to the nosier measurement) for response frequency.⁴

Methods

Participants

Eighty-eight naïve students from the University of Haifa were recruited. 67% of which were female, ages 19–34 (M = 24.21, SD = 2.92). To circumvent issues of the sensitivity of the data, our stopping rule for data collection was that all hypotheses reach a conclusive BF₁₀ (< 0.33 or > 3), regardless of whether the pattern of results fits our predictions or not. See pre-registration on the OSF project for more details (Hemed et al. 2017). On Experiments 2a and 2b (both also with a within-subject design), we found an effect size of Cohen’s d ~ 0.35 for the RT contrast of action-effects present, inaction-effects absent vs. Inaction Effects absent. We did not conduct a priori power analysis, but given the sample obtained using the Bayesian analysis stopping rule, our sample had a posteriori statistical power (1 − β) of ~ 0.95 to detect a similar effect.

Task and design

As in Experiment 3a, we used Respond and Do not respond auditory cues (here we used tones with the frequency of 440 and 1046 Hz to make them easily distinguishable). If a participant responded before a randomly selected timepoint, the trial was considered a response trial, and if they did not—a no-response trial. The timepoints were sampled from a random distribution, with the same parameters as in Experiment 2b. Action-effects and inaction-effects were independent of the auditory cues and depended solely on the experimental condition. During the practice block, no action-effects or inaction-effects were shown, and no auditory cues were played (i.e., a trial included only the 850 ms response window and 700 ms ITI). The experiment had a within-subject design, where the experimental conditions used in the study were manipulated in separate blocks and in a random order, as in Experiments 2a–2b.

Procedure and apparatus

Participants first performed a practice block (32 trials), during which they received feedback from the experimenter. Then, they were familiarized with the Respond/Do not respond tones and completed the four experimental conditions in four separate experimental blocks, in a random order (200 trials each, 50% Response-tone trials), as in Experiments 2a–2b. The equipment used was identical to Experiment 2b.

Results

Data pre-processing

Two participants were excluded before any pre-processing as they failed to comprehend the instructions, requiring a 2nd run of the practice block. No-Response trials (51.25% of raw data) were not analyzed. We filtered out seven participants (~ 8% of N = 88), which were outliers (± 2 SD) in response frequency (two participants; ~ 2.28%) or response speed (five participants; ~ 5.68). Out of the remaining subjects (92% of raw data) we filtered incorrect trials (~ 2.63%), fast or slow responses (0.02% and 0.03%; respectively). Filtration of invalid Response-trials (both complete participants and individual trials) resulted in the loss of 10.4% of the data.

Data analysis

As in Experiments 2a–2b, we used paired samples t tests to compare between the different conditions. First, we analyzed the response time data (see Fig. 6A–C). As predicted, a two-way within-subject ANOVA revealed that action-effects had a significant influence on RT [F(1, 80) = 49.07, p < 0.0001, Partial-η² = 0.380], while inaction-effects did not [F(1, 80) = 1.17, p = 0.280, Partial-η² = 0.010] or the interaction [F(1, 80) = 2.74, p = 0.100, Partial-η² = 0.030]. We continued to compare the action-effect present, inaction-effects absent condition to all others. As predicted, we found that when both action-effects and inaction-effects were present, RT was not significantly different [Two-tail—t(80) = 0.52, p = 0.602, Cohen's d = 0.04, 95% CI (− 0.12, 0.21), BF 1:0 = 0.14]. Also, as predicted we found that RT was slower when action-effects were absent, regardless of whether inaction-effects were present [Upper-tail—t(80) = 4.82, p < 0.001, Cohen's d = 0.41, 95% CI (0.24, 0.59), BF 1:0 = 4910.21], or absent [Upper-tail—t(80) = 6.32, p < 0.001, Cohen's d = 0.56, 95% CI (0.37, 0.74), BF 1:0 = 1,727,065.59].

Fig. 6

Experiment 3b. Response speed increases with the presence of action-effect but is insensitive to the presence or absence of inaction-effects (A–C). Response frequency, on the other hand, is facilitated by the presence of action-effects, but is not affected by the presence of inaction-effects (with a non-significant interaction; B and D). A and B Individual and group means of response time (A) and response frequency (B). Error bars indicate 95% CI of estimated marginal means. Dashed lines indicate the grand average. C and D Bayesian Estimation of the contrasts between the action-effects present, inaction-effects absent condition and all other conditions. Horizontal lines indicate 95% HDI

Second, we analyzed the response frequency data (see Fig. 6B–D). A two-way repeated-measures ANOVA found that action-effects significantly influenced RF [F(1, 80) = 24.69, p < 0.0001, Partial-η² = 0.240], but inaction-effects did not [F(1, 80) = 1.72, p = 0.190, Partial-η² = 0.020], with a marginally significant interaction between the two [F(1, 80) = 3.64, p = 0.060, Partial-η² = 0.040]. We continued to compare all conditions to the baseline condition (action-effects present, inaction-effects absent). In contrast with our predictions, we did not find significantly lower response frequency when both inaction-effects and action-effects were present [Lower-tail—t(80) = − 0.48, p = 0.318, Cohen's d = − 0.06, 95% CI (− 0.32, 0.19), BF 1:0 = 0.19]. However, we did confirm our prediction that response frequency is higher on the baseline condition (action-effects present, inaction-effects absent) compared with the condition where only inaction-effects are present [Lower-tail—t(80) = − 2.72, p = 0.004, Cohen's d = − 0.35, 95% CI (− 0.62, − 0.09), BF 1:0 = 7.58] or when both action-effects and inaction-effects are absent [Lower-tail—t(80) = − 4.85, p < 0.001, Cohen's d = − 0.65, 95% CI (− 0.93, − 0.36), BF 1:0 = 5525.65].

General discussion

The past decade or so of study converged on the position that SOA can be parsed as originating from conceptual or from sensorimotor sources (Dewey and Knoblich 2014; Moore 2016; Moore et al. 2009b; Synofzik et al. 2008; Wen and Haggard 2020).

The current study adds to this growing consensus by dissociating between sensorimotor and conceptual SOA based on their functional (input–output) behavior and their downstream reinforcing effects. Specifically, conceptual SOA is, among other influences, also driven by a general-purpose judgment of contingency (which we initially predicted to follow the Delta-P rule, [P(E|R)—P(E|¬R)]) and reinforces volitional action. The effect of this influence was weak and inconsistent in our experiments potentially because there is more 'cognition' at play (and hence less experimental control) in situations where no tangible rewards are to be obtained (White 1959).

Conversely, sensorimotor SOA follows a simpler—conditional probability—function P(E|R) and reinforces response execution or the specific motor program that is credited with successfully predicting the effect; empirically, this effect is more robust compared to the effect of 'Delta-P' on response frequency.

Crucially, modulation of RT was found to be fully indifferent to the presence or absence of inaction-effects, as predicted. This supports the assumption that this 'evaluation' of agency is available only following a motor action (Wolpert et al. 1995). We plot a summary of the findings of the current study in Fig. 7 below and continue by discussing the theoretical implications of our findings, followed by several caveats of the current study.

Fig. 7

Forest plots of the study's findings. Response time (top row) is reinforced by the presence of action-effects and insensitive to the presence or absence of inaction-effects. In contrast, response frequency (bottom row) is weakly facilitated by action-effects but also weakly reduced by the presence of inaction-effects. The colored plus signs depict the Cohen’s d effect size, the vertical line is the effect size reported on the results section for each of the contrasts performed between the ‘baseline’ experimental condition—action-effects present, inaction-effects absent and each other experimental condition. The horizontal line is the corresponding 95% CI. The black dot indicates the average effect size across all experiments for this contrast

Theoretical implications

Some of us (Karsh and Eitam 2015b) proposed the Control-Based-Response-Selection-Framework (abbreviated CBRS) as a framework interpreting the findings that SOA reinforces effective actions as well as outlining the potential factors modulating such reinforcement. The model is composed of two levels, based on the different types of information they 'consume'. One level of the model is based on a general purpose cognitive process (i.e., cognition) that forms the conceptual SOA—a causal judgement of action-outcome contingency such as Delta-P or based on applying explicit knowledge of the environment. This general purpose process influences action-selection at the consciously accessible, person-level (“Whether to act, or with which effector”), here measured as response frequency. Our working hypothesis is that this level may also be affected by the motor-system but only indirectly, potentially through interpreting sensations such as the fluency of responding (Chambon and Haggard 2012; Synofzik et al. 2008; cf. Wen 2019). The second level of the model is modular, and based on sensorimotor processes and is unaffected by higher cognitions such as beliefs, desires or causality judgements (e.g., ones of the form of Delta-P). This level utilizes a 'Comparator' (see introduction) that provides a sensorimotor prediction of the consequences of (and only given) a motor response. The function of this level is to evaluate the effectiveness of a motor program by testing its ability to predict the effect of that motor program on the environment–-utilizing the results of the sensorimotor predictions tested by the comparator. Responses are reinforced relatively to the degree they led to a confirmation of sensorimotor prediction/minimization of sensory prediction error (SPE)—by crediting the specific motor-program that is related to the recent prediction of the Comparator. Thus, the sensorimotor level reinforces actions on a sub-person, consciously inaccessible level (here measured as response latency). In other terms, the control-based-response-selection framework, argues that control over the environment reinforces action selection and action execution—based on a sensorimotor and non-sensorimotor evaluation of the control an action has over the environment.

The current study provides direct support for the CBRS framework. As described above—the sensorimotor level SOA (but not the conceptual SOA) can modulate response-speed. Here we find that modulation is sensitive only to the presence or absence of action-effects, P(E|R) and not to the presence or absence of effects that occur when no motor response was produced, P(E|¬R), which is what is predicted if a comparator-like mechanism is involved.

As for modulation of action-selection (e.g., whether to respond), our current results are mixed. On one hand, we did not find a strong influence of Delta-P—a functional description that successfully captured people’s (and other animals) judgment of contingency, including the special case of causality, on response frequency. On the other hand, we found that response frequency was inhibited by the presence of inaction-effects (contra to response speed) and, to a lesser degree, facilitated by action-effects (with no clear interaction between the two).

The latter does not provide strong evidence that Delta-P is the prominent computation used by participants in the current study to select what to do or how much to do it which is somewhat reasonable, given cases in which people sometimes diverge from Delta-P even for causality judgements per-se (see Spellman 1996 for a review). It is not all that surprising that on the effect of the conceptual SOA on response frequency is less robust, given that both people's judgements are influenced by a myriad of factors that might not be well understood yet (Wen 2019) and are not under sufficient experimental control and/or may vary between contexts. For example, evidence from a different paradigm indicate that low-level temporal delay could diminish response frequency in general, potentially by affecting sensorimotor processes (Karsh et al. 2021). However, it is not clear whether the SPE related to the temporal delay reduced response frequency directly or through conceptual SOA, and how it is weighted. A second source of variability in response frequency is that action selection (indexed here by response frequency) is itself affected by more factors (in comparison to execution). Hence, both the input (conceptual SOA) and output (action selection) are ‘noisier’ and more multidetermined than sensorimotor processes and response execution.

Indeed, our study finds that response frequency, is most certainly not influenced only by a sensorimotor prediction. Which is in striking contrast with response speed. This peripheral effect of 'own-action effects' is also consistent with CBRS which specifies that the selection of actions (i.e., volitional action) is influenced by multiple inputs of which the judgement of one’s SOA of perceived changes is but one and not necessarily the most important. Other, potentially more influential inputs may include abstract knowledge about the situation (e.g., task instructions), one’s attitudes towards the experimental situations, the inclination to explore the environment, degree of engagement with the task or mere perception of how one’s performing on the task. As none of the above (per CBRS) serve as inputs to the process reinforcing the specific motor program selected, they contribute to the dissociation between measures that are sensitive to only the modular elements of the motor-system (as is RT in the current experimental context) and ones that are less modular being related to higher cognitions such as beliefs, etc.

Here we would also like to address a possible criticism of the current study. It was suggested by one of our reviewers that mere information about performance, or response accuracy, drives response frequency, rather than information regarding control over the environment. There is no denying that in the task used in this study information regarding performance is confounded with information regarding control—simply because participants are required to press the correct key to receive action-effects. As elaborated above, CBRS, our theoretical framework, allows for information regarding expectations or performance to influence action-selection via conceptual SOA. While in theory, information about performance and specifically here, about response accuracy could have facilitated response frequency, we find it unlikely that it did in the current study, for the following reasons. First, by this interpretation information about response accuracy should have been positively correlated with response frequency. That is, receiving feedback about being accurate should facilitate further responses (i.e. increase response frequency). But in the current study we find no consistent correlation between accuracy (and hence, performance feedback) and frequency of responding, undermining this hypothesis (see supplementary materials section for the analyses). Second, success in our task is composed of not one, but three factors—responding using the correct key (accuracy), responding prior to the end of the response window, and adhering to a specified response frequency over the long run (e.g., responding on 50% of the trials). Regarding the speed of a response and selecting the correct key, feedback about performance is readily available—if participants did not respond accurately or quickly enough, they did not receive action-effects. Information regarding performance in terms of meeting the required response frequency was given very sparsely (e.g., every 200 trials for experiments 2a–2b and 3-b). Although feedback on response accuracy is readily available, as we write above it was not correlated with response frequency, so again, there is no basis to the claim that it influenced response frequency. Third, participants across all conditions responded correctly to the cue—regardless of whether they received feedback about their response frequency at any point in time (i.e., participants on the action-effect absent groups, in experiments, 1 and 3a). Fourth, response frequency in the action-effect present, inaction-effect absent condition was greater than on the action-effect present, inaction-effect present condition—although both received identical feedback on their response accuracy (see supplementary materials section for response accuracy data). Finally, in previous studies by our group (Karsh and Eitam 2015a; Karsh et al. 2016) as well as others (Penton et al. 2018) employed a free-choice version of the task used here. In that version, participants are asked to respond by selecting, in each trial, a key at random in response to a general imperative cue. The typical pattern is that participants tend to choose the key that is associated with the highest probability of leading to an action-effect, at the expense of the other keys. This is in fact a demonstration of response frequency being associated with poorer performance on the task, as it signals deviation from random responding (more strongly so as people’s perception of randomness is akin to probability matching; Bar-Hillel and Wagenaar 1991). In one of the above studies (Karsh and Eitam 2015a), no association between participants' ratings of their intention to cause an effect and their perceived success in responding randomly (the task goal) was found. If participants were to have mistakenly perceived the action-effects as feedback on successfully random—a positive correlation should have been detected, rather than no correlation at all.

Note that all the above lies somewhat besides the key point of the current study—which is that sensorimotor information (here, the conditional probability of an effect given a response) reinforces response speed, but other types of information do not. Admittedly, the current study cannot completely rule out the possibility that information regarding performance or response accuracy specifically, facilitated response frequency, regardless of how unlikely we think this explanation is. Future studies could answer this question using version of our task where information regarding control and information on response accuracy are dissociated, for example using one of the free-choice variations of our task (cf. Karsh and Eitam 2015a), one similar to the task we used here where incorrect responses also lead to action-effects, or by having the action effects fully informative about correctness but to some degree uncontrolled (e.g., spatially unpredictable).

Predictions predictions

More broadly, the current study’s findings are relevant for a current debate on how does the mind integrate information to make predictions about upcoming events (Dogge et al. 2019; Press et al. 2020; Yon and Frith 2021). Dogge et al. (2019) argued that while sensorimotor-based internal models (e.g., the comparator) are fit to make predictions regarding bodily-sensations (e.g., being tickled vs. tickling oneself; Blakemore et al. 2000), they are a poor fit for predicting extra-body effects (like the action-effects in our study). Specifically, they argue that in the context of paradigms used to study the influence of action-effects on perception (like sensory attenuation or intentional binding), sensorimotor mechanisms provide a poor explanation as there is evidence that effects that are considered to be implicit measures of agency, such as intentional binding are sensitive to top-down influences like beliefs and explicit knowledge (see also the Introduction section above). As an alternative they proposed a hybrid internal model (i.e., comparator) with two alternative routes—one uses an efference copy (a 'forward model' similar to the original Comparator model), while the other uses conceptual information such as beliefs and causal reasoning. Both models can make predictions regarding the perceived effect of an action, but they are used in different circumstances. The lower-level process is used for overlearned and body-related effects (e.g., sense of being tickled), while the higher-level process is used in novel contexts and events that are related with the environment (and possibly less with own-actions). Their model does not impose rigid constraints on whether the low- or high-level processes can be used for a specific prediction, only indicates what might be the general function of each process. This model does share some similarity with CBRS, although (a) CBRS highlights the impact of the prediction process on further action-selection and (b) in CBRS the two levels can share some information but make qualitatively different predictions, regardless of whether a specific contingency is overlearned or novel (see our work on rapid updating of action’s effectiveness in dynamic environments by what seems to be the low-level process; Hemed et al. 2020).

The current study moves this discussion forward by dissociating between (a) the simultaneous operation of a purely (modular) sensorimotor forward model-based prediction and (b) a general-domain process like causality judgements. While the former (i.e., the Comparator) reinforces motor programming when a sensorimotor prediction is confirmed, (cf. Tanaka et al. 2021) the latter reinforces the action that is judged to be causally effective.

Predictions postdictions

The focus of CBRS is on the dissociation between sensorimotor and conceptual types of SOA. However, there are other ways to parse SOA, for example, by considering processes that incorporate only prediction and ones that consider both prediction and 'postdiction', sometimes termed retrospective and prospective SOA, respectively (Chambon and Haggard 2013).

The utility of this dissociation can be demonstrated by considering an intentional binding study (Moore et al. 2009a). Moore and colleagues manipulated the probability of receiving action- and inaction-effects (i.e., Delta-P). They found out that a high probability for action-effects led to intentional binding effects regardless of Delta-P and even on trials in which no effect followed the action. Conversely, when the conditional probability of action-effects was low, intentional binding was found only following action-effects and only if Delta-P was positive. The authors concluded that probability of action-effects and Delta-P may be used by two different processes to evaluate effectiveness, similarly to our point in this work. Crucially though, they argued that the mechanism that is sensitive only to the action-effect probability is a sensorimotor predictive process, (i.e., the Comparator) that induces ‘prospective’ SOA. On the other hand, Delta-P was attributed to a conceptual, ‘postdictive’ process, i.e., causal inference, as it occurred only following action-effects and was dependent on Delta-P.

While our findings relate to the dissociation found by Moore et al.’s (2009a), they offer a different perspective on the parsing of prospective and retrospective agency.

First, Moore et al., used a measure of intentional binding as a proxy for SOA, a measure that includes a deliberate estimation of the time that elapsed between two events, usually an own-action and a candidate action-effect. Importantly, the measure is de-facto retrospective and has been showed to be also affected by 'cognitions' about the situation (Desantis et al. 2011).

Second, as others have stated (Gozli 2019; cf. Gozli and Dolcini 2018), associating sensorimotor processes with prospective SOA and conceptual processes with retrospective SOA maybe misguided as both involve both prediction and postdiction. Our proposal here is that motor programs are reinforced postdictively by a modular sensorimotor process. Elsewhere, we have shown that sensorimotor SOA as measured by facilitation of reaction times is also highly sensitive to the factors regarding prediction (e.g., precision; Hemed et al. 2020).

Relatedly, Gozli and Dolcini (2018) and Gozli and Gao (2019) also suggested how the reinforcement of action (and specifically exploration) can result from loss of control over the environment, in the context of hedonic stimuli (Gozli and Dolcini 2018; Gozli and Gao 2019). While there seems to be some hedonic attribute to control (and its loss; see introduction), it is not yet clear what level of action-selection this applies to. Our previous findings (Hemed et al. 2020) have shown that loss of control inhibits action rather than facilitates it, at least when the sensorimotor SOA is concerned (measured by RT). Regarding the conceptual SOA, the simple answer is that we are not sure. The current study was not designed to answer how dynamically degrading action-outcome contingency would influence response frequency (we review below a study by Penton et al. 2010that did test such dynamically changing contingencies). We speculate that it would reduce response frequency, as we found that lack of action-effects inhibits response frequency. Still, it could be that a dynamic change in action-outcome contingency similar to what Gozli and Gao (2019) suggest would reinforce actions through other mechanisms that are not related to CBRS (e.g., explicit decision for exploration; Watanabe and Taga 2009; Zaadnoordijk et al. 2018).

Subjective reports of SOA

A final note refers to the current study's results regarding people’s self-reported SOA. We do not present these findings in full here (but see Supplementary Materials) as the experimental designs in the current study were geared to dissociate between the influence of factors shown to be associated with the influence of the two ‘types’ of SOA on behavioral measures rather than to sensitively measure people’s judgement of agency (conceptual SOA). More specifically, three of the five experiments in the current study used a within-subject design and regardless of the design, subjective reports were always collected only at the end of each experiment rather than during the experimental blocks. Notwithstanding this caveat, it is interesting to note that participants’ subjective reports were not strongly associated with Delta-P. Generally, participants in conditions where action-effects were present reported similar levels of feeling of control over the environment regardless of the presence of inaction-effects. This leads to the question of whether the causal judgement or ‘regularity detection’ mechanism suggested by Wen and Haggard (2020) is different from a subjective judgement of agency. Importantly, two recent studies show that response frequency, Delta-P and causality judgements are correlated, at least in the context of obtaining desired outcomes. Both studies used a free-operant task with varying probabilities of action- and inaction-effects signaling monetary gains, (O’Callaghan et al. 2019; Vaghi et al. 2019).

As an interim conclusion, we speculate that in the context of tangible outcomes (vs. value-free, action-effects) response frequency could follow a different computation, one where response frequency is scaled by contingency and reward outcome. Another possible explanation for this discrepancy may be found in a recent study by Yon et al. (2020). In the study, the conceptual component of agency was quantified using several approaches, including signal detection, it was found- that explicit judgements of agency are biased upward (“I am in control”), due to overweighting of action-effect occurrences (differently from the unbiased description of causality suggested by Delta-P; Wasserman et al. 1983, but see Spellman 1996). Yet a third possibility for the discrepancy between previous and current findings on the relationship between Delta-P and people's deliberate judgements of agency is that the link between the conceptual SOA and behavior is itself context-specific (Tapal et al. 2017). This may indeed be the case as humans tend to repeat the most effective actions (in the neutral sense of merely influencing the environment) when exploring a novel environment, but may not tend to do so when they have a clear goal or an urgent need that requires fulfillment—when actions that are most conductive to the goal/need are selected (Nafcha et al. 2016; White 1959). We contrast this with the fixed or decontextualized relationship between behavior and reinforcement from a mere sensorimotor prediction error (i.e., the sensorimotor SOA). The lack of sensitivity to the context of the latter form of reinforcement is also seemingly due to its modular nature and specifically, its lack of conceptual input (see Heald et al. 2021).

Actions and inactions

One caveat that we would like to note regarding the current work, relates to an assumption we make regarding the sensorimotor SOA. Our predictions are premised on the assumption that the sensorimotor evaluation of an action’s effectiveness relies on an efference copy, hence action-effects are meaningful to the sensorimotor SOA and inaction-effects are meaningless. However, some might say that this is a problematic assumption as there is evidence that there is an efference copy even for planned or imagined actions. Below we discuss other findings, from studies using experimental tasks and measures which are both similar and different than ours. For additional theoretical and empirical comparisons other than the ones discussed below, please refer to the extended general discussion section in the supplemental materials.

First, Penton and colleagues (Penton et al. 2018), tested the influence of action-effects and inaction-effects on response time and frequency, using a variant of our free-choice task (Karsh and Eitam 2015a). On each trial, their participants were asked to decide whether to respond or not, and if they did respond, they were asked to select a key at random, out of four keys that were associated with different action-effect probabilities (0, 0.3, 0.6 or 0.9). On different blocks, the probability of inaction-effects was either 0, 0.3, 0.6, or 0.9, each identified by a differently colored frame shown on the screen. Penton et al., found that response frequency was modified by both action-effects and inaction-effects, and somewhat in line with our findings, that response frequency is weakly facilitated by action-effects and is more strongly inhibited by inaction-effects. However, they also found that response speed was influenced by the conditional probability of action-effects only when there was a low probability of inaction-effects, while we repeatedly find that response speed was influenced strictly by the presence or absence of action-effects, regardless of the presence or absence of inaction-effects. The findings by Penton and colleagues (Penton et al. 2018) regarding response frequency fit the CBRS framework's predictions—the conceptual evaluation of effectiveness considers information both from own-action effects and externally generated effects. However, their data on response speed are different than ours (and, more importantly, conflicts theoretically).

One possibility for the source of the apparent discrepancy in results is that is that in Penton et al.’s study participants prepared their responses in advance and withheld them after planning their response. Unlike some of the previous studies using the task, there was no attentional probe, so participants were always required to use only a specific set of responses (cf. Karsh and Eitam 2015a; Hemed et al. 2020). In our study, it was impossible for participants to prepare a response in advance and then decide not to execute it, as a specific response was required per cue. However, in Penton et al.’s study participants were asked to first select at random whether to respond or forgo the trial, and then select at random a key to respond with. Studies involving the measurement of scalp potentials (EEG), and specifically a specific evoked response potential (ERP) that has been shown to reflect the selection of a response (i.e., which hand to respond with), the Lateralized Readiness Potential (LRP) in the context of stop-signal tasks showed LRP's even when responses were withheld (Huster et al. 2013; Li et al. 2008). If this was indeed the case in Penton and colleagues' study an efference copy could have been generated even if the action was not eventually executed. This would be consistent with our theoretical proposal.

Another possibility is that Penton and colleagues detected the influence of inaction-effects on response speed due to the comparative ease of their task—on response-trials, participants were required to respond with any random key out of the response set. Because they did not need to attend any spatial cue as in the current study, their participants had ample cognitive resources to evaluate the action-outcome contingency of each block. Again, by this account, therefore the knowledge of these probabilities influenced response speed in their study and not in ours—simply because as it was not available to our participants, which were cognitively taxed due to the cued-response task. This explanation is hard to accept as responding randomly is arguably a more difficult task than cued responding (it is sometimes used as a manipulation of mental load) as one needs to hold and update at least a partial tally of the different responses she emitted. This alternative explanation can be also rejected empirically as accuracy in our task was almost always above 90% (see supplementary materials), and participants' mean response speeds were around half of the duration of the response window, showing that the task was quite easy for them. Thus, it is very unlikely that if we would have used a free-choice paradigm like Penton et al.’s, we would have allowed our participants more cognitive resources, enabling them to evaluate the inaction-effect probability and bias their response speed.

Finally, another difference between the two studies that could potentially explain the difference in results is the existence of contextual cues. In Penton et al.’s, a colored frame surrounding the experimental window, uniquely identified the probability of inaction-effects. Hypothetically, subjects could have learned the mapping between colors and probability values (there were only four colors and four probability values, see above) and could have used this information to predict when an inaction-effect is likely. If this sort of prediction influenced their response speed, this comes as evidence against our point that response speed in our task is mostly sensitive to sensorimotor processes and that if our participants were only aware of the probability of inaction-effects our pattern of results would have changed (e.g., slower RTs for the action-effect present, inaction-effect present condition). However, we believe that this explanation for the differences between the studies can also be rejected. Contrary to the dynamically changing contingencies in Penton et al.'s study in our study the contingencies either did not change throughout the experiment (Experiments 1 and 3a) or changed on separate (long) blocks, once every 200 trials (Experiments 2a–2b and 3b). Both cases gave give participants ample opportunity to consciously evaluate the action-effect and inaction-effect conditional probabilities.

Although there are multiple procedural differences between our study and Penton and colleagues', we suspect that the main reason for the ostensive differences between the results stems from the difference in sizes of the samples. The current study reports that data of more than 300 participants across several replications while Penton and colleagues' results reflect a single study with a fifth of our total sample size. Thus, further studies are required to settle the apparent discrepancy between the two studies, due to the relative similarity between the two tasks.

Another study that is relevant to the current study's findings is Elsner and Hommel (2004; Experiment 2). Elsner and Hommel used a Go/No-Go bidirectional association acquisition task where participants first learned action- and inaction-effect pairings between specific keys and tones. In the next phase, the tones served as response-cues, and participants were asked to respond either with the previously associated response, or with the alternative response. In some of the experiment's conditions, it was found that responding with the previously associated, effect-compatible response was faster than responding with the effect-incompatible one. This is brought as empirical evidence for the hallmark of ideomotor—a bidirectional sensorimotor association. This congruence effect was found both when the conditional probability of action-effect was high, but inaction-effects were absent (Delta-P = 0.6) and when the conditional probability of both action-effects and inaction-effects were equally high (0.8; Delta-P = 0). However, when the probability of action-effects was only slightly higher compared with that of inaction-effects (it was 0.80 and 0.50, respectively, i.e., Delta-P = 0.3), no facilitation of response speed was found. Similarly, when the conditional probability of action-effects was 0.5 or lower (and Delta-P was 0.0) no response speed facilitation on association-compatible blocks was found. The authors suggested that sensorimotor associations are acquired through two modes—Delta-P being positive and high (i.e., when inaction-effects were absent) or when Delta-P is naught but the probability for both action-effects and inaction-effects is high.

These findings are not fully compatible with our claim, given the null finding that no sensorimotor associations were formed when action-effect probability was high and inaction-effect probability was moderate (i.e., Delta-P = 0.3). The most similar counterpart for this situation in our study is the action-effect present, inaction-effect present condition in Experiment 1 (as they had a p = 1 probability for action-effect given an action, and a p = 0.8 probability for inaction-effects given no-action). Which yields a slightly positive value of Delta-P (with high frequency of action- and inaction-effects). The results in Experiment 1 are similar to those found on other experiments for this condition, although on Experiments 2–3 the conditional probability for both action-effects and inaction-effect is 1, making Delta-P exactly 0. One could further argue that our results for the action-effect present, inaction-effect present stem from the high frequency of action-effects and inaction-effects, as Elsner and Hommel found that high frequency of action- and inaction-effects can drive sensorimotor associations when Delta-P is 0.

As in the current study we included only two conditions where Delta-P was 0, the action-effect present, inaction-effect present and action-effect absent, inaction-effect absent. Exploring several other conditions where Delta-P is 0 (e.g., like one where both action-effect probability and inaction-effect probability are 0.3) could have answered the question of whether the facilitation we observed for response speed on the action-effect present, inaction-effect present occurred from sheer frequency of feedback, as Elsner and Hommel’s study suggests or from high action-effect probability as we argue. If indeed sheer frequency or Delta-P alone can drive sensorimotor processes, then our claim that sensorimotor SOA relies on action-effect probability alone will be undermined.

Although we have shown that facilitation in response speed, which we attribute to sensorimotor processes alone, followed action-effects presence and was indifferent to the presence or absence of inaction-effects one thing has to be considered in terms of the relevance of the results, which is a difference in the methods used on the two studies. While Elsner and Hommel used an action-effect contingency learning phase on the 'test' phase, there were no action-effects and inaction-effects present. Thus, their manipulation for testing the influence of previously acquired sensorimotor associations was whether compatibility effects are found when action- and inaction-effects are removed. In a previous study we have shown that removing action-effects was immediately (i.e., trial by trail) deleterious to response speed, let alone a long experimental block (Hemed et al. 2020). As the 'test' phase in Elsner and Hommel's study spanned many minutes and trials—this begs the question of how can the same sensorimotor process be responsible for both our findings and theirs, when on one setting it is immune to extinction, and on the other it is highly sensitive to extinctions. We find that the difference in sensitivity to extinction potentially undermines the applicability of their findings to our study, as it suggests that different mental processes are probed by the two studies.

On a more general note, regarding the task used by Elsner and Hommel (2004). As elaborated above, this paradigm involves an extensive acquisition and test phase. A 'learning' phase which is then followed by a 'test' phase. In a recent paper, Sun and colleagues (In press), show that Elsner and Hommel’s effects can in fact be created and explained by what they term 'propositions' to mean explicit (conscious) causal inferences. That is, the results used by Elsner and Hommel, that are argued to be evidence for the automatic creation and/or application of passively acquired associations can also be explained by people's explicit and conscious understanding of action-effect relations. These findings set Elsner and Hommel's study (and paradigm) further apart than the current study and especially lowers the relevance of their results to the modular sensorimotor processes that we hypothesize underly the facilitation of response speed on our study. The findings by Sun and colleagues, however, are fully compatible with our key argument that the effect of bona-fide sensorimotor processes on behavior is insensitive to inaction-effects (Sunet al. 2020). Other studies have used different behavioral measures of sensorimotor and conceptual SOA, and found results which only partially match ours. In a recent study, Weller et al. (2020) have shown that both explicit judgement of agency and intentional binding are increased when participants receive inaction-effects, although to a lesser extent compared with actions lead to effects. Interestingly, Weller et al. (2020) found also that subjective reports of agency were influenced by inaction-effects, similarly to our response frequency measure, that we believe to reflect a conceptual SOA more akin to a subjective agency report (but see above). While it could be that our task was less sensitive, than theirs in measuring response speed it does not seem likely given we have found robust evidence for the lack of difference in response speed for the action-effect present conditions (by recording the rather minute facilitation of response speed observed in both conditions), regardless of the presence or absence of inaction-effects. Finally, it is important to note that it is not at all clear whether intentional binding stems from a Comparator-like process (Suzuki et al. 2019), so the comparison between our results and Weller et al.’s may be not very informative.

Another interesting finding comes from a study which used, sensory attenuation as a measure of 'implicit SOA' (Kilteni et al. 2018). In the study, a small motor applied pressure to a participants’ arm who were asked to match the reference force by either pressing down on a button or imaging pressing it down (while their muscle activity was monitored to make sure that they only imagined the action). Immediately after, they were asked to reproduce the force applied to their arm by pressing down on a force sensor. In both action and imagined-action conditions participants showed sensory attenuation—the reproduced pressure that should have reflected the reference pressure they received was lower compared to a baseline condition, where participants did not press the button nor imagined pressing it. The authors argued that the motor planning during imagery was enough to provide an efference copy that arguably was fed to the comparator, yielding attenuation. It is important to remember that in our task participants were not asked to imagine the no-action to the imperative cue, and that Kilteni et al., gave their participants substantial motor-imagery training prior to testing, so it can be argued that our participants simply did not imagine the movement as their participants did. A future study could potentially test our claims by recording the LRP in response to the cue and see whether participants did or did not imagine the actions spontaneously on inaction-trials. Also, explicitly asking our participants to imagine the actions on no-action trials could be an interesting control condition to our task.

Conclusion

We have shown that a response’s effectiveness can be evaluated simultaneously by at least two different processes (at the least, as additional ones may be discovered) as proposed in the Control-Based Response Selection Framework (CBRS; Karsh and Eitam 2015b) and partially supported by a recent study (Wen and Haggard 2020). One such evaluation is based on sensorimotor-prediction and culminates in what we believe is more than a sensorimotor prediction error—possibly a confirmation or disconfirmation of a sensorimotor prediction following an action—which is directly informative to the actual control a motor program has just afforded over the environment. Here and elsewhere, we argue that the result of the sensorimotor prediction in turn influences consciously inaccessible response-selection processes such as motor programming. A different evaluation of action’s effectiveness is non-sensorimotor, but conceptual and is based on knowledge, potentially influencing consciously accessible processes (e.g., whether to respond or withhold response). The effect of the latter judgement is far less robust because of at least two factors—first, being cognitive it is highly sensitive to the far more variable mental state (i.e., activated knowledge) in a participant's mind—e.g., what they find interesting in the task, their level of boredom, the degree they judge a stimulus as being task relevant etc. Second, this judgement is not the sole or even the most important influence on selection of actions and is hence easily washed out by stronger influences (e.g., opportunity for reward). Notwithstanding the difference in complexity of the two processes, the current study is the first to document their differential influence on different aspects of response selection.