Meta-Psychology, 2023, vol 7, MP.2020.2640 https://doi.org/10.15626/MP.2020.2640 Article type: Original Article Published under the CC-BY4.0 license Open data: Yes Open materials: Yes Open and reproducible analysis: Yes Open reviews and editorial process: Yes Preregistration: Yes Edited by: Rickard Carlsson Reviewed by: Ignazio Ziano, Ulrich Schimmack Analysis reproduced by: Lucija Batinović All supplementary files can be accessed at OSF: https://doi.org/10.17605/OSF.IO/4SZ2Q The effectiveness of the “But-you-are-free” technique: Meta-analysis and re-examination of the technique Adrien Alejandro Fillon1, Lionel Souchet2, Alexandre Pascual3, and Fabien Girandola2 1ERA Chair in Science and Innovation Policy & Studies, University of Cyprus 2Department of Social Psychology, Aix-Marseille University 3Department of Social Psychology, University of Bordeaux The “But you are free. . . ” (BYAF) technique is a technique to increase compliance (for example, to give spare change for the bus), by adding the words “But you are free to accept or refuse” to the request. In this pre-registered meta-analysis, we examine the effect of the BYAF technique in 52 experiments (N = 19528). An analysis of 74 effect sizes showed a medium effect (g = 0.44, 95% confidence intervals (CI) [0.36, 0.51]) for the BYAF technique. A moderator analysis found a stronger effect for face- to-face interactivity over other types of interactivities. All the other moderators we used were not statistically significant. We did not find any differences between arti- cles published before and after Carpenter’s (2013) meta-analysis. An examination of risk of bias showed that only seven studies were of “low risk”, and a meta-analysis of these studies showed no effect of the BYAF (g = 0.11, 95% CI [-0.18, 0.40]) We also found that most recent studies on the subject are too low-powered to detect the effect found by Carpenter (2013), and the reproducibility rates were critically low (R-index = 9.77%, Z-curve expected discovery rate = 6%). We propose some improvements to the design and experiments to ensure the effects found in the literature exist and are replicable. All materials are available on https://osf.io/8eqa5/ Keywords: But-you-are-free, Commitment, Compliance, Meta-analysis Introduction The But-You-Are-Free (BYAF) technique is a commit- ment technique invented and used by Guéguen and Pas- cual (2000). This technique consists of an addition of the words “but you are free” during a request to en- hance the acceptance of the request. The BYAF tech- nique is one of many techniques (see Pratkanis, 2007 for a review) used as commitment techniques, based on the reactance theory (Brehm, 1966). Contrary to other techniques, the BYAF is easy to use – you only need to add one sentence to the request. For exam- ple, Guéguen and Pascual (2000) observed 10% of com- pliance rate with the request "Sorry Madam/Sir, would you have some coins to take the bus, please?" (Control condition), whereas 47.5% was obtained with "Sorry Madam/Sir, would you have some coins to take the bus, please? But you are free to accept or to refuse." (BYAF condition). The “BYAF” technique can be combined to other techniques such as the “foot in the door” tech- nique to further increase compliance. Furthermore, this technique can be applied in many situations, such as face-to-face interaction, but also in indirect interaction, for example with the use of the internet (e.g., e-mail, (Pascual, 2002). But how does it work? The exact wording (i.e., “but you are free”) is not required to en- hance compliance, as other wording “but obviously do not feel obliged” (Guéguen et al., 2013, p. 129) is as effective. The technique relies on the salience of the tar- get’s freedom in their decision-making process. The ac- knowledgement that one can say “no” leads to say “yes” more often, and to be more committed, as shown by the amount of money given in most of the studies (e.g., Guéguen and Pascual, 2000). As commitment theory (Kiesler, 1971; Kiesler and Sakumura, 1966) postulates, it is possible to manipulate the degree of commitment by manipulating the degree of perceived choice when performing the act. As such, the BYAF technique can be considered as a non-pressure manipulation used to enhance compliance. Original study and its follow-up In the original study (Guéguen and Pascual, 2000), researchers indicated in the subject section that four confederates, 2 men and 2 women on average age of 20-22 years old asked 40 men and 40 women cho- sen at random in the street. In the Procedure section, they indicated that the experiment was made in a mall. In the control condition, the confederates say “Sorry https://doi.org/10.15626/MP.2020.2640 https://doi.org/10.17605/OSF.IO/4SZ2Q 2 Madam/Sir, would you have some coins to take the bus, please?” and in the BYAF condition "Sorry Madam/Sir, would you have some coins to take the bus, please? But you are free to accept or to refuse." The confed- erate then noted if the participant accepted to give money, and noted the amount given before giving it back to the participant and debriefed him. In the re- sult section, researchers indicated that 10% of subjects accepted the request in the control group, and 47.5% in the BYAF group, whereas the mean amount was 0.48$ in the control group and 1.04$ in the BYAF group (all differences were statistically significant at an α level of 0.05). Researchers indicated that this experiment shows the effectiveness of the BYAF technique to in- crease the probability of compliance, in saying yes to the request, and the implication of the subject, in giving a higher amount of money. In 2013, Carpenter con- ducted a meta-analysis of the BYAF technique with 42 studies published after the original described above. His goal was to summarize the effect size of this technique and show some probable mediators and moderators. In- deed, researchers wanted to show if face-to-face inter- action was important to the BYAF technique, and if the type of choice (prosocial, offer, or selfish) and the time of the request (immediate or delayed) influenced the BYAF effect. Also, as the first research are based on a monetary request, it was important to assess that BYAF works in another context, such as a signature for a pe- tition. The meta-analysis showed that the sample-size weighted correlation between the presence and absence of the BYAF technique and the proportion of those who complied with the request was r = .13 (i.e., d = 0.26), which is, according to the author, a moderate-sized in- crease in effectiveness with the use of the BYAF tech- nique. It is typically considered a small to medium effect size (Sawilowsky, 2009). The sampling error explained 22% of the variation in effect size. The confidence inter- val of the correlation was not reported. Carpenter iden- tified several moderators. An immediate request led to an r = .18 (i.e., d = 0.37), and a delayed request to an r = .07 (i.e., d = 0.14), which showed the importance to position the BYAF technique close to the targeted re- quest. Prosocial requests were as likely to work (r = .16, d = 0.32) as selfish requests (r = .16, d = 0.32). Concerning the analysis of publication bias, Carpenter correlated the sample sizes and effect sizes and found an r = -.30. This result means that there is the possi- bility that, as the sample size increases, the effect de- creases, potentially to a null effect. This result suggests that publication bias is present and that the effect size estimate is inflated. Thus, the actual effect size might be small. Also, researchers used the trim-and-fill tech- nique (Duval and Tweedie, 2000) but did not provide the plot associated. The trim-and-fill technique leads to a reduction of the effect size by .04 (from an r = .13 to an r = .09, d = 0.18). Some meta-analysts indicated that the Trim and fill technique performs poorly in the presence of substantial between-study heterogeneity (J. Higgins, Chandler, et al., 2022). Finally, as Carpenter pointed out, nearly all the experiments were conducted either by Guéguen or Pascual (see Table 1), but they found the strongest and the smallest effect sizes for the technique. One major problem of the Carpenter (2013) meta-analysis is some studies were flagged as of risk of having fabricated data (Brown, 2020). The flagged studies have the strongest effect sizes found (Odds Ratio for Dufourcq-Brana et al., 2006 OR = 6.57; Guéguen and Pascual, 2000 OR = 8.14; Pascual and Guéguen, 2002 OR = 6), thus, eliminating these results from our analysis might show a null effect of the BYAF technique. Also, it is possible that research on this subject improves over time, with larger sample sizes, and stronger meth- ods, leading to convergence to the “true” effect size of the BYAF technique on compliance. In most cases in psychology, the original effect sizes are inflated (Schäfer and Schwarz, 2019). This is the reason why we con- duct a novel preregistered and open meta-analysis on the BYAF technique over compliance, with a look at the inconsistencies we can find between our analysis and the one from Carpenter (2013). Moderators We want to investigate the moderators that can in- fluence the effect of the BYAF technique. The research on the subject shows that the moderators that can in- fluence the technique are the type of request (pro-social vs. selfish), the temporality (immediate or delayed), the gender of the subject and of the confederate (man vs. woman), the culture (individualistic vs. collectivistic), the interactivity (face-to-face vs. indirect), and the type of freedom evocation (“but-you-are-free” vs. other). We also want to test if there are substantial differences be- tween the effect sizes found before and after the Car- penter (2013) meta-analysis. Type of request As Carpenter (2013) pointed out, the effectiveness of the BYAF technique might rely upon the type of request. For Carpenter and Boster (2009), the compliance- gaining techniques work better for pro-social benefits, like giving to a charity, rather than for selfish reasons, like giving to take the bus. Nonetheless, Carpenter (2013) found no difference in compliance rate for the pro-social and selfish types of requests. We seek to redo the analysis with the same hypothesis, given that the larger number of studies involved could give a better 3 estimate of the effect size, and possibly could detect a moderator effect of the type of request. In doing so, our hypothesis is the same as in Carpenter’s (2013) meta- analysis: the compliance rate will be higher for the pro- social type of request than for the selfish type of request. Temporality Temporality was called “immediate or delayed” in Carpenter’s (2013) analysis. Indeed, depending on the studies, the researchers can look at whether the partic- ipant complied with the request immediately after us- ing the technique (e.g., when they asked for money, the original technique), or after a certain amount of time (e.g., by sending an email and then testing at whether the participant had made a purchase, Grassini et al., 2012). We seek to replicate the effect of tem- porality found in the Carpenter’s meta-analysis. Re- searchers found that the compliance rate was lower when the confederate was absent (delayed condition) than present (immediate condition). Two reasons are possible: an easier reactance involved with the absence of the confederate, or the wanting to have a better self- representation when the researcher is present. We seek to redo the analysis with the addition of new studies to find that the immediate use of the BYAF technique is more effective than the delayed use. Subject gender Studies seem to indicate that men are less compli- ant than women (Grosch and Rau, 2016). For exam- ple, one study found that men cheat more than women (Fischbacher and Föllmi-Heusi, 2013). Grosch and Rau (2016) indicated that this difference can be explained by the cultural roles of men and women, as women are seen as more pro-social than men. Thus, we think that Female participants will comply more to the request in the BYAF condition than men. Confederate gender Many experiments have shown that confederate gen- der influences the compliance rate. For example, Vaughn et al. (2009) have only found an effect of com- pliance when the confederate was a woman. Long et al. (1996) found that women were more helped than men. On the contrary, Dolinska and Dolinski (2006) found that both sexes have a better chance to find compliers when confederate sex matches the participant sex. This difference can be explained by cultural variation. Since most of the experiments were conducted in France, we think that the BYAF technique will be more effective if the confederate is a woman. Indeed, we hypothesize that participants will comply more to women confeder- ate than to men confederate in the BYAF condition. Culture In pro-social culture such as in China, one could ex- pect more compliance than in a more individualistic cul- ture such as in France (see Hamamura et al., 2018). There are at least three reasons for this hypothesis. On general, the theory of commitment is more effective for individualistic than for collective culture (Kim and Sherman, 2007), because people in individualistic cul- ture have a more internal locus of control (Channouf, 1990; Desrumaux, 1996), and people are more easily reactant (Jonas et al., 2009). Thus, the BYAF technique which reduces reactance should work better for peo- ple in an individualistic culture. Indeed, Pascual et al. (2012) showed that the BYAF technique induces more compliance in individualistic countries (i.e., France, Ro- mania) than collectivistic countries (i.e., Ivory Coast, China, and Russia). According to Triandis (1989), indi- vidualist cultures include Northern and Western Europe as well as North America, whereas collectivist cultures would be characteristic of Asia, Africa, and South Amer- ica. Participants from an individualistic country would comply more with the BYAF technique than participants from a collectivistic country. Interactivity If the BYAF technique has a different effect depending on the gender of the participant, or/and the gender of the confederate, it implies that this difference is within a “face-to-face” interaction. Furthermore, the differ- ence between temporality (immediate or delayed), im- plies a difference between a “face-to-face” interaction and more distal interactions. We believe that partici- pants are more engaged when the interaction is in “face- to-face” rather than in a more indirect interaction, via email, phone call, or internet. Type of freedom evocation The BYAF technique is an induction in a sentence (typically “but you are free to accept or to refuse”) and induce a feeling of freeness making the recipient more willing to accept the demand, or to comply. Other evocations include propositions such as “do not feel obliged”, “do as you wish”, or “feel free to refuse”. There are possibilities that some evocations are better than others to induce compliance. Indeed, the propo- sition “but you are free to refuse” is the most salient, leading to the best understanding by the recipient that he/she is free to accept or not. It should have a stronger effect on compliance than the other possibilities of evok- ing freedom. 4 Before and After Carpenter’s analysis Garmendia et al. (2019) have shown that 46% of meta-analyses have their conclusions altered by false data, with fraudulent/plagiarized studies, or errors. As we previously showed, Carpenter analysis has this prob- lem. Original effect sizes are inflated (Schäfer and Schwarz, 2019) and we tend to think that most recent research is of better quality than before the crisis in so- cial science (Motyl et al., 2017). In Carpenter’s (2013) meta-analysis, the use of the Trim-and-Fill method re- duced the effect size found close to the null, we hypoth- esize that the effect will be lower after Carpenter’s anal- ysis than before. Summary hypotheses Main hypotheses People tend to comply more with the “but you are free” technique than with direct asking. Confirmatory hypotheses The compliance rate will be higher for 1) the proso- cial type of request than for the selfish type of request and 2) immediate asking than delayed. Exploratory hypotheses The compliance rate will be higher (a) for women than for men, (b) for women confederate than for men confederate, (c) from an individualistic country than from a collectivistic country, (d) in a “face to face” inter- action than in other types of interaction, (e) with the ex- act proposition “but you are free” than the others types of evocation and (f) in studies on the Carpenter (2013) meta-analysis than for the studies made after. Method Open-science, replicability, and our current study We preregistered our analysis, following PRISMA (Moher et al., 2009) checklist and made available all our data and our analysis in R/Rmarkdown in an OSF (link = https://osf.io/8eqa5/). R packages used can be found in supplementary. Literature search We systematically searched Google Scholar (for suit- ability for meta-analyses see Gehanno et al., 2013; Martín-Martín et al., 2018; Walters, 2007) with the fol- lowing term but you are free, as Carpenter did in 2013. We provide an overview of the search process in Fig- ure 1. The database searches achieved 1760 hits. We also searched articles by scanning reference sections of Figure 1 Meta-analysis flow diagram (adapted from PRISMA 2020) found articles and using the “related articles” and “cited by” options in Google Scholar. Based on reviewer feed- back, we asked for unpublished studies in the ADRIPS, EADM, and EASP social networks, without any addi- tional results. After adjusting for duplicates, 81 sources remained. To minimize possible potential publication bias, we con- tacted all identified authors in person and requested un- published manuscripts. We were provided with twenty- two additional articles leading to a total of 103 sources. All abstracts, tables, and results sections of empirical sources were scanned to assess their relevance. After this step, 29 articles remained as potentially includable articles. Our eligibility criterion is the use of the “But you are free” technique with a direct measure of com- pliance. We only include experimental designs, with a clear contrast between the BYAF technique and a control group, with an asking being saying “yes/no”, money, clicking on a button online, or sending a postal mail. We exclude studies 1) that do not measure direct compliance or are using a scale to measure the strength of compliance, 2) without a control group, and that con- trasts the BYAF technique with another technique and 3) that do not provide the exact term for the BYAF tech- nique, for whom the term is disconnected/too far away https://osf.io/8eqa5/ 5 from the term “but you are free”. Finally, we exclude studies with missing statistics or statistics that are not reported: Studies that do not report crucial measures such as the number of participants or standard needed for calculating the effect size deviation will be excluded from the sample. We briefly read through all articles to examine whether they met our inclusion criteria. A total of 7 articles were qualified for the exclusion, leading to a total sum of 22 identified articles with codable data. Finally, a total of 52 samples were included in this meta- analysis leading to a sum of 74 effect sizes. We provided a list of all included experiments in Table 1. We used a data extraction sheet that was already successfully used in other meta-analyses (e.g., Fillon et al., 2021; Yeung et al., 2021). The coding process for the pre-tests was completed by two coders to ensure high inter-rater re- liability. We documented and reported all decisions in detail. After testing, one review author extracted all data and provided detailed information about coding decisions. A second author verified the coding. Dis- agreements were resolved by discussion between the two authors. All coding decisions were documented in the extraction sheet. We added in OSF available raw data and emails with authors. We documented in col- umn “source” the extraction of data. Coding Included studies We included a total of 52 experiments with a total of 19528 participants. The final sample consists of 18 published and 4 unpublished studies. Most studies were conducted in a face-to-face experimental design, in the street; others were made online, via an online video game or by email, phone, or postal letters. An overview of all included studies is provided in Table 1. Analysis We ran our analysis in R. We used the following meta-analysis related packages to conduct our analyses: metafor, psych, compute.es, MBESS, MAd, powerAnaly- sis, metaforest, esc, metaviz, puniform, zcurve (see sup- plementary for the whole R packages used). Given the range of different types of studies and designs, we ex- pected heterogeneity in the sample to be relatively high. Therefore, a random-effects model was used. We coded the sheet with the total number of participants in each group (experimental via the BYAF technique, control) and the number of participants who comply in each group. In most cases, the numbers were provided but for some, we computed them from the test available. All conversions and coding decisions were documented. We preregistered to use cohen’s d as effect size but used Hedges’ g instead because it corrects for low sample size (Delacre et al., 2021). We produced forest plots of the effect size distribution. A meta-analysis examined the overall main effect of the bias; a meta-regression was conducted to assess the impact of the described mod- erators. Statistical heterogeneity was determined using the Tau² test and quantified using I², which represents the percentage of the total variation in a set of stud- ies that is due to heterogeneity (Higgins, 2003). This yielded a point estimate, confidence interval, and p- value, along with statistics for heterogeneity, assessed using the Q-statistics, and the I2 statistic. We detected significant heterogeneity and therefore proceeded to ex- plore potential moderators. We also performed analy- ses for the presence of publication bias, including fun- nel plots and statistical tests for publication bias (pub- lication status as a moderator) and funnel plot asym- metry tests (Trim-and-fill method, rank correlation test, Egger’s unweighted regression symmetry test, etc.). Fi- nally, we tested for robustness via the Graphical Display of Study Heterogeneity (Gosh) and plotted a Z-curve to estimate replicability. Moderator analyses We tested subgroups and moderators using a com- parison of fixed-effects meta-analysis models. Most of our hypotheses are exploratory; we tested the type of request and immediate or delayed as confirmatory, since they were already studied in the Carpenter (2013) meta-analysis. For the other moderators, we conducted exploratory analyses. Results The But-you-are-free main effect In an analysis of all studies on the impact of the BYAF effect on compliance, we found an effect of g = 0.44 [0.36, 0.51]. We found considerable heterogeneity (Q (73) = 271.67, p < .001, I² = .80.7%) in the observed effect sizes. The variation in effect-sizes was greater than would be expected from sampling error alone, in- dicating that moderator variables might be accountable for the variance in the effects. A meta-analysis forest plot is provided in Figure 2. Study design and measures as moderators We summarized all moderator findings in Table 2. Overall, the only exploratory moderator that has an im- pact on the BYAF effect was the type of interactivity, as face-to-face interactivity has a significantly higher number of compliers than the others combined (email, phone, postal letter, and internet). On the other side, 6 Table 1 All experiments included in the meta-analysis Article N Interactivity Culture Published 1 Barbier (2018) 422 Internet France No 2 Carpenter & Pascual (2016) 131 Face-to-face USA Yes 3 Carpenter & Pascual (2016) 320 Face-to-face France Yes 4 Carpenter & Pascual (2016) 240 Face-to-face Norway Yes 5 Dufourcq-Brana (2007) 400 Email France No 6 Dufourcq-Brana (2007) 60 Face-to-face France No 7 Dufourcq-Brana (2007) 100 Face-to-face France No 8 Farley et al. (2019) 45 Face-to-face USA Yes 9 Farley et al. (2019) 40 Face-to-face USA Yes 10 Grassini et al. (2012) 900 Email France Yes 11 Guéguen & Pascual (2000) 80 Face-to-face France Yes 12 Guéguen & Pascual (2005) 159 Face-to-face France Yes 13 Guéguen et al. (2002) 600 Email France Yes 14 Guéguen et al. (2010) 100 Face-to-face France Yes 15 Guéguen et al. (2013) 2160 Face-to-face France Yes 16 Guéguen et al. (2013) 160 Face-to-face France Yes 17 Guéguen et al. (2013) 4421 Face-to-face France Yes 18 Guéguen et al. (2013) 400 Face-to-face France Yes 19 Guéguen et al. (2013) 100 Face-to-face France Yes 20 Guéguen et al. (2013) 2608 Phone France Yes 21 Guéguen et al. (2013) 4515 Email France Yes 22 Guéguen et al. (2013) 2230 Postal letter France Yes 23 Guéguen et al. (2013) 400 Postal letter France Yes 24 Guéguen et al. (2013) 344 Face-to-face France Yes 25 Guéguen et al. (2013) 300 Face-to-face France Yes 26 Guéguen et al. (2013) 400 Face-to-face France Yes 27 Guéguen et al. (2015) 120 Face-to-face France Yes 28 Guéguen et al. (2017) 60 Face-to-face France Yes 29 Marchand et al. (2009) 74 Face-to-face France Yes 30 Meineri et al. (2016) 60 Face-to-face France Yes 31 Meineri et al. (2016) 649 Face-to-face France Yes 32 Pascual & Guéguen (2002) 80 Face-to-face France Yes 33 Pascual & Guéguen (2002) 120 Face-to-face France Yes 34 Pascual & Guéguen (2002) 200 Face-to-face France Yes 35 Pascual & Guéguen (2002) 306 Face-to-face France Yes 36 Pascual & Guéguen (2002) 126 Face-to-face France Yes 37 Pascual (2002) 181 Face-to-face France No 38 Pascual (2002) 320 Face-to-face France No 39 Pascual (2002) 167 Face-to-face France No 40 Pascual (2002) 306 Face-to-face France No 41 Pascual (2002) 220 Face-to-face France No 42 Pascual et al. (2012) 609 Face-to-face France, Ivory Coast Yes 43 Pascual et al. (2012) 360 Face-to-face France, Romania, Russia Yes 44 Pascual et al. (2012) 360 Face-to-face France, Romania, Russia Yes 45 Pascual et al. (2012) 128 Face-to-face France, China Yes 46 Pascual et al. (2002) 400 Email France Yes 47 Pascual et al. (2009) 120 Face-to-face France Yes 48 Pascual et al. (2015) 60 Face-to-face France Yes 49 Pascual et al. (2015) 160 Face-to-face France Yes 50 Pascual et al. (2020) 314 Face-to-face France, China Yes 51 Pascual et al. (2020) 788 Face-to-face France, Moldavia, Tunisia Yes 52 Silone et al. (2016) 155 Postal letter France Yes 7 Figure 2 Meta-analysis forest plot for all studies RE Model −2 −0.5 1 2.5 4 Observed Outcome Silone et al. (2016) / 1 / 1 Pascual et al. (2020) / 2 / 3 Pascual et al. (2020) / 2 / 2 Pascual et al. (2020) / 2 / 1 Pascual et al. (2020) / 1 / 2 Pascual et al. (2020) / 1 / 1 Pascual et al. (2015) / 2 / 1 Pascual et al. (2015) / 1 / 1 Pascual et al. (2009) / 1 / 1 Pascual et al. (2002) / 1 / 1 Pascual et al (2012) / 4 / 2 Pascual et al (2012) / 4 / 1 Pascual et al (2012) / 3 / 3 Pascual et al (2012) / 3 / 2 Pascual et al (2012) / 3 / 1 Pascual et al (2012) / 2 / 3 Pascual et al (2012) / 2 / 2 Pascual et al (2012) / 2 / 1 Pascual et al (2012) / 1 / 2 Pascual et al (2012) / 1 / 1 Pascual (2002) / 7 / 4 Pascual (2002) / 7 / 3 Pascual (2002) / 7 / 2 Pascual (2002) / 7 / 1 Pascual (2002) / 6 / 2 Pascual (2002) / 6 / 1 Pascual (2002) / 5 / 4 Pascual (2002) / 5 / 3 Pascual (2002) / 5 / 2 Pascual (2002) / 5 / 1 Pascual (2002) / 11 / 1 Pascual (2002) / 10 / 1 Pascual & Gueguen (2002) / 5 / 1 Pascual & Gueguen (2002) / 4 / 2 Pascual & Gueguen (2002) / 4 / 1 Pascual & Gueguen (2002) / 3 / 2 Pascual & Gueguen (2002) / 3 / 1 Pascual & Gueguen (2002) / 2 / 1 Pascual & Gueguen (2002) / 1 / 1 Meineri et al. (2016) / 2 / 1 Meineri et al. (2016) / 1 / 1 Marchand et al. (2009) / 1 / 1 Gueguen et al. (2017) / 1 / 1 Gueguen et al. (2015) / 1 / 1 Gueguen et al. (2013) / 9 / 1 Gueguen et al. (2013) / 8 / 1 Gueguen et al. (2013) / 7 / 1 Gueguen et al. (2013) / 6 / 1 Gueguen et al. (2013) / 5 / 1 Gueguen et al. (2013) / 3 / 1 Gueguen et al. (2013) / 2 / 1 Gueguen et al. (2013) / 13 / 2 Gueguen et al. (2013) / 13 / 1 Gueguen et al. (2013) / 12 / 1 Gueguen et al. (2013) / 11 / 2 Gueguen et al. (2013) / 11 / 1 Gueguen et al. (2013) / 10 / 2 Gueguen et al. (2013) / 10 / 1 Gueguen et al. (2013) / 1 / 1 Gueguen et al. (2010) / 1 / 1 Gueguen et al. (2002) / 1 / 1 Gueguen & Pascual (2005) / 1 / 1 Gueguen & Pascual (2000) / 1 / 1 Grassini et al. (2012) / 1 / 1 Farley et al. (2019) / 2 / 1 Farley et al. (2019) / 1 / 1 Dufourcq−Brana (2007) / 3 / 1 Dufourcq−Brana (2007) / 2 / 1 Dufourcq−Brana (2007) / 1 / 1 Carpenter & Pascual (2016) / 2 / 3 Carpenter & Pascual (2016) / 2 / 2 Carpenter & Pascual (2016) / 2 / 1 Carpenter & Pascual (2016) / 1 / 1 Barbier (2018) / 4 / 1 155 115 132 130 80 40 82 54 66 400 64 64 60 60 60 60 60 60 387 222 28 19 22 25 80 80 26 28 23 31 220 171 126 83 101 50 50 120 80 378 30 37 60 61 1324 4515 1625 100 253 2374 80 100 100 150 86 86 100 100 1080 100 900 159 80 900 40 35 100 60 400 60 104 29 89 119 −0.32 [−0.66, 0.03] 0.42 [−0.09, 0.93] 0.46 [ 0.16, 0.76] 0.55 [ 0.25, 0.86] 0.69 [ 0.31, 1.08] 0.31 [−0.18, 0.81] 0.35 [−0.03, 0.73] 0.23 [−0.69, 1.15] 0.47 [ 0.03, 0.92] −0.22 [−0.42, −0.02] 0.12 [−0.36, 0.60] 0.69 [ 0.19, 1.19] 0.29 [−0.15, 0.72] 0.56 [ 0.11, 1.00] 0.48 [ 0.04, 0.92] 0.22 [−0.22, 0.65] 0.53 [ 0.09, 0.97] 0.50 [ 0.06, 0.93] 0.20 [ 0.00, 0.41] 0.29 [ 0.03, 0.56] 0.67 [−0.01, 1.35] 0.75 [−0.14, 1.65] 0.92 [ 0.10, 1.74] 0.07 [−0.72, 0.86] 0.54 [ 0.15, 0.92] 0.45 [ 0.07, 0.83] 0.17 [−0.70, 1.03] −0.03 [−0.71, 0.64] −0.07 [−0.84, 0.71] 0.36 [−0.28, 1.01] 0.51 [ 0.24, 0.78] 0.28 [ 0.00, 0.55] −0.11 [−0.45, 0.24] 0.35 [−0.06, 0.75] 0.30 [−0.09, 0.69] 0.51 [ 0.03, 0.99] 0.96 [ 0.46, 1.46] 0.41 [ 0.03, 0.79] 0.98 [ 0.52, 1.44] 0.29 [ 0.10, 0.48] 0.59 [−0.03, 1.21] 0.50 [−0.06, 1.05] 1.12 [ 0.58, 1.66] 0.51 [ 0.07, 0.95] 0.32 [ 0.21, 0.42] 0.36 [ 0.30, 0.42] 0.43 [ 0.33, 0.53] 1.04 [ 0.63, 1.46] 0.52 [ 0.27, 0.77] 0.29 [ 0.22, 0.36] 0.39 [ 0.01, 0.77] 0.51 [ 0.17, 0.86] 0.69 [ 0.35, 1.04] 0.41 [ 0.11, 0.71] 0.91 [ 0.53, 1.29] 0.89 [ 0.51, 1.28] 0.46 [ 0.12, 0.81] 0.33 [−0.01, 0.67] 0.69 [ 0.58, 0.80] −0.15 [−0.54, 0.24] 0.63 [ 0.49, 0.78] 0.59 [ 0.28, 0.91] 1.15 [ 0.68, 1.61] 0.35 [ 0.22, 0.48] 1.70 [ 0.99, 2.41] 0.68 [−0.12, 1.47] 0.59 [ 0.19, 0.99] 1.02 [ 0.49, 1.56] −0.19 [−0.39, 0.00] 0.63 [ 0.23, 1.04] 0.67 [ 0.16, 1.18] 0.29 [−0.46, 1.03] −0.07 [−0.48, 0.34] 0.02 [−0.27, 0.31] 0.44 [ 0.36, 0.51] Author(s), Year, and Study # Observed [95% CI]Sample size 8 the two confirmatory moderators had a significant ef- fect, as we found that a face-to-face interaction led to a stronger effect than the other forms of interactivity, and a direct request led to a stronger effect than a delayed request. Subject gender We hypothesized that the BYAF technique would in- crease compliance to a higher degree with women than with men. While we found a slightly larger effect size of the BYAF technique for women, this difference was not statistically significant. Confederate gender We hypothesized that the BYAF technique would in- crease compliance to a higher degree with women than with men confederates. We did not find support for this hypothesis, as the test for the difference was non- significant. We also performed an ANOVA on the con- federate and subject gender moderators to find if there might be an interaction effect. The ANOVA revealed no statistically significant interaction effect (Q (3) = 2.18, p = 0.54). Culture We hypothesized that the BYAF technique would in- crease compliance to a higher degree in individualistic cultures than in collectivistic cultures. Our results in- dicate a higher effect size of the BYAF technique in in- dividualistic culture than collectivistic, but the result is not significant. Interactivity We hypothesized that the BYAF technique would in- crease compliance to a higher degree in Face-to-face in- teraction than the other types of interaction. Our re- sults indicate a higher and significant effect size of the BYAF technique with the face-to-face interaction than the other, yet we caution against drawing any gen- eral conclusions from these findings as we did not find enough effect sizes for the “other” moderators. For ex- ample, we only collected one effect size for the use of the technique by phone. Freedom evocation We hypothesized a stronger effect of the BYAF tech- nique with the exact term “but you are free” than other terms. On the contrary, our results indicate a higher effect of the combined other framing, while the effect is not significant. Carpenter’s analysis We hypothesized a stronger effect size via the coding of the Carpenter’s (2013) meta-analysis than the effect sizes found in the experiments made after the Carpen- ter analysis. We did not find any differences between the studies made before and after Carpenter’s analysis, as the average effect sizes are very similar. Type of request We hypothesized a higher number of compliers with the BYAF technique in a prosocial request than a self- ish one. Our result tends to indicate the contrary, par- ticipants complied more with a selfish request than a prosocial request with the BYAF technique, but the ef- fect is not significant. Temporality We hypothesized that the effect of the BYAF tech- nique would be stronger for immediate requests and weaker for delayed ones. Our results corroborate the hypothesis; we found a stronger and significant effect for immediate requests (g = 0.47, 95% CI [0.41; 0.54]) than for delayed requests (g = 0.25, 95% CI [0.03, 0.47]). Publication bias We tested for the presence of publication bias using several methods, and a summary of publication bias analyses is provided in Table 3. We ran publication bias analyses on collapsed effect sizes by study, with one ef- fect size per study. Point estimates are consistent, and methods that produce confidence intervals show sub- stantial overlap in confidence intervals for each method. The range of estimates goes from 0.25 to 0.56. The trim and fill method indicates an asymmetry of the fun- nel with 17 studies missing on the left side, confirmed with a significant Egger’s regression test. The asymme- try of a funnel plot can be caused by two effects: pub- lication bias or other factors (e.g., poor methodologi- cal quality, true heterogeneity, artefactual, or chance; Egger et al., 1997). The distinction between publica- tion bias and other factors relies on where the missing studies are in the funnel plot. If the missing studies are in the significant area (i.e., the white area inside the funnel plot), it means that the meta-analysis lacks significant effect sizes, which are mainly due to other factors. If the missing studies are in the non-significant area (i.e., the darker areas of the funnel plot), it prob- ably indicates a sign of publication bias. Based on the Funnel plot (Figure 3) and the Trim-and-Fill plot (Fig- ure 4), our results indicate the presence for both signs, 9 Table 2 Moderator analysis of the but you are free technique Moderator k N Mean g 95% CI Difference p Subject gender Woman 38 9316 0.48 [0.40, 0.56] Man 41 8008 0.42 [0.35, 0.50] -0.059 [-0.17, 0.05] .28 Confederate gender Woman 50 4355 0.45 [0.36, 0.54] Man 26 2048 0.41 [0.27, 0.55] -0.04 [-0.21, 0.13] .62 Culture Individualistic 65 18550 0.45 [0.37, 0.53] Collectivistic 9 978 0.32 [0.20, 0.44] 0.13 [-0.01, 0.28] .08 Interactivity Face-to-face 64 9101 0.49 [0.42, 0.56] By e-mail 5 7115 0.19 [-0.13, 0.52] By phone 1 1625 0.43 [0.33, 0.53] By postal letter 2 1479 0.02 [-0.60, 0.64] By internet 2 208 -0.01 [-0.25, 0.23] Overall other than Face-to-face 10 10427 0.15 [-0.05, 0.36] -0.34** [-0.55, -0.13] .002 Freedom evocation « But you are free » 59 14069 0.42 [0.34, 0.50] Other 13 5218 0.53 [0.36, 0.71] 0.11 [-0.08, 0.30] .26 Carpenter Before 54 16835 0.44 [0.35, 0.52] After 20 2693 0.43 [0.27, 0.60] 0.007 [-0.18, 0.19] .95 Type of request Selfish 40 12603 0.50 [0.41, 0.60] Prosocial 34 6925 0.36 [0.26, 0.47] 0.14 [-0.005, 0.29] .06 Temporality Immediate 63 10451 0.47 [0.41, 0.54] Delayed 12 9212 0.25 [0.03, 0.47] 0.23 [-0.004, 0.45] .05 Note. k = number of samples; N = total number of individuals in k; mean g = average Hedge’s g effect size, CI = lower and upper limits of 95% confidence interval, * p < .05, two-tailed, **p <.01, two-tailed, *** p < .001, two-tailed. as we found support for a lack of significant and non- significant studies. These results are strengthened by the Three-parameter selection model (3PSM) estimate, for which the likelihood ratio test is close to the sig- nificance threshold, which could indicate selective re- porting (Hedges, 1992). In the case of inconsisten- cies between estimators, the 3PSM is a better indication (Carter et al., 2019), and, in our case, does not exclude a possible publication bias. Overall, while some estima- tors indicate a possible publication bias, the more robust test for high heterogeneity do not favor the possibility for selective reporting. But this result is accompanied by a possible problem of poor methodological quality leading to a (rather small) inflated effect, from a found effect of 0.44 to an estimated mean effect between 0.34 and 0.38. We ran a p-curve and p-uniform analysis which respectively found an estimated g = 0.41 and g = 0.38. The p-uniform analysis found 45 significant ef- fect sizes, and the p-curve analysis indicated presence of evidential values and no absence of evidential values (see supplementary for the P-curve Table). As requested by the editor, we ran a statcheck (Nuijten, 2018) on the statistics we used to retrieve the number of participants in each condition and found only one inconsistent result which did not affect the overall result. Robustness We did not pre-register an estimation of Robustness. Still, we ran a script to create a Graphical Display of Study Heterogeneity (GOSH) to assess the robustness of effect size found. We provide the R script in supple- mentary rather than in the Rmarkdown because of the 10 Table 3 Publication biases analyses results Publication bias analysis method Results and adjusted models Three-parameter selection model Likelihood Ratio Test: 3.39, p = .07 Adjusted Model: g = 0.38, 95% CI [0.26, 0.50] PET b = 0.34 [0.25, 042], p <.001 PEESE b = 0.36 [0.30, 0.42], p <.001 Puniform Adjusted Model: g = 0.45, 95% CI [0.37 0.56], 45 significant Henmi & Copas (2010) Adjusted Model: g = 0.36, 95% CI [0.26, 0.51] Trim and fill funnel plot asymmetry 17 studies missing on the left side. Rank correlation test (Begg & Mazumdar, 1994) Kendall’s tau = 0.14, p = .09 Egger’s regression test z = 2.06, p = .04 Note. Values in parentheses indicate 95% confidence intervals [lower bound, upper bound]. Figure 3 Funnel plot for all studies Observed Outcome S ta n d a rd E rr o r 0 .4 7 1 0 .3 5 3 0 .2 3 5 0 .1 1 8 0 −1.5 −1 −0.5 0 0.5 1 1.5 2 time consumption used in the analysis. On our recent computer, the analysis took between 3 and 4 hours. One test of robustness includes the leave-one-out analysis, a method of analysis (Olkin et al., 2012) made to see the influence of one effect size on heterogeneity. Another possibility is to estimate the influence of a subgroup in meta-analyses, which leads to a very high number of meta-analyses to perform to find the whole combination of effect sizes that could influence the robustness of the analysis. In fact, with 74 effect sizes found, it leads to 1.88x102̂2 meta-analysis, which makes the comparison Figure 4 Trim-and-Fill funnel plot 0.0 0.1 0.2 0.3 0.4 0.5 −1 0 1 Hedge's g S ta n d a rd E rr o r Note. The 17 missing studies are shown in black. We used the Trim-and-Fill method to see studies on the left with a random model, with the addition of the Egger regression test shown as the red line. impossible. The GOSH makes the analysis graphical, by plotting one meta-analysis as a dot. If dots are homo- geneously displayed, the effect found is robust, while if two or more clusters are found, it means that at least one subgroup influences too much the overall effect size found. Our GOSH plot can be found in Figure 5. The figure presented is in a homogenous circle form, show- 11 Figure 5 GOSH plot For Robustness Note. The plot helps to see how heterogeneity varies between overall estimates for every left-out meta-analysis. We can see that for every meta-analysis, the overall estimate varies be- tween 0.3 and 0.6, with heterogeneity between I²=60% and I² = 90%. ing that all meta-analyses have an average estimate be- tween 0.3 and 0.6, and heterogeneity between I²=60% and I² = 90%. We conclude that the meta-analysis esti- mate is robust to leave-out studies. Z-curve analysis Based on feedback from a reviewer, we created a z- curve analysis (Figure 6, Bartoš and Schimmack, 2021). The Z-curve is a method for estimating publication bias and possibility of false positives. The observed discovery rate is of 45% (64 significant tests out of 141). The ex- pected discovery rate, or the mean power before selec- tion for significance, is of 6%. The expected replication rate, or the mean power after selection for significance, is of 73%. Thus, we see that the power of studies after selection for significance is far higher than before. This is a clear indication of publication bias with a high false positive risk. Risk Of Bias 2 (ROB2) As asked by the editor, we conducted a ROB2 check (J. Higgins, Thomas, et al., 2022; McGuinness and Hig- gins, 2021). We detailed the check by domain alongside the assessment in the spreadsheet. Overall, we found that nearly 40% of studies did not randomize or de- clare the randomization of the participants, nearly 40% lacked an explanation of missing data, and 50% had Figure 6 Z-curve Analysis of the But-you-are-free effect (expectation maximization, EM method) BYAF (with EM) z−scores D e n si ty 0 1 2 3 4 5 6 0 1 2 3 4 Range: 0.01 to 5.18 74 tests, 15 significant Observed discovery rate: 0.20 95% CI [0.12 ,0.32] Expected discovery rate: 0.18 95% CI [0.05 ,0.46] Expected replicability rate: 0.22 95% CI [0.14 ,0.51] a bias in the measurement of the outcome because we cannot trust the studies made with Guéguen’s students (see Brown, 2020). We found no bias due to devia- tion from the intended intervention because all inter- ventions were straightforward, with the measurement of the direct behavior. Finally, no study declared a pre- planification (see Figure 7). After conducting an overall risk of bias, we created a Traffic-light plot visualizing the risks by study (see Fig- ure 8). The complete Plot is in supplementary materials on OSF. We found only seven studies on low-risk and decided to run another meta-analysis on these studies. Our seven studies indicated no effect of the BYAF technique, with a g = 0.11, 95% CI [-0.18; 0.40]. The heterogeneity was huge, with a I² = 95%. A forest plot of the effect can be found in Figure 9. Based on an exchange with the editor, we conducted a third meta- analysis, including all studies with an overall rate of “low risk” and “some concerns”. The result of the meta- analysis is g = 0.38, 95% CI [0.27; 0.49] and I² = 84%. Discussion We conducted three meta-analyses for the BYAF tech- nique. We tested several moderators and found support for a contextual effect of the technique on compliance. Including all studies, we found a direct medium effect of the BYAF technique (g = 0.44) consistent across most of 12 Figure 7 Risk of bias in studies included in our meta-analysis Overall risk of bias Bias in selection of the reported result Bias in measurement of the outcome Bias due to missing outcome data Bias due to deviations from intended interventions Bias arising from the randomization process 0% 25% 50% 75% 100% Low risk Some concerns High risk No information Figure 8 Traffic-light plot of the ten firsts studies included in our meta-analysis our moderators. Excluding high-risk studies, the effect found was weaker (g = 0.38) and nonexistent with only low risk of bias studies (g = 0.11, CI including the null). Confirmatory moderators Type of request We initially hypothesized that the efficacy of the BYAF technique might be higher for prosocial requests than selfish requests, as Carpenter (2013) first hypothesized. In his meta-analysis, he did not find evidence that proso- cial requests were associated with a higher level of com- pliance. With the addition of new effect sizes based on new experiments, we also did not find a significant dif- ference, but our difference is now in the other direc- tion: our results indicate a non-significant higher effect size for selfish requests. This result, while surprising, might be confounded with other moderators. Indeed, selfish requests are often made face-to-face and imme- diately, two conditions with high averaged effect sizes, while prosocial requests were often made indirectly and in delayed condition, two conditions with lower aver- aged effect sizes. In the prosocial condition, the effect size found (g = 0.36) was medium, indicating that this moderator does not play a fundamental role in the ef- fectiveness of the BYAF technique: it might work inde- pendently of this contextual effect. Temporality Our moderator analysis revealed that the effect of the BYAF technique is stronger for immediate rather than for delayed requests, while being at the threshold for significance (α= .05, p = .05). This finding is in accor- dance with our hypothesis, and the findings of Carpen- ter (2013). Indeed, the effect found in the immediate condition was medium to strong (g = 0.47) and weak in the delayed condition (g = 0.25). This finding is not surprising, since we only added two effect sizes to the delayed condition regarding Carpenter’s meta-analysis. Most recent works in the BYAF literature are made via the immediate condition. The effectiveness of the BYAF technique is impacted by the temporality moderator: once the demand is delayed, we cannot be sure that the BYAF technique can be effective, which shows the importance for the participant to be directly linked to the confederate. Exploratory moderator Subject and confederate gender We hypothesized that the BYAF technique can make women comply more than men and that individuals would comply more with a woman confederate. We found no support for a gender effect of moderation. Indeed, across the four conditions, the effect sizes re- main constant (between g = 0.41 and g = 0.48). Also, the result from the ANOVA reveals no interaction effect: the gender of the individual does not interact with the gender of the confederate. Culture We hypothesized that the BYAF technique could be stronger in individualistic countries than in collectivis- tic countries. Our results could possibly corroborate this hypothesis. However, the p-value is not significant, 13 Figure 9 Forest plot of “low risk” studies included in our meta-analysis RE Model −2 −0.5 1 2.5 4 Effect of BYAF technique on compliance Silone et al. (2016) / 1 / 1 Pascual et al. (2002) / 1 / 1 Pascual (2002) / 11 / 1 Gueguen et al. (2013) / 8 / 1 Gueguen et al. (2002) / 1 / 1 Dufourcq−Brana (2007) / 1 / 1 Carpenter & Pascual (2016) / 1 / 1 155 400 220 4515 900 400 89 −0.32 [−0.66, 0.03] −0.22 [−0.42, −0.02] 0.51 [ 0.24, 0.78] 0.36 [ 0.30, 0.42] 0.63 [ 0.49, 0.78] −0.19 [−0.39, 0.00] −0.07 [−0.48, 0.34] 0.11 [−0.18, 0.41] Author(s), Year, and Study # Observed [95% CI]Sample size and we only found 9 effect sizes for participants in col- lectivistic countries, which limits our possibility of ex- planation. Nonetheless, we found that the BYAF tech- nique can be more effective in an individualistic setting. This might be in part due to the easiness for people in individualistic countries to be reactant to the asking, and more effectiveness of the BYAF technique to lower the reactance in this situation. Other mental processes might be active in individualistic countries to influence people not to comply, but they remain unknown. Interactivity We hypothesized that face-to-face interaction would lead to more compliance with the BYAF effect than other types of interaction. Overall, we found a significant difference in this direction: the face-to-face interaction found the highest average effect size (g = 0.51). In more detail, we found that phoning could be a good way to exercise the BYAF technique with a medium ef- fect size (g = 0.43), but we only found one study with this type of interaction. E-mail can also be an effec- tive way to use the BYAF technique, but the effect size found was considerably lower (g = 0.19) and included the null. We call for further examination of this condi- tion of interactivity, since the results are not clear. For the other types of interactivities (i.e., postal letter, in- ternet) we found no effect of the BYAF technique, but we are limited by the number of studies included, with only 2 effect sizes found for each condition. Overall, we found a significant difference between the face-to- face interaction and the others, but we cannot draw a definitive conclusion due to too few effect sizes in the other conditions. Freedom evocation The goal of this moderator was to understand if the exact term “But you are free” was necessary for the ef- fect to appear. We found that it was not the case, as the effects found were not different between the exact term and others. The combination of the other terms leads to a higher non-significant average effect size, signaling a possible more effective way or term to induce com- pliance than the standard term “but you are free”. But what were the other types of evocation used that give 14 the highest effect sizes? Given the forest plot (See sup- plementary metarials), we see that at least three studies give a very high effect size. In the first (Farley et al., 2019, study 2, g = 1.70) the confederate added the term “feel free to say no”. In the second (Guéguen et al., 2013, study 11, g = 0.91), the confederate added the term “Do as you wish” and in the third (Pascual and Guéguen, 2002, study 7, g = 0.75), the confederate added the term “you are not obliged”. In comparing the three terms, we do not find any patterns leading to a meaningful conclusion about how they lead to a stronger effect of the BYAF technique. The only com- mon point between the three studies is that they have very few participants (respectively 40, 86, and 19) lead- ing to a probable overestimate of the effect size. Before and After Carpenter (2013) Finally, we wanted to see if any differences were made between the studies before and after the Carpen- ter (2013) analysis to see if they lead to a different effect size found. Carpenter (Carpenter, 2013) found an aver- age effect size of r = .13. Once our overall effect size (g = 0.45) was transformed in correlation, we found an r = 0.22 of the technique, two times higher than Car- penter found. This result still holds for the analysis we made of the identical dataset used by Carpenter. Why do we have so much difference? We found several errors in the Carpenter (Carpenter, 2013) analysis. For exam- ple, Carpenter used one experiment (Dufourcq-Brana, 2007) two times. Also, Carpenter made ambiguous and not reported decisions in his study. For example, for the experiments with two measures (e.g., Guéguen et al., 2002; Marchand et al., 2009; Pascual, 2002), he decided to take one of them and did not make trans- parent the reason why. In our analysis, we decided to merge them except if one variable is not includable as reported in our preregistration. We found several errors in the original papers, some tests were not compatible with the reported number of participants (e.g., Guéguen et al., 2013; Pascual et al., 2002, study 10). All the discrepancies found are made open in the commentary columns in the dataset. For the publication bias sec- tion, Carpenter only used the Trim-and-Fill technique, leading to no missing studies. We do not know how re- searchers used the algorithm (bilateral or left-centered, as recommended) and the Trim-and-Fill plot is not avail- able. Also, researchers did not report the heterogeneity (I² or tau²) found in the article, while giving the per- centage of variability explained by sampling error. They still found that the BYAF technique only accounts for 22% of the variation, a condition in which the trim- and-fill tool alone might not be sensitive (Carter et al., 2019). Thus, we think that the use of this only publica- tion bias estimator is not enough to assess the credibility of the effect size found. Finally, with the use of the Trim- and-Fill, Carpenter (2013) found an overall corrected effect size of r = 0.04. We found that: 1) the aver- aged effect size found was much higher than the one reported by Carpenter (2013) with the overall sample, 2) the averaged effect size did not differ from before and after the analysis made in 2013, 3) there was a lack of transparency of the choices made in 2013, leading to some errors and curious effect sizes taken into ac- count and 4) no enough assessment of possible publica- tion bias leading to think that the effect size found was more meaningful than it possibly is. Implication With all studies included, we found a medium ef- fect size, but only one meaningful moderator, as the BYAF technique works better in the face-to-face condi- tion than in others, with possible covariates. Also, we have several publication bias estimators flagging pos- sible problems in relation to the experiments on this technique. We did not find that temporality is impor- tant to the effectiveness of the BYAF technique. More surprisingly, we did not find that subject and confed- erate genders were important. Also, we did not find differences between a selfish and a prosocial request and found quite the contrary, as selfish requests were more prone to the BYAF technique than prosocial. Our results indicate that participants seem not to process the request more carefully for a selfish request than for a prosocial one. The interactivity moderator was sig- nificant, but with too few studies for most modalities, and the merging of them can mislead our results. Fi- nally, culture was barely significant, with far more par- ticipants from France than the other countries, and we cannot be sure that the effect is clearly related to cul- ture and not to country and/or confederates in these countries. Overall, we did not find any consistent ev- idence for possible moderators. We have few publica- tion bias estimators that indicate a possibility of publi- cation bias. We found a little asymmetry in our funnel plot, for significant and non-significant results, via dif- ferent techniques. According to Egger et al. (1997), four possibilities are to consider for this asymmetry: se- lection bias, poor methodological quality, true hetero- geneity, and artefactual. For the selection bias, it might be possible to have location and language bias. For ex- ample, most of the original experiments on compliance were said to be made in the same street in the same city (Vannes, France), and others in Bordeaux (France). Also, it is possible that the “but you are free” and “vous- êtes-libre-de” do not have the same meaning, most im- portantly once translated into the language in collec- 15 tivistic countries. We found selective reporting in the Carpenter (2013) meta-analysis (reported in a commen- tary in the dataset). By looking at the original articles, we found lacking and inconsistent data we had to ask the author (we reported their answer in OSF). We also found several poor methodological qualities: a lot of the studies we found have very low power when compared to the effect size found in Carpenter’s analysis. For ex- ample, with a correlation of r = 0.13 transformed to a d = 0.26, a power of 95%, equal number of participants in each group, α of 5%, and a one-tailed test (since we do not want the control group being more effective than the BYAF), we would need 321 participants per group to have a chance to detect the effectiveness of the tech- nique (See supplementary materials for more details). In the forest plot of articles published after the Carpen- ter (2013) analysis (see supplementary materials), we find that only one article (i.e., Grassini et al., 2012) has the necessary power to detect an effect. Unfortunately, this experiment was made via e-mail and does not give us information about the standard face-to-face use of the technique, eliminating possible unknown covariates linked to the use of an online store. Overall, given the smallest effect size of interest of r = .13, no studies con- ducted are enough powered to ensure that the effect of the BYAF technique leads to compliance. For true het- erogeneity, we see that the confidence interval is mostly high, due to too low sample size. Limitations Sample size and Power In the first published paper on the BYAF technique, researchers employed 20 participants per condition (Guéguen and Pascual, 2000). Afterward, Carpenter found a very low effect size for the BYAF technique, which implies the need for a large sample (n = 321 per condition for 95% power, n = 240 per condition for 80% power and an alpha of 0.05, as shown in the implication section). In the last experiment on the subject (Farley et al., 2019), researchers assigned 25 participants to the BYAF group, and 20 to the control group. In between, we found no studies with enough participants in sample size to possibly detect an effect if the effect exists. Low sample size is a major concern for the possibility to put into evidence the effectiveness of the BYAF technique. To see the power of each study in the meta-analysis, we performed a power test (Figure 10). We set the test with a r = 0.13 and alpha = 0.05. The redder the area, the less power, the greener, the more. We found 5 studies in the green area and only two in the yellow area. The average power is 9.70% and the replicability index 0% which means that we have less than 10% of chance to Figure 10 Power test of the articles published after Carpenter’s (2013) analysis 0.0 0.1 0.2 0.3 0.4 0.5 100% 25.5% 10% 7.2% 6.2% 5.8% −1 0 1 Effect S ta n d a rd E rr o r P o w e r 0.05 0.20 0.40 0.60 0.80 1.00 Power α = 0.05, δ = 0.13 | medpower = 9.7%, d33% = 0.31, d66% = 0.49 | E = 12, O = 47, pTES < 0.001, R−Index = 0% Note.. We set alpha to 0.05 and an effect size to r = 0.13, the effect size found by Carpenter (2013). The redder the area, the less power, the greener, the more. We found no studies in the green area and only one in the yellow area. The average power is 9.20% and the replicability index 0% which means that we have less than 10% of chance to reject H0 when there is a true effect, and no chance at all to replicate one study (see Motyl et al., 2017 for R-index). reject H0 when there is a true effect, and no chance at all to replicate one study (see Motyl et al., 2017 for R- index). Also, the Z-curve showed a very low discovery rate of 6%. Guéguen’s work One main reason for conducting this meta-analysis was to see how reliable the effect of the But You Are Free technique was. One major limitation of the present meta-analysis is that nearly all the studies using this technique had Guéguen’s authorship or were made by a Ph.D. student or close collaborator of Guéguen. We tried to make a meta-analysis without Guéguen’s name and found a similar effect size of g = 0.48 [0.28; 0.68] with a total N = 1010 and n = 457 participants from Pascual and collaborators (2021) study. Most implau- sible Odds ratio comes from Guéguen’s study, as we found Odds higher than 5 and some close to 10, with the huge exception of Farley and collaborators (2019) 16 whose results were higher than OR = 23, mostly be- cause of a lack of power (the data were 19/20 compli- ers in the BYAF condition, 9/20 in the control condi- tion). We checked these studies using the ROB2 tool and found that they were problematic for many rea- sons such as no randomization, most confederates are young students aware of the experimentation, no pre- registration or curious way of selecting the participants. As Brown (2020) shows, we cannot trust the young student’s confederates of Guéguen, because some fab- ricated their data. Finally, we conducted a “low risk” meta-analysis which showed no result of the effect. This result clearly questions the existence of the BYAF effect. Limitations in moderators We tried to test several moderators to reduce hetero- geneity: when and how can we ensure that the BYAF is effective? For most of them, the numbers of exper- iments were particularly low. Also, when aggregating them, we did not find any differences between them, and even if we did, we could not draw a strong conclu- sion because these moderators are, for some, very dif- ferent from each other. For the moderators with more than 10 effect sizes, we did not find any differences, and we cannot explain why the heterogeneity persists in the effects found. The only significant moderator we found was the one from our confirmatory hypothesis tempo- rality, as we found that immediate requests are more effective than delayed ones. Finally, we did not find any evidence that moderators can diminish the hetero- geneity of the BYAF technique, leading to the conclusion that: 1) we did not take into account the most impor- tant moderators, mostly because researchers failed to raise attention to them, 2) they are no important mod- erators in the BYAF technique, which contradicts the moderators found for others techniques (see Carpenter, 2013 for a review of some) or 3) the publication bias and/or the possibility of a truly random effect leads to an inflated effect size. Culture While it might be less important than the issues raised above, we cannot be sure that our simple di- chotomy in individualistic versus collectivistic countries is well appropriate for this technique. Indeed, the BYAF technique might rely on subtle or important differences between countries, as some studies on cross-cultural psychology pointed out. For example, Boskł (2020) found that male complied far less to male in Poland, but not in England, based on a sociocultural model. We do not know if the distinction we made was the best pos- sible and we cannot compare countries because, France aside, all the others have experiments from only one study. Approximation of effect While we made transparent how we coded our ef- fect, they are not all closely similar. Indeed, we have, for some studies, merged two conditions altogether to have a control group. In other studies, we took only one possible effect size, the one most closely related to the BYAF effect. Nonetheless, it might still be possible that our decisions lead to bias. This drawback may apply to almost every meta-analysis in empirical science, but we tried to improve transparency and complete reports to ensure having less bias possible. Finally, the ROB2 check was made only by the first author, and as trans- parent as it is, the coding is subjective and can lead to a selection of “low risk” studies different from another coder. Direction for future research The BYAF technique Since the first meta-analysis, we did not find any analysis powered enough to detect an effect of the BYAF technique. The most conservative meta-analysis we made, with only the “low risk” studies, questioned the existence of the effect. The main direction to take is to make a well-powered study with the main and original context of the appearance of the technique, in face-to- face interaction with a request for a spare for the bus. This replication should be made by several confederates from the two genders, in many places across the world. Also, this amount of work can be done with collabora- tive replication to see how the effect varies across dif- ferent contexts and environments. At best, the study should be a pre-registered experiment or registered re- port based on the minimum effect size of interest of r = .13, with a power of 90% and alpha of 0.05, lead- ing to a required sample size of 616 participants. The ROB2 check helped us detail what could be needed for the quality of the study. First, one should carefully ex- plain the randomization and selection of participants in the street. Confederates should not be aware of the ex- perimental conditions and should not be the one who select the participants. Researchers also need to report the targeted subject who didn’t decide to reply at all. Confederates should be of all ages, because only (very) young students were confederates in studies included in the present meta-analysis (in most studies, the mean age of confederates is close to 20 years old). 17 Moderators Once a well-designed, highly powered study is made, it would be possible to investigate some moderators. For example, one type of moderator might be highly rele- vant. The interactivity (Face-to-face or in a more indi- rect setting), and the immediate or delayed moderators were significant, which means that the presence of the confederate might be a necessity for the BYAF technique to work. One direction is to do studies in an internet setting, leading to a refining of the BYAF technique to a nudge, an easy and cheap intervention in the choice architecture (Thaler and Sunstein, 2009), aiming to im- prove the acceptance to a request. The difference found between the internet and face-to-face setting could lead to a huge improvement to understand how the BYAF technique works. Also, the only study we have in an e- mail setting shows an effect size in the range of effects found in nudge theory (DellaVigna and Linos, 2020). Another direction to investigate is the respective impact of gender, age, and culture. We tried to investigate the impact of gender and found no effect, but we could not control for age, which can impact the relationship between gender of the confederate and participant, in the face-to-face setting. Having the help of confederates from multiple age and gender can help understand the impact of these social cues on the helping of others to the request. Also, once controlling for gender and sex, we can move on and enhance the theory by construing upon cultural variation, in different countries and cul- tures. Finally, we did not find any differences between the exact term of evocation “But-you-are-free” and oth- ers, now we propose not to pursue in this direction, un- til a well-powered preregistered replication of the initial effect is made. Author Contact Adrien Fillon, ERA Chair in Science and Innova- tion Policy & Studies (SInnoPSis),University of Cyprus, adrienfillon@hotmail.fr Conflict of Interest and Funding The authors declared no potential conflicts of interest with respect to the authorship and/or publication of this article. One author, who provided data and verified the coding, was an important author in the literature. How- ever, the main coder was independent of the literature. Coding and verifications were made transparent in the Excel file and the source for the code is provided in the Excel file (column N). The authors received no financial support for the re- search and/or authorship of this article. Author Contributions Adrien worked under the supervision of Lionel and Fabien at Aix-Marseille University for conducting the pre-registered meta-analysis. Adrien wrote the pre-registration, with verification and registration by Alexandre, Lionel, and Fabien. Adrien and Alexan- dre conducted the search of the literature, developed the coding scheme, and coded the articles. Adrien provided the RMarkdown code and analyses. Adrien summarized the methods and results and wrote the manuscript. Adrien, Alexandre, Lionel, and Fabien fi- nalized the manuscript for submission. Open Science Practices This article earned the Preregistration+, Open Data and the Open Materials badge for preregistering the hypothesis and analysis before data collection, and for making the data and materials openly available. It has been verified that the analysis reproduced the results presented in the article. The entire editorial process, including the open reviews, is published in the online supplement. References Bartoš, F., & Schimmack, U. (2021). Zcurve: An Im- plementation of Z-Curves. Retrieved November 26, 2021, from https://CRAN.R- project.org/ package=zcurve Boskł, P. (2020). 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OSF. https: //doi.org/10.17605/OSF.IO/YTGRP https://doi.org/10.1177/1069397112450859 https://doi.org/10.1177/1069397112450859 https://doi.org/10.4324/9780203818565 https://doi.org/10.4324/9780203818565 https://doi.org/10.22237/jmasm/1257035100 https://doi.org/10.22237/jmasm/1257035100 https://doi.org/10.3389/fpsyg.2019.00813 https://doi.org/10.3389/fpsyg.2019.00813 https://doi.org/10.1037/0033-295X.96.3.506 https://doi.org/10.1037/0033-295X.96.3.506 https://doi.org/10.2224/sbp.2009.37.4.441 https://doi.org/10.2224/sbp.2009.37.4.441 https://doi.org/10.1016/j.ipm.2006.08.006 https://doi.org/10.1016/j.ipm.2006.08.006 https://doi.org/10.17605/OSF.IO/YTGRP https://doi.org/10.17605/OSF.IO/YTGRP Introduction Original study and its follow-up Moderators Type of request Temporality Subject gender Confederate gender Culture Interactivity Type of freedom evocation Before and After Carpenter’s analysis Summary hypotheses Main hypotheses Confirmatory hypotheses Exploratory hypotheses Method Open-science, replicability, and our current study Literature search Coding Included studies Analysis Moderator analyses Results The But-you-are-free main effect Study design and measures as moderators Subject gender Confederate gender Culture Interactivity Freedom evocation Carpenter’s analysis Type of request Temporality Publication bias Robustness Z-curve analysis Risk Of Bias 2 (ROB2) Discussion Confirmatory moderators Type of request Temporality Exploratory moderator Subject and confederate gender Culture Interactivity Freedom evocation Before and After Carpenter (2013) Implication Limitations Sample size and Power Guéguen’s work Limitations in moderators Culture Approximation of effect Direction for future research The BYAF technique Moderators Author Contact Conflict of Interest and Funding Author Contributions Open Science Practices