The search of studies was designed to update the 2012 meta-analysis by Arias et al. (2013). Thus, the following search strategies were employed: a) search in broad databases PsycInfo, ERIC, EBSCO, and Google Scholar; b) search in gender violence observatories (v.gr., www.work-with-perpetrators.eu; www.VAWnet.org; www.mincava.umn.edu; www.courtinnovation.org; www.cienciaspenales.net; www.iresweb.org); c) contacting prominent researchers in the field (that is, researchers who were the corresponding authors of all the papers found, both the included and excluded papers); and d) review of all the bibliography in the references lists of all the papers found, and previous meta-analytical reviews. The most productive keywords were: “batterer”, “intervention program”, “evaluation”, “assessment”, “effectiveness”, “intimate partner violence”, “partner-violent men”, “recidivism”, “reoffending”, “attrition”, “domestic violence”, “court mandates batterer intervention”, and “prison intervention”.

The relation of keywords was generated by a system of successive approximations whereby the initial keywords of previous meta-analyses determined the inclusion of relevant keywords from all the papers found.

Bearing in mind the objectives of the meta-analysis, the following inclusion criteria were applied to the papers eligible in the search: a) they reported the number of participants; b) they provided the recidivism rate of the sample of subjects who completed the intervention; c) they applied an experimental or quasi-experimental design (with or without control group); d) they indicated theoretical approach, contents, and duration of the intervention program; and e) they stipulated the follow-up period for measuring recidivism. Studies involving a 6-month follow-up period or shorter were excluded owing to the lack of validity in the measures. A total of 25 papers were included under these criteria, with 62 effect sizes, and a sample total of 20,860 intervened batterers. The study search flowchart is shown in Figure 1.

A meta-analysis of experiments was performed by correcting the effect sizes according to the distribution of artifacts (Schmidt & Hunter, 2015). As the measure of recidivism was normally expressed in percentages, or when this was not the case they could be computed, in this analysis the measure of recidivism was defined as the percentage of batterers who had reoffended in gender violence (data on recidivism in other offences were excluded) during the follow-up period. Two indices have been proposed for calculating the effect size in proportions: Cohen’s h and Hedges and Olkin’s (1985) δ, leading to slightly higher, but qualitatively similar results to h (Arias et al., 2013). In this meta-analysis, Hedges and Olkin’s δ was employed. Nonetheless, all of the analyses with h were replicated and obtained qualitatively similar results. In terms of interpretation, δ and h are interchangeable with Cohen’s d, and an effect size of 0.20, 0.50, 0.80 is considered to be small, medium, and large, respectively. However, this classification has generated discrepant interpretations, where small effect sizes were classified as negligible by certain authors but relevant by others. Hence, the effect size was transformed into percentiles (Monteiro et al., 2018) and the magnitude was interpreted in terms of percentage superiority over all possibilities (Vilariño et al., 2018).

As for the effects of the calculus of δ, in previous reviews it has been calculated with control groups both in experimental and quasi-experimental designs. The results showed the type of design mediated differences in effect sizes. However, the type of analysis design is not an effect of the intervention. That is, the differences in results were due to the test value, not the intervention. For this reason, and in order to homogenize the inter-studies contrast value, to control the bias of control groups in primary studies and to include interventions without control groups, the contrast value of recidivism was calculated as reoffending without intervention and the recidivism rate weighted by the sample error of the control group total (Schmidt & Hunter, 2015), which was .22 in ORs and .28 in CRs. Computed effect sizes from primary studies (see Appendix), the following statistics were calculated: sample size weighted mean effect size (d), standard deviation of d (SD_d), standard deviation predicted for sampling error alone (SD_pre), standard deviation of d after removing sampling error variance (SD_res), mean true effect size (δ), standard deviation of δ (SD_δ), percentage of variance attributable to statistical artifacts (%Var), 95% confidence interval for d (95% CI_d), and 80% credibility interval for δ (80% CI_δ).

Though results opened the door to further meta-analyses (the variance explained by artifactual errors was below 75%, i.e., 75% rule; Schmidt & Hunter, 1981), further meta-analyses were impossible as number of sizes (k ≤ 3) or sample sizes (N < 400) were insufficient, or no other moderators had been defined in the primary studies.

When meta-analyses are calculated for the study of moderators for the grouping of variables according to levels, the results do not include the comparison between meta-analyses. Thus, the results were insufficient, as is the case of the analysis of intervention models where significant effects were observed in ORs, but if they were the same or higher in one condition or another was not reported. The same occurred with the duration of the intervention, and the follow-up period. To overcome this contingency, the solution proposed by Amado et al. (2015) was adopted, where the statistic q_s was calculated to compare two effect sizes by converting r, and then comparing the r_s. Furthermore, the results of the meta-analysis were also quite limited in discerning the implications for practice, in this case, the intervention. Regarding the implications of the meta-analysis on professional practice, Fariña et al. (2017) recommend, according to the specific objectives at hand, sensitivity estimation (statistical U), effect quantifying (in present meta-analytical analysis, the efficacy of the intervention, BESD), and the probability of superiority.

As CRs were gathered with different measurement instruments, the correction for the criterion unreliability was computed with Mosier’s (1943) composite reliability coefficient, r = .87.

For the analysis of moderators, the following recidivism variables were encoded (ORs, N = 19,429 and k = 46, and CRs, N = 1,351 and k = 16); follow-up time (≤ 12 months, N = 3,509 and k = 21, and > 12 months, N = 16,050 and k = 26); treatment duration (< 16 sessions/weeks, N = 3,631 and k = 14; and >16 sessions/weeks, N = 15,878 and k = 32); intervention level (individual vs. multi-level); type of sessions (individual sessions, group sessions or combined sessions); and type of treatment (Duluth Model: N = 15,027 and k = 25; CBTPs: N = 1,629 and k = 9, and OTIs: N = 2,853 and k = 12).

The encoding was carried out by an encoder who noted the levels of each of the categories created and described by researchers, and marked exactly where they were referred to in the text. In the encoding of the type of intervention, the criterion stated by the authors of the primary studies was applied, but it should be noted that increasingly interventions based on the Duluth Model also include cognitive-behavioural training techniques for anger management, and CBTPs a gender perspective (e.g., patriarchal attitudes and values). Notwithstanding, the approach ascribed to the intervention was in line with the models proposed. A second encoder reviewed all of the studies using the same encoding system. Thereafter, both the registered categories, and the exact correspondence in the encodings were checked to estimate the true concordance (k) with the kappa statistic (Arce et al., 2000). Kappa corrects the random effect in concordance, but not the correspondence in encodings. Thus, the registration of a category by two encoders in two different places are two encoding errors in the true kappa (lack of correspondence), whereas it is encoded as correct with Cohen’s kappa. Moreover, consistency between two encoders is not sufficient for estimating the fidelity of encodings (i.e., coding correctness in relation to the content of the category), which would require for the encoding to remain stable through time, intra-encoder, and in other evaluation contexts (coders in other studies). The true concordance inter- and intra-encoders was very good (k > .81). Moreover, the encoders were consistent in other contexts i.e., evaluations (Arias et al., 2013; Gallego et al., 2019). Bearing in mind the inter- and intra-evaluator and inter-context consistency of coders, encodings were reliable, that is, reflected the original data.

The results showed a significantly higher rate (+.1540), Z = 12.32, p < .001, of recidivism measured in CRs, than in ORs. Thus, ORs masked a significant amount of recidivism (not surprisingly, because many couples refuse to collaborate, a predictable behaviour associated to revictimization; Brame et al., 2015; and concealment of injuries; Arce, Fariña, Seijo, et al., 2015). Moreover, the confidence margin of the mean rate of recidivism, higher in CRs than in ORs, CI 95% [.1491, .1589], revealed it was stable around 15%.

Taking into account that the efficacy of a treatment varies according to the variable measured, an analysis of outliers was carried out for each measure, ORs and CRs. Data showed that one of the studies, Stith et al. (2004) with CRs, was an extreme value (± 3 * IQR). As for the effect sizes of studies measuring recidivism in ORs, no extreme cases were observed nor outliers with the criterion ± 1.5 * IQR, but extreme cases were observed with a much more conservative criterion ± 2SD (Chauvenet’s criterion). This criterion requires that each meta-analysis should verify the correct classification of outliers and inconvenient studies (contrary to the hypothesis of analysis), or moderators (Tukey, 1960). Thus, a meta-analysis was performed with and without these studies to determine their impact and their effects on estimators. Moreover, a meta-analysis with and without extreme values was performed.

The meta-analysis of the total effect size of the studies on the efficacy of batterer interventions (see Table 1) showed, for 62 effect sizes and for a sample of 20,860 batterers, a positive, significant (confidence interval for d does not include zero), and medium-moderate mean true effect size, δ = 0.44, for batterer interventions. However, these results were not generalizable (credibility interval for δ includes zero) to all studies on batterer interventions, since interventions may have negative effects. Likewise, the results without outliers (N = 20,215 and k = 59) showed a positive, significant (confidence interval for d does not include zero), medium magnitude, and generalizable (credibility interval for δ does not include zero), i.e., batterer interventions had no negative effects (on recidivism) mean true effect size, δ ≈ 0.50. Comparatively, the effect sizes with and without atypical values were equivalent, q_s = .024, ns. Thus, the elimination of outliers excluded inconvenient results that had no effects on global results. In terms of net intervention, efficacy (reduction in recidivism rate) would be approximately 21.49% (r = .2149), but with a negative lower limit, i.e., an increase in recidivism of 6.49% (80% LCV [lower credibility value] converted to r = -.0649). The magnitude of the effect size was greater than 62.17% of all possibilities, and 24.34% of all the positive effect sizes of the interventions.

Nevertheless, the percentage of variance explained by artifactual errors was below 75% in both meta-analyses, so these results were mediated by moderators of effect.

The most extensively researched moderator is the variable measuring effects (criterion), i.e., recidivism, which has been assessed in primary studies in both ORs (i.e., police, courts, correctional institutions), and CRs.

The meta-analysis on the studies measuring intervention efficacy on the recidivism rate in CRs (see Table 1), with a sample of 1,351 batterers and 16 effect sizes, revealed that interventions had no effect on recidivism, with a null (δ = 0.005) mean true effect size (U1 = 0.007, i.e., the independence of the distributions of treated and non-treated batterers was only 0.7%), and could be negative by up to -0.10 or, in other words, the intervention could have a negative effect increasing recidivism rate by up to 4.99% (r = -.0499). The lack of effects of the intervention measured in the recidivism rate in CRs was not mediated by moderators (% VAR > 75). Thus, the results were conclusive. The results were replicated (see Table 1) including the extreme case (N = 1,340 and k = 15), which underpins their stability.

The meta-analysis on studies estimating intervention efficacy on recidivism in ORs, with a sample of 19,509 batterers and 46 effect sizes, showed (see Table 1) a positive, significant (confidence interval for d does not include zero), small-medium (δ = 0.45) and non-generalizable (credibility interval for δ includes zero) mean true effect size in the intervention, with possible negative effects of up to 4.99% (80% LCV converted to r = -.0499), which were mediated by moderators of the relationship between treatment and recidivism (% VAR > 75%). Without outliers (N = 18,875 and k = 44), the results were replicated: a positive, significant, medium, and mediated by moderators mean true effect size, but generalizable (credibility interval for δ does not include zero) to all the studies. Comparatively, the effect size of the meta-analysis with and without outliers were similar, q_s = .029, ns. In short, the effects of outliers were constrained to the lack of generalization of the results to all of the studies, so by eliminating them we would be discarding inconvenient results, not real outliers. Thus, the mean recidivism reduction rate in ORs due to the intervention (versus non-intervened offenders) was 21.95%, but with a lower negative limit, that is, an increase in recidivism of up to 4.99%. Succinctly, on average, interventions reduced recidivism in ORs, but they could also have adverse effects by increasing recidivism rate by more than 50% (Taylor & Maxwell, 2009). The magnitude of the effect was higher than 62.55% of all possibilities, and higher than 25.1% of all the positive effect sizes for batterer interventions. Thus, the positive intervention effect is explained by the measurement method, ROs, rather than the measured construct, recidivism (Podsakoff et al., 2003). However, the percentage of variance explained by artifactual errors was lower than 75%. So, the results were mediated by moderators.

The recidivism follow-up period is a critical factor for criterion validity. In fact, short follow-up periods can artificially increase the efficacy rate, given that approximately 2/3 of reoffending occurs in the first two years (Redondo et al., 2001). According to Gondolf, 2000 and Jones and Gondolf (2002), reoffending occurs in batterers in half the time, and there is widespread agreement that most battery goes unreported, and not documented in ORs (European Union Agency for Fundamental Rights, 2014). For this reason, the follow-up period was taken as a moderator of the results of the intervention and were subdivided into short follow-up periods of 6 to 12 months, and long follow-up periods of more than 12 months, a classification attested to be valid (Arias et al., 2013; Gondolf, 2000).

The meta-analysis on the efficacy of batterer interventions in short follow-up periods, i.e., 12-month or less in ORs (see Table 1), with a sample of 3,509 batterers and a total of 21 effect sizes, found a positive and significant (confidence interval for d does not include zero) mean true effect size (δ = 0.35), but not generalizable to other studies (credibility interval for δ includes zero), and of a small magnitude. These results were replicated in the meta-analysis without outliers (N = 2,875, k = 19), with a positive, and significant (confidence interval for d does not include zero) mean true effect size of moderate magnitude (δ = 0.69), which was generalizable to other studies (credibility interval for δ does not include zero). Comparatively, the effect size of the intervention in the meta-analysis without outliers was significantly higher than with outliers, q_s = .164, p < .01, which was an unexpected and incongruous result (outliers diminished the efficacy of the intervention). Therefore, the results should be analysed without outliers. In practical terms, batterer interventions reduced the recidivism rate in ORs by an average 32.61%, without interventions with adverse effects, (80% LCV = .23), and the effect size was higher than 68.79% of all possibilities and 37.58% of all positive intervention effect sizes. However, these results were mediated by moderators, both in the meta-analysis with all of the effect sizes, and without outliers (% VAR < 75).

The meta-analysis on the efficacy of batterer interventions on 12-month follow-up periods longer in ORs (see Table 1), with 26 effect sizes and a sample of 16,050 batterers, revealed a positive and significant (confidence interval for d does not include zero) mean true effect size of moderate magnitude (δ ≈ 0.50). Moreover, this result was generalizable to other studies (credibility interval for δ does not include zero), but was mediated by moderators (% VAR < 75). As for the reduction in the recidivism rate in ORs, batterer interventions reduced the recidivism rate by 23.34% (r = .2334) and, once again, without detecting negative intervention effects (80% LCV = .11). The magnitude of the effect size was above the 63.31% of all possibilities and 26.62% of all the positive intervention effect sizes.

The mean true effect size of the intervention in ORs with a short follow-up period of up to 12 months (δ = 0.69) or less was significantly larger, q_s = .101, p < .05, than that obtained for the long follow-up period of more than 12 months (δ = 0.48).

Moderators could not be analysed as Ns (< 400) or effect sizes were insufficient (k ≤ 3).

Another moderator reported in the literature as having effects on the intervention is the modality of the intervention, categorized as interventions based on the Duluth Model, Cognitive-Behavioural Treatment interventions, and Other Type of Interventions (Arias et al., 2013; Babcock et al. 2004; Feder & Wilson, 2005; Levesque & Gelles, 1998).

Meta-analysis of the effects on recidivism in ORs for interventions based on the Duluth Model with a sample of 15,027 batterers, and 25 effect sizes revealed (see Table 1) a positive and significant (confidence interval for d does not include zero) mean true effect size of small magnitude (d = 0.37). Moreover, these results were not generalizable (credibility interval for δ includes zero) to all studies with interventions based on the Duluth Model. These results were replicated without outliers (N = 14,393, k = 23), with the exception that they were generalizable to all the studies (credibility interval for δ does not include zero). Comparatively, the effect sizes of all the studies, and those without outliers were similar, q_s = .034, ns. Thus, the outliers were not such, but inconvenient studies with negative effects. In practical terms, interventions based on the Duluth Model reduced on average recidivism by 18.19% (r = .1819), with potential negative effects of up to 9.95% (80% LCV converted to r = -.0995), and an effect size above 60.25% of all possibilities, and 20.50% of all the positive intervention effect sizes. However, the results were mediated by moderators (% VAR < 75).

The meta-analysis of the effects of batterer interventions with CBTPs on recidivism in ORs (see Table 1), with a total of 9 effect sizes and a sample of 1,629 batterers, exhibited a positive, significant for the intervention (confidence interval for d does not include zero), and of a large magnitude (δ = 0.88) mean true effect size, implying an average reduction in the recidivism rate of 40.27% (r = .4027). The generalization of the true effect size could not be studied as the variance was zero (i.e., the studies of this meta-analysis were not randomly distributed); thus, it was analysed with the effect size weighted by sampling error (conservative estimate versus the true size), and was generalizable (credibility interval for d does not include zero) to other studies, and without negative effects, 80% CI [0.70, 1.06]. Additionally, the lower limit of the effect (90% of the interventions surpassed this limit) was 33.40% (80% LCV converted to r = .3340). The magnitude of the effect size was higher than 73.24% of all possibilities, and 46.48% of all the positive intervention effect sizes.

The meta-analysis of the effects of Other Types of Intervention (OTIs) on recidivism in ORs (see Table 1), with a total of 12 effect sizes, and a sample of 2,853 batterers, found a positive, moderate, and significant (confidence interval for d does not include zero) mean true effect size (δ = 0.63), generalizable to all the studies (credibility interval for δ does not include zero). The reduction in the recidivism rate with OTIs (versus the rate for non-intervened batterers) was on average 30.04% (r = .3004), and without interventions with negative effects, and a minimum threshold in the reduction of the recidivism rate of 20.08% (80% LCV converted to r = .2008). The reduction in the recidivism rate by OTIs (versus the rate for non-intervened batterers) was on average 30.48%, without negative effects, and with a minimum threshold in the reduction of recidivism of 20.55%. The magnitude of the effect size was higher than 67.36% of all possibilities, and 34.72% of all the positive intervention effect sizes. Nevertheless, the effect of these intervention modalities on recidivism was mediated by moderators (% VAR < 75). Once again, the analysis of moderators in the different types of interventions was not possible due to insufficient Ns and ks.

Comparatively, the effect of the intervention on the reduction of recidivism was significantly higher in the CBTPs than in the Duluth Model, q_s = .243, p < .01 and in the OTIs, q_s = .117, p < .01, and in the OTIs than in the Duluth Model, q_s = .126, p < .01.

A further moderator of the effects that is systematically reviewed concerns the duration of the intervention (Arias et al., 2013; Babcock et al., 2004). In accordance with Babcock et al. (2004), two categories were created: short duration for programs under 16 sessions/weeks (4 months) and long duration for programs of more than 16 weeks/sessions.

The results of the meta-analysis for short interventions (< 16 sessions), with a total of 14 effect sizes and 3,631 batterers (see Table 1), showed a non-significant (confidence interval for d includes zero) mean true effect size and, consequently, it was not generalizable to other studies. The meta-analysis replicated without outliers (N = 2,997, k = 12) found a positive and significant (credibility interval for δ does not include zero) mean true effect size of small magnitude (δ = 0.29), not generalizable (credibility interval for δ includes zero), and mediated by moderators (% VAR < 75) that could not be analysed owing to the insufficient Ns and ks. The comparison of effect sizes with all of the studies with the exclusion of outliers revealed significant differences, q_s = .129, p < .01, ranging from a non-significant (all of the studies) to a significant (without outliers) mean true effect size. Thus, the outliers were not such, but inconvenient studies with very negative effects. In fact, brief programs can increase the recidivism rate by 39.5% (80% LCV converted to r = .3950).

Regarding long intervention programs (> 16 sessions), the results of the meta-analysis with a total of 32 effect sizes and a sample of 15,878 batterers (see Table 1) displayed a positive and significant (confidence interval for d does not include zero) mean true effect size of moderate magnitude (δ = 0.55), generalizable to other studies (credibility interval for δ does not include zero). As for the efficacy of the intervention, long interventions reduced the recidivism rate in ORs by 26.52% (r = .2652), and without interventions with negative effects, and a minimum threshold in the reduction of recidivism of 10.44% (80% LCV converted to r = .1044). The magnitude of the effect size was higher than 65.17% of all possibilities and 30.34% of all the positive intervention effect sizes. However, the average effect size was mediated by moderators (% VAR < 75) that were not studied owing to insufficient Ns and ks.

Comparatively, long programs were more effective in reducing recidivism in comparison to short interventions, q_s= .257, p < .01.