Our search criteria were narrow to ensure that the research question was addressed. That is, a given study had to compare the strength change in an untrained limb when the homologous muscle was trained on the opposite limb. The unilateral training protocol did not have to follow a specific training manipulating frequency, duration, intensity, or type of training because the interest in the results (cross-education of strength) was a training protocol compared between a dominant and non-dominant limb in the same study sample. Additionally, studies were required to include separate training groups of the dominant and non-dominant limb along with a non-exercise control within the same study. The inclusion of a time-match, non-exercise control for each study would increase confidence that the cross-education of strength, if observed, was from the unilateral training. Studies were excluded if it was not written in English, did not include humans, and did not include resistance training. The small number of studies included for this analysis was not due to a lack of searching. As noted in Supplementary Table 1, we reviewed nearly 1,000 papers and provided reasons for their exclusion.

Our search was conducted in line with PRISMA guidelines (Page et al. 2021). The acquisition of studies was completed using Cochrane Library, PubMed, and Scopus from February 2022 to May 2022 with no limitations in publication dates (Fig. 1). Relevant studies were identified using the terms: “directionality cross-education strength training”; “right-hand strength training or left-hand strength training”; “right–left limb training cross-education”; and “dominant limb in cross-education of strength”. Other studies under the references of selected papers that met the inclusion criteria were additionally reviewed. Terms such as “dominant limb training crossover effect of strength” and “dominance in crossover effect strength” were also used, but zero relevant studies were found. The first author (V.W.) completed the search, and V.W., J.S.S., and J.L. independently extracted the data from the included papers. V.W. and J.L. independently conducted the meta-analysis. V.W. and J.S.S. independently evaluated the quality of the included studies using the risk of bias tool 2 (RoBII) (Sterne et al. 2019).

PRISMA flowchart of the studies included for the present meta-analysis

An editable spreadsheet was prepared to capture the following: author name and year of publication, whether the study included a group training the dominant limb (with non-dominant untrained) and a group training the non-dominant limb (with dominant limb untrained) in the same study, whether the study included a time-matched non-exercise control group, sample size for each group, portion of the body trained, exercise completed, type of strength test utilized, the change scores for each group, and the standard deviation of the change score for each group. If data were reported as standard errors, they were converted to standard deviations by using the appropriate formula (i.e., multiplied by the square root of the sample size). The standard deviation of the difference score between measurements was used when reported directly but was estimated when not reported.

All data were analyzed by multiple investigators as a quality control measure in an effort to maximize accuracy (V.W. and J.L.). Effect sizes were calculated for each study using the mean difference and the standard deviation of the difference (commonly known as Cohen’s dz) (Dankel and Loenneke 2018). If the standard deviation was not reported but an exact p value was, then the t value was calculated using the inverse of the cumulative distribution function. The t value was then used to calculate the change score standard deviation. We normalized the mean difference to the standard deviation of the difference, rather than using pretest and posttest standard deviations, because we were interested in capturing the magnitude of the variability within the intervention itself. If the variability of the change was not provided (and could not be calculated from the data provided), the standard deviation of the change was estimated using the following formula:

$$_change}=\sqrt})}^+ })}^-(2r\times \mathrm\times \mathrm)].}$$

SD represents the standard deviation and r represents the correlation coefficient between the pretest and the posttest scores. We used 0.9 as the pre–post correlation, since this correlation on strength tests would be expected to be large (Dankel et al. 2020). The standardized effect size and the standard error of this standardized effect size were computed as follows (Borenstein et al. 2021):

$$Standardized\,ES=\frac_- _}_-1\right)_+\left(_-1\right)_}_+_-2}}},$$

$$Standardized\,SE= \sqrt_+ _}_* _}+\frac^}_+ _)}}.$$

ES represents the effect size, N1 represents the sample size of the exercise group, N2 represents the size of the control group, \(_\) represents the variance of the exercise group, \(_\) represents the variance of the control group, and SE represents the standard error.

All statistics were computed using the robumeta package (version 2.0) and metafor package (version 3.0–2) within R Studio (version 1.4.1717). We implemented these two packages to account for dependency between effect sizes. All studies were weighted using the inverse variance weight and effect sizes are reported in standardized units (Cohen’s d). Three separate comparisons were made and visually displayed as forest plots: (1) cross-education effect from dominant to non-dominant limb vs. non-exercise control; (2) cross-education effect from non-dominant to dominant limb vs. non-exercise control; and (3) cross-education from dominant to non-dominant limb vs. cross-education from non-dominant to dominant limb. Forest plots provide point estimates of the individual effect sizes in graphical form as boxes with 95% confidence intervals surrounding each block. The overall effect is included at the bottom of the plot as a diamond with a width equivalent to the confidence interval for the estimated effect (forest.robu function in the robumeta package).

In robumeta, we ran a correlated effects model with small sample corrections. The default correlation was 0.8; however, we also ran sensitivity analysis to determine the effect of rho on tau2. We also ran the analysis using the robust function of metafor (Restricted ML). To reduce problems associated with using a normal distribution, we implemented the argument tdist = TRUE with the rma.mv function, which applies the Knapp and Hartung adjustment to the analysis. We included estimates from metafor to include prediction intervals. Prediction intervals provide information of where the effect size of a new study would fall if this study was selected at random from the same population of the studies already included in the meta-analysis.

In the control groups, two limbs on each participant were not trained (i.e., these participants did not train; thus, both limbs were not trained) and, therefore, comparing the cross-education of strength to the intervention groups (dominant-limb vs non-dominant-limb training) was feasible with either limb. Of the three studies included in this review, two of them (Farthing et al. 2005; Othman et al. 2019) reported the cross-education data of the control group from both limbs. However, the Farthing and colleagues (2005) study, randomized the non-exercise control group limbs into a “trained” and “untrained” limb. In other words, it is not known which untrained limb (dominant or non-dominant) from the control group was used. One of the three studies (Coombs et al. 2016) only reported data for the control group without determining the side that the control data was from.