1 Introduction

The growth of social accountability in corporations would encourage different ethical perspectives among leaders (Schaltegger and Burritt 2018). The level of regard and feeling in a family environment during interactions with management is known as "interactional justice" (Aljawarneh et al. 2022; Krishnan 2016; Flaherty and Moss 2007). The bad emotional states result from a feeling of being unfairly treated (Fox et al. 2001). To address this, organizations must provide relevant data and respond politely and humanely for the interactional justice environment to be appreciated, which increases the performance of employees and impacts feelings and attitudes (Miao et al. 2021). Thus, since physiological outcomes are tied to ethical behavior in workplaces, interactional justice is more closely related to loyalty (Robbins et al. 2012; Robbins and Judge 2013). Similarly, worthy leaders give their staff a sense of dignity, involve them in decisions, and improve workplace equity (Yogasari and Budiasih 2019). Therefore, fair and courteous managers can develop employees with a positive outlook, boost their happiness and trust, and encourage them to aim for a high-performing rating (Cropanzano et al. 2002; Chiaburu and Lim 2008). Leaders' interpersonal tactics with members display their development and empowerment (Fujimoto and Uddin 2021). For example, transactional leadership has four traits: the promise of and allocation of rewards conditional on performance; the active style, acting correctly in advance to manage upcoming concerns; and the passive style, which, when issues emerge as not going as planned, takes remedial action. Transformational leadership is the charisma that inspires subordinates to persevere in the face of challenging goals, providing individualized attention, and reinforcing subordinates' minds to solve recent problems (Tepper and Percy 1994).

There is change and no consensus on leadership definitions. For example, a report of more than 587 studies of leadership definitions in 1993 revealed 221 various concepts. These definitions started in the 1920s and were seen as encouraging cooperation, loyalty, respect, and obedience. In the 1940s, leadership was regarded as directing beyond position and power, whereas in the 1950s, it was seen as the authority and actions of the group. In the twentieth century, leadership was deemed accountable and took responsibility for decisions made by an organization. Despite differences in definitions, they all focus on the leader as a person and their behavior, effects, or interactions with members (Bass and Bass 2009). However, the best leader combines transactional and transformational leadership, two distinct leadership philosophies (Avolio et al. 1999). Another primary example is that ethical leadership is integrity and honesty, including dependability in behavior and the ability to promote moral guidelines with fairness and impartiality in decision-making, as well as outright caring behavior with sympathy. Other definitions of good leadership, for example, include servant leaders who openly express their intrinsic ideas and convictions, while authentic leaders put others' needs ahead of their own. Both types of leaders are regarded as ethical by their followers (Robbins and Judge 2013; Yukl et al. 2013). Furthermore, violence is less likely to occur with reasonable management support and objective leadership with moderate procedural, distributive, and interactional justice (Samsudin et al. 2020). The absence of a passive leadership style and the presence of interactional justice play a primary role in organizational commitment (Vázquez-Rodríguez et al. 2021). The direct relationship between the leader and the follower in interactional justice is necessary for an innovative culture, behavioral commitment, and citizenship (Khan et al. 2018). Considering interactional justice as a part of leadership, leaders of interactional justice have implications for fostering innovation, engagement, good behavior, and trust (Agarwal 2014). For example, a clinical experiment on Danish soldiers uncovered that the higher levels of perceived interactional justice for soldiers in connection to their relationship with leaders were related to a lower likelihood of trauma (Elrond et al. 2018). In terms of organizational justice, only interactional justice was related to transformational leadership (De Cremer et al. 2007). Stronger subordinates' connection to the organization is expected of transformational leadership conduct that is seen as polite, honest, and in line with ethical norms (Thompson et al. 2021).

Employees' evaluations of ethical leadership and managerial conduct constitute organizational justice, where ethical leadership influences perceived fairness. Diversity, customer relations, innovation, service delivery, and management are other factors that are also negatively related to employee exposure to workplace bullying (Ahmad 2018; Sánchez et al. 2020). In addition, ethical leadership can indirectly and directly impact employee happiness and commitment by interacting equitably (Neubert et al. 2009). In other leadership classifications, the authentic leader reduces negative office gossip about peers and supervisors, considering perceived interactional justice (Kurian and Nafukho 2021). Two other cases showed that the emotional regulation of staff did not moderate the relationship between benevolent leadership and interactional justice but moderated the relationship between moral leadership and interactional justice (Lin et al. 2022).

This study was conducted in the first quarter of 2023 to answer the following questions:

  1. (1)

    Empirically, is there a substantial direct relationship between leadership styles and interactional justice in the literature with consistent results?

  2. (2)

    Among the diverse leadership definitions, are there similarities in the concepts? And are there major leadership styles in literature?

  3. (3)

    What are the literature findings about the direct or indirect impact of leadership and interactional justice on each other or other variables in a relationship inside organizations?

This study examines the relationship between leadership styles and interactional justice, presenting valuable insights for organizations aiming to create a positive work environment. Understanding how different leadership styles impact interactional justice helps leaders foster a culture of fairness and positive interactions, improving employee satisfaction and engagement. Additionally, knowing the different meanings of leadership styles and whether they vary helps decision-makers focus on the major types of leadership by enhancing the positive ones and alleviating the impact of the negative ones (Hassan et al. 2023). Remarkably, revealing the significance of leadership and interactional justice has a vital connection to workers feeling comfortable. The primary leadership styles could affect the subordinates positively or negatively inside the organization. These types of leadership and engagement initiate productive actions and commitment instead of counterproductive behavior (Holtz and Harold 2008; Zhu et al. 2013). Practically, perceiving interactional justice has implications for future leaders in encouraging innovation and engagement. In other words, perceiving interactional justice impacts future leaders' willingness to support their subordinates, which, in turn, would affect their psychology. As a result, this feeling of interactional justice impacts employees and organizations (Elovainio et al. 2010; Levenda et al. 2021).

This study targets researchers in organizational behavior and leadership and practitioners in human resource management; additionally, students in related fields might also find it helpful. The study provides a valuable perspective for enforcing leadership strategies to enhance positive interactions and employee satisfaction. In Sect. 2, this study presents the study methodology regarding the search strategy, inclusion criteria, and the study model. Section 3 analyzes and explains all the techniques utilized in the meta-analysis. Section 4 provides a systematic literature review of leadership style definitions and the relationships between these styles and interactional justice. Finally, the discussion is in Sect. 5, and the conclusions and recommendations are in Sect. 6.

2 Methodology

To answer the research questions, this study combines theoretical and empirical methods to prove its solidity and efficiency. Thus, the conceptual framework was supported by the current literature review. Simultaneously, the empirical evidence is gathered through a meta-analysis that applies strict methodologies to scrutinize data from specified studies. The ideal search engines for synthesizing evidence are yet unknown; however, this study utilized "ProQuest" because it contains various databases (Gusenbauer and Haddaway 2020). Again, the goal is to empirically investigate the direct relationship between leadership styles and interactional justice by harnessing the meta-analysis methodology; second, to search for and define the many existing concepts of leadership styles to understand their characteristics; and third, to systematically review and determine the relationship between those two concepts and their impact on other variables in an established relationship. To promote the resilience of the analysis, this study operated with more than one analytical technique: a classical meta-analysis by utilizing Fisher effect size, WLS (weighted least squares), WAAP (weighted average of absolute values of Pearson correlations), and robust Bayesian approaches, where the structure was organized based on Hansen et al. (2021).

2.1 Search strategy

By utilizing the “ProQuest” database, the criteria were to choose "leadership" on the first research tap of the site and "interactional justice" on the next one, with a term for both "anywhere" appearing. The study chose the "peer-reviewed scholarly articles" and "English" ones; after that, there were 3595 articles. However, many of these articles were unrelated, although the words "leadership" and "interactional justice" appeared in the references and introduction of the text, without achieving the study objective, which is to investigate leadership styles, definitions, and their relationship to interactional justice relationships, as well as the impact these two variables can have when they are in a relationship, together or with other elements.

2.2 Inclusion criteria

The study modified the search to include new criteria: the "interactional justice" and "leadership" variables should be found in "all abstract and summary text," and they should be "articles" in peer-reviewed "scholarly journals" and in "English" anywhere at any time. Despite that, the search results showed 42 articles, of which only 36 were related to the research objectives. This study used the following criteria to collect data:

  1. (1)

    In the meta-analysis, the selection was from the related 36 studies, where the condition was that these studies should have a Pearson correlation between leadership styles and interactional justice. Therefore, some studies were excluded from the analysis regarding that or in cases where interactional justice and primary leadership styles were classified into multiple categories or represented by small concepts. Eighteen valid studies were included, and four were duplicated as they examined two assorted styles of leadership relationships with interactional justice. Accordingly, 22 relationships were examined.

  2. (2)

    Among the 36 articles, this study compiled the definitions of leadership styles from 43 relationships.

  3. (3)

    In the systematic literature review, this study investigated 36 related articles about leadership styles and interactional justice, whether they were discovered with each other or were connected to other elements in a relationship.

Based on that, Fig. 1 illustrates the research methodology. Notably, in this study, the concept of “status of leadership” or “status of interactional justice” points out their situation in an investigation: independent, dependent, mediator, or moderator. Additionally, “leadership style” infers, for example, transformational, transactional, authentic leadership, or other types mentioned in the analysis.

Fig. 1
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The research model

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3 Meta-analysis techniques

The study in meta-analysis employed a spectrum of techniques, including Fisher’s effect size estimates, 'WLS and WAAP,' and robust Bayesian methods. The total number of participants in the meta-analysis was 6384 in 22 cases, with an average of 336, while the average number of male participants was 51.02%.

3.1 Meta-analysis for continuous effect size estimates

In this analysis, the effect-sized Pearson correlations (r) were converted into Fisher's Z values based on Campbell's Collaboration.org website. Table 1 below shows the results of the effect size between leadership styles and interactional justice. This study aims to deliver a more comprehensive examination, allowing for a sufficient understanding of the research results. Therefore, it included the outlier study (Zoghbi-Manrique-de-Lara and Suárez-Acosta 2014). While it was an outlier in this analysis afterward, the “WLS and WAAP” and Cohen's d scale in the robust Bayesian meta-analysis techniques disclosed that it was significant. For supplementary information on meta-analysis and outliers, see Steel et al. (2021). However, the effect size for all leadership styles was substantial, and the Z value is still more considerable than 2.58 (p < 0.01), which implies a significant link between all the investigated leadership styles and interactional justice. The overall Q statistic (Q = 451.294, df = 21, p < 0.01) disclosed remarkable heterogeneity between the analyzed studies, as shown in Fig. 2, which means potential factors might influence this relationship. For this reason, this study elaborated more on conducting meta-regression analysis for predictors of the relationship.

Table 1 Fisher’s effect size estimates for included studies
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Fig. 2
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Funnel plot for all studies

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3.2 Meta-regression analysis for predictors of the relationship

In Table 2, the meta-regression estimations were conducted to explore the effects of various predictors on the relationship between leadership and interactional justice utilizing "unrestricted expectation maximization estimation." This part shows many scenarios concerning predictors of this relationship by including factors (the study location, status of leadership, status of interactional justice, leadership style) and other covariates (number of participants, male percentage) into the relationship. The study location and male participants were significant, as was the binary of the study location and the number of participants (p < 0.01). Eventually, the displayed factors jointly assist significantly in predicting this relationship.

Table 2 Meta-regression for predictors of the association between leadership and interactional justice
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3.3 WLS and WAAP methods

This study in Table 3 elaborated more on giving accurate results by utilizing the WAAP–WLS method because it offers a lower bias than traditional estimations while keeping each of its significant statistical features, and reliable estimates with statistical power greater than 80% are given perfect weights to remove reporting bias (Stanley et al. 2017). The model tests indicate that the WLS and WAAP methods generated significant results, confirming a strong relationship between leadership and interactional justice (t = 16.228, df = 21, p < 0.001). Significantly, 22 studies included in the analysis met the criteria for being adequately powered, with statistical power exceeding 80%. The relationship mean estimates were consistent across both the WLS and WAAP methods (estimated correlation coefficient (ρ) = 0.645, p < 0.001). This implies a positive and significant association, and the narrow confidence interval further supports the robustness of the relationship because it gives higher precision in estimating the correlation coefficient, as illustrated in Fig. 3. The multiplicative heterogeneity estimates were identical for both WLS and WAAP, with an estimate of (4.069) regarding that it shows a significant degree of variation in the effect estimates and is far from (0.645) among the 22 studies (Lardier et al. 2019; Thompson and Sharp 1999).

Table 3 WLS–WAAP model
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Fig. 3
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Mean model estimates (p)

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3.4 Robust Bayesian meta-analysis

Bayesian modeling methods were utilized because of their power to enclose prior information, handle heterogeneity, and provide more robust estimation and uncertainty quantification compared to classical approaches (Moeltner et al. 2007). Based on the study of Berkhout et al. (2023), Table 4 displays the model selection probabilities (P(M)), probability of a model given observed data (P(M|data)), and robust Bayes factor (Inclusion BF). Half of the models support the effect model, which establishes its importance, where the high certainty (P(M|data) = 1.000) and the robust inclusion (BF of 6266.758) boost the reliability of this link. The heterogeneity model also receives support, with high certainty and a remarkably high inclusion rate (BF of 3.216 × 10 + 57). Publication bias was present in most cases (32 out of 36 models), with a low certainty value of 0.467 and an inclusion BF of 0.875, showing inconclusive evidence regarding the existence of publication bias.

Table 4 Robust Bayesian Met-analysis model summary
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Table 5 clarifies the model-averaged estimates, utilizes Cohen's d scale to estimate the effect size, and ensures consistency throughout the analysis, enabling a robust interpretation of the results (Colonnesi et al. 2010), in which Cohen's d is a widely accepted metric that standardizes the difference between means (Cohen et al. 2013). Regarding this, the calculated mean effect size (δ) is higher than 0.80 (1.453), which presents a considerable effect and proves a substantial relationship between leadership and interactional justice. However, the heterogeneity (τ) reveals a moderate diversity in the effect sizes across the studies due to the mean estimate of 0.440. Yet, Fig. 4 presents the model-averaged forest plot, illustrating the effect sizes based on Cohen's d scale in the robust Bayesian meta-analysis. Notably, this approach has revealed a significant study outlier that went unnoticed in Fisher’s method. Primarily, the outlier study is marked by a 95% CI of [1.94, 2.48], demonstrating a significantly different effect size from zero. Consistently, the effect sizes observed in these studies exhibit a potent relationship between leadership and interactional justice.

Table 5 Model averaged estimates
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Fig. 4
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Model averaged forest plot

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4 Systematic literature review

4.1 Description of the sample

In the systematic review analysis, the total number of participants was 15,406, with 51% males, as the participants in the sample were from different continents and the studies were conducted on students, teachers, and workers in diverse disciplines. Most studies used surveys for data collection, such as self-administered, online, or scenario simulation methods, and one used a structured clinical interview. Yet, in Fig. 5, the sample is distributed based on leadership and interactional justice status (independent, dependent, moderator, and mediator) in the chosen relationships.

Fig. 5
figure 5

Status of leadership and interactional justice in the relationships

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4.2 Leadership styles and definitions

Importantly, this study sorted and summarized the classifications of leadership styles and definitions in Table 6 according to their frequencies in the 36 scholarly articles, from the most frequent to the least frequent. Therefore, the most dominant type classifications were ethical leadership in ten studies and transformational and transactional leadership in six. This review finds that the bulk of research focuses on the main three styles of leadership and their subcategories or, surprisingly, gives different classifications to the exact characteristics of other leadership styles. In other words, there is a high degree of similarity between the definitions of leaders’ styles and the descriptions of good and bad leaders.

Table 6 Leadership styles and definitions
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Looking at the prevailing main leadership styles, transactional leadership represents a conditioned payoff because they act in a way that instructs others what to do and attaches specific monetary rewards to the completion of explicit goals but still adheres to conventional methods of operation and has two subcategories: the active is proactive to prevent fault, but the passive one reacts to modify the drawback (Vázquez-Rodríguez et al. 2021; Visser and Scheepers 2022). Transformational leadership is a charismatic leader who inspires workers, provides intellectual stimulation, and fosters trust by paying attention to workers personally and encouraging them to commit to goals, surpass expectations, and show ethical standards (De Cremer et al. 2007; Sánchez et al. 2020; Thompson et al. 2021). Ethical leadership leads to subordinates' devotion to the boss because they follow ethical standards, behave equitably with staff, demonstrate moral transactional elements, advance workplace fairness, and avoid bullying (Ahmad 2018; Charoensap et al. 2019; Wang et al. 2017; Wang and Chan 2020; Zoghbi-Manrique-de-Lara and Suárez-Acosta 2014).

4.3 Systematic review

This section presents some of the descriptive results of the numeric findings in analyzing the 36 scholarly articles in Table 7. This table is ordered by the status of leadership in the relationship as follows: independent, mediator, moderator, dependent, and as a part of interactional justice.

Table 7 Systematic review for leadership and interactional justice
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The benevolent leaders had a direct effect on interactional justice. Those leaders were like angels in all three cultures—Taiwan, Turkey, and the United States—but authoritarian leaders were perceived as devils only in the United States and Turkey (Gumusluoglu et al. 2020). Through interactional justice, servant leadership is more likely to foster a change-friendly environment (Kool and van Dierendonck 2012). In addition, in settings with higher levels of moderators (empowering leadership and interactional justice), the relationship between workers' identification and their ability to handle new obstacles was strong (Paolino 2020). An environment of interactional justice was associated with ethical leadership, and this relationship, in turn, led to higher workplace citizenship among nursing staff (Qiu et al. 2020). Directly, moral leaders were responsible for interactional justice and affected the perception of empowerment factors: impact, competence, self-determination, and importance. However, when international justice was a mediator between moral leadership and empowerment, the relationship was positively significant in one dimension: self-determination (Li et al. 2012). The fairness of the interpersonal treatment received from supervisors significantly impacted employees' job happiness, and the relation-oriented leader was a significant predictor of this pleasure in finding justice (Bakotić and Bulog 2021). Where interactional justice served as a mediator, transformational leadership did not impact effect- or cognition-based trust. But once more, transactional leadership, in turn, significantly influenced affect- and cognition-based trust, with interactional justice serving as a mediator (Visser and Scheepers 2022). Remarkably, the moderator's ethical leadership enhanced the mediating effect of interactional justice. There was a significant positive effect on satisfaction and a negative influence on leaving work (Wang and Chan 2020).

5 Discussion

The meta-analysis of the findings from 22 cases, operating different techniques, established the strength of the relationship with noticeable heterogeneity between studies, while the proof for publication bias is still uncertain (P(M|data) = 0.347), which indicates the necessity of considering this in subsequent analyses. Using Fisher’s effect size, one study was an outlier, but it was essential in the WLS and WAAP methods and Cohen's d methods. However, this study suggests that different leadership styles have varying degrees of association with interactional justice, as shown by the significant heterogeneity of the effect sizes among all utilized methods. Still, leadership is significantly correlated with interactional justice (p < 0.01). These results indicate that these leadership styles can play influential roles in influencing organizational justice and should be considered by organizations when developing leadership strategies. Nonetheless, it is critical to note the existence of heterogeneity across the studies, indicating the intervention of other contextual factors influencing these relationships. For example, the analysis of predictor factors and covariates exhibited that they impact leadership and interactional justice, which is vital when examining other associations. This includes study location, leadership style, number of participants, and the status of both leadership and interactional justice in a relationship.

This study collected 43 definitions of leadership styles from 36 scholarly articles. It appears that transformational leadership, with its four types of charismatic, inspirational, personalized attention, and stimulating thinking, is the ethical leader. In the same way, transactional leadership, with its four types (reward promising, reward giving, active management, and passive management), is considered ethical and fair to energize workers and compensate them for their efforts. On the other hand, some traits of transactional leadership may be seen as unfavorable by workers because the active style puts staff under pressure and blames them in advance to prevent faults without socially caring, and the passive style acts after the problems occur. Studies by Agarwal (2014), Andrade and Ramirez (2019), and Elrond et al. (2018) blended the two concepts, leadership and interactional justice, into one, explicitly or implicitly. Similarly, Habib et al. (2020) claimed that interpersonal leadership is a mixed type of interactional justice and transformational leadership. Paradoxically, there is a relationship between these two concepts and not just one part. Interactional justice occurs when employees are treated with dignity and respect, which is how they perceive the interactional justice of a leader. Even though transformational leadership is a broader definition of a good leadership style, there are redundancies in the classifications of leadership, such as benevolent, authentic, servant, and management-exchange leadership, which were not considered in the Habib et al. (2020) study and made interactional justice just limited to the transformational leadership style.

Systematically, by analyzing 36 scholarly articles, regardless of the leadership and interactional justice status in the relationship (independent, dependent, mediator, or moderator), in general, they have interconnection with each other, and they influence other variables in a relationship. Just one study conducted in Belgium was different: the Wynendaele et al. (2021) study, which indicated that the indirect influence of a self-work schedule via the mediator (leader-management exchange) on interactional justice was negatively related (p < 0.10). To elaborate more, this study discusses the systematic review results by trying to compile the same leadership styles into a unified dialogue. In the following passages and according to the literature, there were different leadership styles eventually; regarding the traits, they can be attributed to three primary leadership styles (ethical, transformational, and transactional) with their subcategories. In the subsequent paragraphs in this section, notes of similarities or categories of some leadership styles are clarified in brackets.

Informational justice, to begin with, served as a mediator between ethical leadership, dedication to supervisors, and job happiness but did not affect organizational commitment. On the other hand, interpersonal justice played no role in all these attitudes. In other words, informational justice affected two attitudes: job satisfaction and loyalty to the supervisor in the presence of ethical leadership (Charoensap et al. 2019). Another critical point is that deviant work behavior and organizational commitment are essential attitudes and reactions to interactional justice for peers. However, Zoghbi-Manrique-de-Lara and Suárez-Acosta (2014) showed that ethical leadership was a significant mediator in the relationship between perceived interactional justice toward peers and citizenship behavior; even their study in the current meta-analysis, ironically, has a Fisher’s effect size zero value. Markedly, when moderate ethical leadership was present at higher levels, there was a higher correlation between interactional justice and employees' ethical behavior (Al Halbusi et al. 2019). Likewise, servant leadership (which empowers staff as transformational leadership and treats them ethically as ethical leadership) and contingent reward leadership (transactional), combined with interpersonal and informational fairness, were more inclined to foster optimism, but servant leadership only proved to encourage change in the presence of interactional justice and optimism (Kool and van Dierendonck 2012). Similarly, Wang et al. (2017) exhibited ethical leadership through the mediator of interactional justice. It had a positive effect on the employees' loyalty to the supervisor. Leaders affect interactional justice directly. Gumusluoglu et al. (2020) found that the mediating role of interactional justice was influential in the United States but not in Taiwan or Turkey, with a positive link to benevolent leadership (it is ethical and transformational leadership regarding caring for staff) and an adverse link to authoritarian leadership. Benevolent and moral (ethical) leadership affected team performance when interactional justice was a mediator factor (Lin et al. 2022). Equally, White et al. (2012) demonstrated that supervisor support, trust, and interactional fairness were dramatically improved through leader-positive rapport management and leader-member interchange (which both combine traits of individualized consideration and transformational leadership). In particular, Wang and Chan (2020) stated that ethical leadership and interactional justice significantly reduced resignation intentions while increasing enthusiasm and job satisfaction. The same was valid for organizational justice, which was perceived at prominent levels with informational and interpersonal components of justice through interactions between employees and their authentic leadership that emphasized the ethical aspects of work. Pay, performance, and processes are examples of this (Kurian and Nafukho 2021).

In addition, employees' impressions of corporate fairness correlated with authentic leadership, procedural justice, and interactional justice. Workers' view of interactional fairness served as a mediator between authentic leadership and peers, and it even lowered negative gossip about peers and supervisors (Cheng et al. 2022). Equally important, Dong and Zhong (2022) disclosed that by establishing intrinsic corporate social responsibility in the presence of interactional justice, responsible leadership (which encourages engagement like personalized-attention transformational) promoted employee work involvement, thereby increasing the efficiency of improving employee work-related connections and achieving organization development. Conversely, Zoghbi-Manrique-de-Lara and Suárez-Acosta (2014) showed that unfavorable injustice toward peers leads employees to react in the form of engaging in deviant work behavior and decreasing organizational citizenship behavior, which makes them more prone to perceiving their leadership as unethical. Employees' perceptions of ethical leadership and interactional justice directly influence whether they commit to organizational citizenship behavior and engage in deviant work behavior.

In Vietnam, charismatic (transformational) environmental leadership influenced environmental employees' work in the presence of organizational justice as a moderator. The moderators of organizational justice were environmental procedural justice and interactional justice. Again, environmentally charismatic leadership influences employee environmental commitment and environmental citizenship in the workplace (Tuan 2019). Furthermore, in Pakistan, interactional justice positively influenced performance in the presence of considerate individuals' leadership (transformational), and the ratio of prediction performance increased from 46 to 48%. The effect of interpersonal leadership (a combination of transformational leadership and behavioral interactional justice) was significantly positive on work engagement (Habib et al. 2020). Similarly, there was a significant positive effect of the moderators' empowering leadership (transformational) and interactional justice on workers' identification and on the way of solving complicated emerging problems (Paolino 2020). Nonetheless, Williams et al. (2016) showed that the relationship between the exchange-leadership member who served as a mediator between interactional justice and tactics was positively significant. Considering transformational leadership as an independent variable, De Cremer et al. (2007) indicated that it is affected by a fair atmosphere in the organization. In another way, when transformational leadership was an independent variable, staff could manage their clash between work and family through the mediator of interactional justice.

Transactional leadership has four characteristics: the promise and allocation of rewards based on performance and achieving goals; the active style, acting correctly in advance to manage upcoming concerns; and the passive style, which takes corrective action when issues emerge and are not progressing as planned (Tepper and Percy 1994). Notwithstanding, literature has approved that the kind of leadership that puts off making decisions and offering feedback to subordinates and does not encourage them is not leadership (Vázquez-Rodríguez et al. 2021). However, transactional leadership concerns itself more with distributive rewards, and this reflects distributive justice (Alamir et al. 2019). Whereas this kind of leadership would achieve the planned goals (Samsudin et al. 2020), subordinates are still constricted to a specific way of doing work (Visser and Scheepers 2022). Furthermore, while transactional leadership focuses on goal-achieving through rewards, promises, and giving, transformational leadership inspires and stimulates thinking toward a goal. As an example of goal-oriented leadership (which has transactional traits) in general, Samsudin et al. (2020) showed that goal-oriented leaders, organizational support, and interactional fairness helped lower the adverse effects of bullying on employees of an organization. On the contrary, laissez-faire leadership (passive-transactional) and negative interactional justice led to the absence of practical organizational commitment in five Spanish prison facilities (Vázquez-Rodríguez et al. 2021). In Croatia, interactional justice and relation-oriented leadership jobs impacted job satisfaction, but task-oriented leadership (which has transactional traits) did not have this impact (Bakotić and Bulog 2021).

6 Conclusions and recommendations

The meta-analysis findings unveiled a link between interactional justice and leadership styles and even the heterogeneity of results between the same style and other styles due to other variables such as study location, relationship status, and the number of participants. In addition, evidence of publication bias was limited, urging more studies in this area. It is also recommended to harness different methods in the analysis to reflect the actual results. Nonetheless, based on the results, organizations should encourage and spotlight the development and undertaking of transparent and trustworthy leadership practices as they impact organizational justice and foster positive work environments and outcomes. Relation-orientation leadership, rapport management leadership, and empowering leadership also play crucial roles in propelling a supportive climate; however, note that these were individual studies on each leadership style. Nevertheless, during the systematic review of leadership and interactional justice relationships, their impact on other variables, and their definitions, it was found that multiple leadership styles emerged; features may be linked to three basic leadership types (ethical leadership, transformational leadership, and transactional leadership) through the other interlacing definitions. Moreover, the relationship between leadership styles and interactional justice was significant in the given sample, whether those two variables were in a direct relationship or with others (indirect). Again, this study establishes that leadership and interactional justice have a significant connection.

Inappropriate leaders conceal information and treat employees disrespectfully to achieve personal or organizational goals, such as through authoritarian leadership or, in some cases, active leadership. The opposite is true; transformational or ethical leaders treat workers with dignity and respect and do not conceal information. Therefore, workers feel satisfied with these types of leadership and engage in productive actions and commitment instead of counterproductive behavior. In practice, perceiving interactional justice impacts future leaders by fostering innovation and engagement. As a result, leaders should consider the psychology of staff and how interactional justice affects employees and organizations. The other case is the definition of leadership; however, it is expected to confuse these concepts. Moral and authentic leadership styles foster moral and ethical standards. Benevolent leadership, showing moral interests in people's jobs and lives, is considered ethical or transformational leadership (personalized attention). Empowering leadership can also be ethical or transformational (inspirational). Since goal-oriented leadership steers individuals toward goals, it can be transactional (promising rewards and giving) or transformational (stimulating thinking). Finally, management-exchange leadership, which fosters trust, ethicality, and interactional justice and develops relationships with subordinates, can be transformational (personalized attention) or ethical. Task-oriented is transactional, while relation-oriented is transformational or ethical.

In conclusion, wise leadership is important through satisfying appropriate interactional justice with workers because this reflects cutting off deviant behavior or wasting organizational resources, which would lift productivity, satisfaction, commitment, trust, and cooperation. Admittedly, the study states that to create justice in the organization, the leadership needs to pursue integrity and ethical conduct. Interactional justice focuses on the interpersonal side of organizational practices, particularly treating staff interpersonally. Informational justice is the fairness of interpersonal communication. That implies that employees can perceive justice in the organization when it provides adequate and truthful information during the decision-making process, as was the case in the study by White et al. (2012), where rapport management leaders utilized appropriate language in interpersonal interaction to control social relationships by protecting employees' individual and group rights and desires. In this study, the implications are that understanding interactional justice is the responsibility of prospective leaders to inspire subordinates and make them involved and creative in the organization. Workers who perceive interactional fairness interchangeably with their leader are willing to engage in productivity and positive behavior. Moreover, it is urgently recommended that the concepts of leadership be unified into three main categories: transformational, transactional, and, in general, ethical leadership (if researchers want to investigate ethical aspects in an organization and how leaders respect staff and treat them with dignity and follow ethical standards); otherwise, there is no need for more ramifications that keep us out of the target and make others confused.

This study finally answers all three research questions: (1) The meta-analysis established a substantial direct relationship between leadership styles and interactional justice, with some degree of dissimilarity in effect size. (2) Looking at their style definitions, an overlap in diverse leadership definitions is proven by noticing their affiliation with the three main leadership styles (ethical, transformational, and transactional). (3) In the literature review, directly or indirectly, there was an impact of leadership and interactional justice on each other and other variables in a relationship inside organizations. Based on that, future research directions should investigate the root causes and limit circumstances that lead to the observed variation in the effect size of the meta-analysis and more into those leadership style concepts and their impact on organizational justice while utilizing a group of different methods in the analysis. Besides, where the study found indeterminate evidence considering the publication bias and has certain methodological limitations, additional investigations would improve the generalizability of the results.