Spiritual over physical formidability determines willingness to fight and sacrifice through loyalty in cross-cultural populations

Significance Despite intermittent interest in and evidence of the importance of nonmaterial factors in war and other extreme forms of intergroup conflict, material factors such as optimal use of physical strength, manpower, and firepower remain the dominant concerns of US and allied military training, decision-making, and related academic literature. In this work, we demonstrate the cross-cultural primacy of personal spiritual over physical formidability on the will to fight in populations from the Middle East, Europe, and North America, including US cadets in whom stronger group loyalty mediates the effect. This empirical examination of spiritual formidability and its link between self and group in willingness to self-sacrifice aims to extend understanding of interpersonal and intergroup conflict and inform considerations of policy.


Sensitivity Analyses
In all studies, we performed a sensitivity analysis, using G*Power (1), to determine which would be the minimum size effect to reject the null hypothesis considering our sample size and assuming an alpha level of .05 and 80% power. Study 1. The results indicate that an p ≥ .194 for a correlation (point biserial model, two tails) would be enough to reject the null hypothesis. Study 2. The results indicate that an p ≥ .208 for a correlation (point biserial model, two tails) would be enough to reject the null hypothesis. Study 3. The results indicate that an χ 2 ≥ .3.841 for a generic χ 2 test would be enough to reject the null hypothesis.
Study 4. The results indicate that an f 2 ≥ .140 for a linear multiple regression (fixed model R 2 deviation from zero) would be enough to reject the null hypothesis.
Study 5. The results indicate that an f 2 ≥ .023 for a linear multiple regression (fixed model R 2 deviation from zero) would be enough to reject the null hypothesis.
Study 6. The results indicate that an f 2 ≥ .013 for a linear multiple regression (fixed model R 2 deviation from zero) would be enough to reject the null hypothesis.
Study 7. The results indicate that an f 2 ≥ .021 for a linear multiple regression (fixed model R 2 deviation from zero) would be enough to reject the null hypothesis.
Study 8. The results indicate that an f 2 ≥ .057 for a linear multiple regression (fixed model R 2 deviation from zero) would be enough to reject the null hypothesis.
Study 9. The results indicate that an f 2 ≥ .030 for a linear multiple regression (fixed model R 2 deviation from zero) would be enough to reject the null hypothesis.
Study 10. The results indicate that an f 2 ≥ .082 for a linear multiple regression (fixed model R 2 deviation from zero) would be enough to reject the null hypothesis.
Study 11. The results indicate that an f 2 ≥ .046 for a linear multiple regression (fixed model R 2 deviation from zero) would be enough to reject the null hypothesis.
In Studies 1-3, all participants who completed all items assessing religiosity, spiritual formidability, and physical formidability were included in the analysis. Similarly, all participants who completed physical and spiritual formidability items and dependent measures in Studies 4-9 were included in the analysis. In Studies 10-11, all participants who completed these items were included in the replication analyses. Participants not completing the loyalty items were excluded from the mediation analysis. Table 5 in the main text contains a detailed description of each sample including Institutional Review Board (IRB) approvals.

Supplementary Methods and Measures
All of the survey items used in Studies 1-11 were validated in previous research (e.g., 1). Across all studies, physical and spiritual Formidability were always presented side by side on the same display regardless of the data collection method.
The measure of physical and spiritual formidability in English is as follows: In the next set of questions you will see images that represent the physical and spiritual formidability of a person, group, country, or institution.
The physical formidability of a person or a group represents the ability and material resources (e.g., access to weapons, size, strength) of a person or group to fight and achieve their objectives. Physical formidability endows the person or group with the material potential to defend themselves or inflict physical damage to the opponent. Data for all studies are available on OSF at the following link: https://osf.io/mvhgj/?view_only=10b8928478964e5684f8fa8ea7d3dbee

Studies 1-3
Religiosity was measured by a single-item scale asking participants to what extent they consider that most Spanish people are religious (from 0 = Not religious at all to 6 = Extremely religious) in Studies 1 and 2. In Study 3, we asked participants if spiritual formidability is more important to predict the behavior of a group than religiosity.
The religious and practicing group was not related to physical or spiritual formidability, r(7) =.10. p=.79 with physical and 0.01, p = .98 for spiritual. For those reporting they are religious but not practicing, religiosity was not related to spiritual formidability, r (70) = -.06, p = .64 and -.12, p = .32 and, for those reporting as non-religious, spiritual formidability and religiosity were not related, r(93) = 0.05. p=0.66 and 0.07, p = .53.

Studies 4-5
Physical and Spiritual Formidability (avg = .90) -As described and displayed in the main text, physical and spiritual formidability were measured on a slider scale that enabled participants to increase or decrease the size and muscularity of an image of a male body. The smallest, thinnest figure corresponded to a value of zero and the largest, most muscular figure corresponded to a value of one.

Willingness to Fight and Commit
Costly Sacrifice (avg = .89) -Costly sacrifices for the country (i.e., ingroup) were measured by a five-item scale adapted from our previous study (1), on scales from 0 (totally disagree) to 6 (totally agree), where participants were asked to what extent, if necessary, they would be willing to display different kinds of self-sacrifice to defend their country as follow: "lose my job or source of income", "go to jail", "use violence", "let my children suffer physical punishment", and "die". In Study 5, this scale includes a sixth item: "If necessary, I would be willing to be exiled from Morocco and be stripped from my Moroccans citizenship to defend Moroccans".

Studies 6-9
Physical and Spiritual Formidability (avg = .89) -Formidability measures mirrored Studies 1-2. Because Study 7 used a paper and pencil version of the survey, we used six bodies to measure each type of formidability (see Figure 1).

Willingness to Fight and Commit
Costly Sacrifice (avg = .92) -This was measured similar to Studies 4-5 except Studies 6-9 did not include the item "let my children suffer physical punishment". Studies 6 and 9 included two additional items: "physically suffer", and "risk harm to friends close to me".

Willingness to Fight and Commit
Costly Sacrifice (avg = .92) -In Study 10, costly sacrifices for the country were measured by a five-item scale ranging from 0 (totally disagree) to 6 (totally agree), where participants were asked to what extent, if necessary, they would be willing to display different kinds of self-sacrifice to defend their country as follows: "lose my job or source of income", "go to jail", "use violence", "let my children suffer physical punishment", and "die". Because cadets generally do not have children, the item "let my children suffer physical punishment" was replaced with "be a prisoner of war" in Study 10. In Study 11 the item "be a prisoner of war" was not included.
Loyalty -Group Loyalty was assessed by a single item asking participants how important it is for them to be loyal, or to show loyalty, to their group.

Mediation Analyses
The analyses used in Studies 10 and 11 to assess the extent to which loyalty to the group mediated the positive correlation between spiritual formidability and costly sacrifices controlled for physical formidability perceptions, age, and gender. For this mediation analysis, we utilized the bias-corrected bootstrapping procedure (5,000 samples) in the indirect macro for SPSS, model 4 (2).