Purpose

We are pivoting from the full 12-item SEB scale (descriptive + prescriptive) to prescriptive SEBs only (6 items). This document re-runs the key analyses from Study 1 (OCBI, UPB), Study 2 (status affordance), and the Study 3 manipulation pilot using only the prescriptive items, and puts the results side by side.

One question is whether prescriptive SEB has predictive power above and beyond status zero-sum beliefs (SZSB). Every model below is therefore fit in several specifications (bivariate → + SZSB → + all preregistered controls), and incremental tests are reported.

Prescriptive items used

Study Distribution-prescriptive Attribute-prescriptive
Study 1 dist_7, dist_8, dist_10 (original wording) attr_6, attr_8, attr_10
Study 2, Study 3 pilot dist_14, dist_15, dist_16 (revised wording) attr_6, attr_8, attr_10

Heads up: Study 1 used the original distribution-prescriptive wording (alpha = .61 in Study 1 notes). Studies 2 and 3 used the revised items that match the six statements in the email to Adam. So the Study 1 composite is not item-identical to the Study 2/3 composite. The alpha table below shows whether this matters.

Measures and items

Item wording below is taken from the question-text row of the Qualtrics exports (raw_study1_data_8_4_25.csv, raw_study2_fulldata_10_8_25.csv, pilot_raw_data_11_11_25.csv). Items marked (R) are reverse-scored (8 - x) in the code. All items use 1 = strongly disagree to 7 = strongly agree unless noted otherwise.

Prescriptive SEB (the predictor used throughout)

Stem (all studies): “To what extent do you agree or disagree with each of the following statements about your team?” followed by “In my team…”

Team referent differs by study:

  • Study 1 and Study 3 pilot: “Think about the team you currently work most closely with in your job. If you work with multiple teams, focus on your primary or main team. If you are not currently part of a team, think about the team you most recently worked with.”
  • Study 2 (managers): “Think about the team you currently manage. If you work with multiple teams, focus on your primary or main team.”
Subscale Study 1 (variable) Study 2 and Study 3 pilot (variable)
Distribution …Everyone who wants status should be able to attain it. (dist_7) …Many members should be able to gain respect and admiration. (dist_14)
Distribution …All members should have the opportunity to be valued and admired. (dist_8) …High status should not be granted to just a few people. (dist_15)
Distribution …Status or influence should not be limited to just a few individuals. (dist_10) …High status should be shared among a wide range of members. (dist_16)
Attribute …High status should be based on a wide variety of attributes. (attr_6) same (attr_6)
Attribute …Everyone should have an opportunity to gain status for the unique skills they bring. (attr_8) same (attr_8)
Attribute …People should recognize a wide range of qualities when determining who deserves status. (attr_10) same (attr_10)

The three attribute items are identical across studies. The distribution items were reworded after Study 1; the Study 2 and pilot wording matches the six statements in the email to Adam.

Descriptive SEB items (dropped in this analysis), shown for reference (dist_1R, dist_2R, dist_5R are reverse-scored; the attribute items are not):

Subscale Item
Distribution (R) …A small number of members receive the most respect and admiration. (dist_1R)
Distribution (R) …Prestige and influence are concentrated in just a few members. (dist_2R)
Distribution (R) …High status is concentrated around certain members and not distributed across all members. (dist_5R)
Attribute …Many different attributes and skills are seen as worthy of respect and admiration. (attr_3)
Attribute …People gain status for contributing in a wide variety of ways. (attr_4)
Attribute …People value a broad range of strengths when offering respect. (attr_5)

Outcomes

Organizational citizenship behavior toward individuals, OCBI (Lee & Allen, 2002; 8 items; Study 1 and Study 3 pilot; 1 = never, 7 = always). Stem: “Please indicate how often you engage in the following behaviors at work:”

  1. Help others who have been absent. (OCBI_1)
  2. Willingly give your time to help others who have work-related problems. (OCBI_2)
  3. Adjust your work schedule to accommodate other employees’ requests for time-off. (OCBI_3)
  4. Go out of the way to make newer employees feel welcome in the work group. (OCBI_4)
  5. Show genuine concern and courtesy toward coworkers, even under the most trying business or personal situations. (OCBI_5)
  6. Give up time to help others who have work or nonwork problems. (OCBI_6)
  7. Assist others with their duties. (OCBI_7)
  8. Share personal property with others to help their work. (OCBI_8)

Unethical pro-organizational behavior, UPB (Umphress et al., 2010; 6 items; Study 1). Stem: “To what extent do you agree or disagree with each of the following statements?”

  1. If it would help my organization, I would misrepresent the truth to make my organization look good. (UPBs_1)
  2. If it would help my organization, I would exaggerate the truth about my company’s products or services to customers and clients. (UPBs_2)
  3. If it would benefit my organization, I would withhold negative information about my company or its products from customers and clients. (UPBs_3)
  4. If my organization needed me to, I would give a good recommendation on the behalf of an incompetent employee in the hope that the person will become another organization’s problem instead of my own. (UPBs_4)
  5. If my organization needed me to, I would withhold issuing a refund to a customer or client accidentally overcharged. (UPBs_5)
  6. If needed, I would conceal information from the public that could be damaging to my organization. (UPBs_6)

Inclusivity (1 item; Study 1, used as a mediator): “I try to include others and make sure they feel valued in my team.” (fv_inclusivity)

Status affordance (Choi & Anderson, 2024; 3 items; Study 2). Managers first listed the initials of up to 10 people they directly oversee; three were randomly selected and each was rated in random order: “Earlier you listed the initials of up to 10 people that you directly oversee at work. Now, we will ask a few questions about one of those individuals: [initials]. To what extent do you agree or disagree with each of the following statements about [initials]?”

  1. I respect [initials]. (affordance{1,2,3}_1)
  2. I admire [initials]. (affordance{1,2,3}_2)
  3. I grant status to [initials]. (affordance{1,2,3}_3)

Dominance and prestige strategies (Study 3 pilot outcomes, and controls in Studies 1 and 2) are listed with the controls below.

Control scales (same wording in all three datasets)

Stem for status zero-sum beliefs, need for status, dominance, and prestige: “To what extent do you agree or disagree with each of the following statements?”

Status zero-sum beliefs, SZSB (Andrews-Fearon & Davidai, 2023, Journal of Experimental Psychology: General, 152(2), 389-409, Appendix A; 8 items listed)

  1. When status for one person is increasing it means that status for another person is decreasing. (SZSB_1)
  2. Status is a limited good, when one person gains in status it inevitably comes at another person’s expense. (SZSB_2)
  3. When one person moves up the social hierarchy it means that another person has to move down the hierarchy. (SZSB_3)
  4. If someone wants to move up the social hierarchy, they have to do so at someone else’s expense. (SZSB_4)
    1. Status is not a finite resource. (SZSB_5R)
    1. When one person has a lot of status it doesn’t mean that someone else lacks status. (SZSB_6R)
  7. Not everyone can be high status. If one person has higher status, someone else must have lower status. (SZSB_7R; scored WITHOUT reversal, see note)
    1. When one person gains in status, it does not mean that someone else is losing status. (SZSB_8R)

SZSB_7R is not reverse-scored (error in the source paper). Appendix A of Andrews-Fearon and Davidai (2023) labels item 7 as “(reverse-coded)”, and the Qualtrics variable name (SZSB_7R) and the earlier Study 1, 2, and 3 scripts follow that label. We treat this as an error in the paper’s appendix and score the item without reversal, for three reasons:

  1. The item is worded in the zero-sum direction (agreement = more zero-sum thinking), unlike the genuinely reverse-worded items 5, 6, and 8.
  2. In all three datasets it correlates positively with items 1 to 4 (r of roughly .5 to .7).
  3. Scoring it as labeled gives SZSB alphas of about .76 (Study 1), .66 (Study 2), and .76 (pilot); scoring it un-reversed gives about .91, .85, and .90, closer to the .86 to .92 the paper reports.

(The paper’s text also says the scale has nine statements, but the appendix lists eight.) Consequence for comparability: SZSB values, and any model that includes SZSB, will differ slightly from the earlier analysis files that reversed item 7. In a Python re-run the prescriptive SEB coefficients barely moved (e.g., Study 1 OCBI b = .353 vs .350), but SZSB became a significant predictor of Study 2 status affordance. To reproduce the old scoring, set szsb_no_reverse <- character(0).

Need for status (Flynn et al., 2006; 8 items)

  1. I want my peers to respect me and hold me in high esteem. (need for status_1)
    1. I am not concerned with my status among my peers. (need for status_2R)
  3. Being a highly valued member of my social group is important to me. (need for status_3)
  4. I would like to cultivate the admiration of my peers. (need for status_4)
  5. I enjoy having influence over other people’s decision making. (need for status_5)
  6. It would please me to have a position of prestige and social standing. (need for status_6)
    1. I don’t care whether others view me with respect and hold me in esteem. (need for status_7R)
  8. I care about how positively others view me. (need for status_8)

Social dominance orientation, SDO (Ho et al., 2015; 8 items). Stem: “Show how much you favor or oppose each idea below. You can work quickly; your first feeling is generally best.”

  1. An ideal society requires some groups to be on top and others to be on the bottom. (sdo_1)
  2. Some groups of people are simply inferior to other groups. (sdo_2)
    1. No one group should dominate in society. (sdo_3R)
    1. Groups at the bottom are just as deserving as groups at the top. (sdo_4R)
  5. Group equality should not be our primary goal. (sdo_5)
  6. It is unjust to try to make groups equal. (sdo_6)
    1. We should do what we can to equalize conditions for different groups. (sdo_7R)
    1. We should work to give all groups an equal chance to succeed. (sdo_8R)

Dominance and prestige (17 items; adapted by Lange et al., 2019 from Cheng et al., 2010, and used by Andrews-Fearon & Davidai, 2023, Appendix B, to measure willingness to use dominance and prestige strategies to attain higher rank. Item wording in the exports matches Appendix B exactly. The preregistrations cite Cheng et al., 2013 for this measure.)

Dominance (8 items)

  1. I enjoy having control over others. (dom_1)
  2. I often try to get my own way regardless of what others may want. (dom_2)
  3. I am willing to use aggressive tactics to get my way. (dom_3)
  4. I try to control others rather than permit them to control me. (dom_4)
    1. I do not aim at having a forceful or dominant personality. (dom_5R)
  6. I want others to know it is better to let me have my way. (dom_6)
    1. I do not enjoy having authority over other people. (dom_7R)
  8. I like when some people are afraid of me. (dom_8)

Prestige (9 items)

  1. I try to get members of my group to respect and admire me. (prest_1)
    1. It does not bother me if people do not want to be like me. (prest_2R)
  3. I enjoy it when others expect me to be successful. (prest_3)
    1. It does not bother me if others do not value my opinion. (prest_4R)
  5. I try to be held in high esteem by those I know. (prest_5)
  6. I like it when my unique talents and abilities are recognized by others. (prest_6)
  7. I like it when I am considered an expert on some matters by others. (prest_7)
  8. I enjoy it when others seek my advice on a variety of matters. (prest_8)
    1. It would not bother me if others do not enjoy hanging out with me. (prest_9R)

Packages and setup

library(tidyverse)
library(qualtRics)  # read_survey()
library(lme4)
library(lmerTest)   # p-values for lmer; load AFTER lme4
library(psych)
library(car)        # VIF
library(lavaan)
library(knitr)
library(kableExtra)

set.seed(2025)


f_study1 <- read_survey("~/Google drive/My Drive/YEAR 2/PROJECTS/DEREK/Status Distribution/Studies/Study 1: Scale/Final Study 1/raw_study1_data_8.4.25.csv")
f_study2 <- read_survey("~/Google drive/My Drive/YEAR 2/PROJECTS/DEREK/Status Distribution/Studies/Study 2: Status Affordance/raw_study2_fulldata_10.8.25.csv")
f_pilot  <- read_survey("~/Google drive/My Drive/YEAR 2/PROJECTS/DEREK/Status Distribution/Studies/Study 3: SEB Manipulation/pilot_raw_data_11.11.25.csv")

controls <- c("szsb", "nfs", "sdo", "dom", "prest")

Helper functions

# Qualtrics exports have 2 header rows (question text, ImportId) under the names.
# `drop_extra` removes additional rows, e.g., a researcher test response.
read_qualtrics <- function(path, drop_extra = 0) {
  raw <- read.csv(path, na.strings = c("", "NA"), stringsAsFactors = FALSE)
  raw[-seq_len(2 + drop_extra), ]
}

# Same exclusion rules as the preregistrations:
# bot screener, attention check, geolocation appearing 3+ times
apply_exclusions <- function(d) {
  d %>%
    rename_with(make.names) %>%   # "need for status_1" -> "need.for.status_1"
    filter(attn_bots != "14285733",
           suppressWarnings(as.numeric(attn)) == 24) %>%
    mutate(geolocation = paste(LocationLatitude, LocationLongitude, sep = "_")) %>%
    group_by(geolocation) %>%
    mutate(geo_frequency = n()) %>%
    ungroup() %>%
    filter(geo_frequency < 3)
}

# Row mean of items; any item name ending in "R" is reverse-coded (8 - x),
# except items listed in `no_reverse` (see SZSB_7R below)
scale_mean <- function(d, items, no_reverse = character(0)) {
  m <- as.data.frame(lapply(d[, items], as.numeric))
  rev_idx <- endsWith(items, "R") & !(items %in% no_reverse)
  m[rev_idx] <- 8 - m[rev_idx]
  rowMeans(m, na.rm = TRUE)
}

# Item lists (names as they appear after read.csv, i.e., spaces become dots)
items_szsb  <- paste0("SZSB_", c(1:4, "5R", "6R", "7R", "8R"))
# SZSB_7R is worded in the zero-sum direction, so it is NOT reverse-scored here.
# Appendix A of Andrews-Fearon & Davidai (2023) mislabels it "(reverse-coded)"; see Measures section.
szsb_no_reverse <- "SZSB_7R"
items_nfs   <- paste0("need.for.status_", c("1", "2R", "3", "4", "5", "6", "7R", "8"))
items_sdo   <- paste0("sdo_", c("1", "2", "3R", "4R", "5", "6", "7R", "8R"))
items_dom   <- paste0("dom_", c("1", "2", "3", "4", "5R", "6", "7R", "8"))
items_prest <- paste0("prest_", c("1", "2R", "3", "4R", "5", "6", "7", "8", "9R"))
items_ocbi  <- paste0("OCBI_", 1:8)
items_upb   <- paste0("UPBs_", 1:6)

items_presc_s1  <- c("dist_7", "dist_8", "dist_10", "attr_6", "attr_8", "attr_10")
items_presc_s23 <- c("dist_14", "dist_15", "dist_16", "attr_6", "attr_8", "attr_10")

# Prescriptive SEB + the preregistered control scales
score_common <- function(d, presc_items) {
  d %>%
    rename_with(make.names) %>%
    mutate(
      presc       = scale_mean(., presc_items),
      presc_dist  = scale_mean(., presc_items[1:3]),
      presc_attr  = scale_mean(., presc_items[4:6]),
      szsb        = scale_mean(., items_szsb, no_reverse = szsb_no_reverse),
      nfs         = scale_mean(., items_nfs),
      sdo         = scale_mean(., items_sdo),
      dom         = scale_mean(., items_dom),
      prest       = scale_mean(., items_prest)
    )
}

# Fit the same set of specifications for any DV (lm or random-intercept lmer)
fit_specs <- function(data, dv, mixed = FALSE, ctrl = controls, covar = NULL) {
  # ctrl : control variables (drop the DV itself if it is also a control, e.g., dominance)
  # covar: extra covariate(s) added to EVERY model (e.g., "cond_high" in the Study 3 pilot)
  ctl <- paste(ctrl, collapse = " + ")
  add <- if (is.null(covar)) "" else paste0(" + ", paste(covar, collapse = " + "))
  rhs <- list(
    bivariate     = paste0("presc", add),
    szsb_only     = paste0("szsb", add),
    plus_szsb     = paste0("presc + szsb", add),
    controls_only = paste0(ctl, add),
    full          = paste0("presc + ", ctl, add)
  )
  map(rhs, function(r) {
    fml <- as.formula(paste(dv, "~", r, if (mixed) "+ (1 | ResponseId)" else ""))
    if (mixed) lmer(fml, data = data) else lm(fml, data = data)
  })
}

# z-score DV and predictors so coefficients are comparable across studies
zscore <- function(data, vars) {
  data %>% mutate(across(all_of(vars), ~ as.numeric(scale(.x))))
}

# Pull one coefficient (works for lm and lmerTest::lmer)
get_coef <- function(model, term = "presc") {
  cf <- summary(model)$coefficients
  tibble(b = cf[term, "Estimate"],
         se = cf[term, "Std. Error"],
         p = cf[term, ncol(cf)])
}

# Incremental value of prescriptive SEB over (a) SZSB alone, (b) all controls
incremental <- function(mods, mixed = FALSE) {
  a <- anova(mods$szsb_only, mods$plus_szsb)
  b <- anova(mods$controls_only, mods$full)
  if (!mixed) {
    tibble(
      comparison = c("SZSB  ->  SZSB + prescriptive SEB",
                     "All controls  ->  + prescriptive SEB"),
      delta_R2 = c(summary(mods$plus_szsb)$r.squared - summary(mods$szsb_only)$r.squared,
                   summary(mods$full)$r.squared - summary(mods$controls_only)$r.squared),
      test_stat = c(a$F[2], b$F[2]),
      p = c(a$`Pr(>F)`[2], b$`Pr(>F)`[2]),
      test = "F"
    )
  } else {
    tibble(
      comparison = c("SZSB  ->  SZSB + prescriptive SEB",
                     "All controls  ->  + prescriptive SEB"),
      delta_R2 = NA_real_,
      test_stat = c(a$Chisq[2], b$Chisq[2]),
      p = c(a$`Pr(>Chisq)`[2], b$`Pr(>Chisq)`[2]),
      test = "LRT chi-sq"
    )
  }
}

fmt_p <- function(p) ifelse(p < .001, "<.001", sub("^0", "", sprintf("%.3f", p)))

Load, exclude, and score

# ---- Study 1 -----------------------------------------------------------------
# Drop first row (test)
s1 <- f_study1 %>%
  slice(-1) %>%
  apply_exclusions() %>%
  score_common(items_presc_s1) %>%
  mutate(ocbi = scale_mean(., items_ocbi),
         upb  = scale_mean(., items_upb),
         inclusivity = as.numeric(fv_inclusivity))

# ---- Study 2 -----------------------------------------------------------------
s2 <- f_study2 %>%
  apply_exclusions() %>%
  filter(ResponseId != "R_3YbMmG50lMF2JPv") %>%   # flagged as bot-like in Study 2 notes
  score_common(items_presc_s23) %>%
  mutate(across(matches("^affordance[123]_[123]$"), as.numeric))

# Must nominate 3 subordinates (preregistered)
s2 <- s2 %>% filter(!is.na(selected1), !is.na(selected2), !is.na(selected3))

# ---- Study 3 pilot (SEB manipulation check) ------------------------------------
p <- f_pilot %>%
  apply_exclusions() %>%
  score_common(items_presc_s23) %>%
  mutate(ocbi = scale_mean(., items_ocbi),
         condition = factor(ifelse(FL_31_DO == "manipulation-lowSEB", "low", "high"),
                            levels = c("low", "high")),   # effect = high - low
         cond_high = as.numeric(condition == "high"))

tibble(
  Study = c("Study 1", "Study 2 (rated 3 subordinates)", "Study 3 pilot"),
  `N raw responses` = c(nrow(f_study1), nrow(f_study2), nrow(f_pilot)),
  `N analyzed`      = c(nrow(s1), nrow(s2), nrow(p))
) %>% kable() %>% kable_styling(full_width = FALSE)
Study N raw responses N analyzed
Study 1 414 390
Study 2 (rated 3 subordinates) 227 157
Study 3 pilot 105 99

Scale reliability and descriptives (prescriptive SEB)

alpha_of <- function(d, items) round(psych::alpha(d[, items] %>% mutate(across(everything(), as.numeric)))$total$raw_alpha, 2)

tibble(
  Study = c("Study 1", "Study 2", "Study 3 pilot"),
  `Alpha, 6-item prescriptive` = c(alpha_of(s1, items_presc_s1),
                                   alpha_of(s2, items_presc_s23),
                                   alpha_of(p,  items_presc_s23)),
  `Alpha, distribution (3)` = c(alpha_of(s1, items_presc_s1[1:3]),
                                alpha_of(s2, items_presc_s23[1:3]),
                                alpha_of(p,  items_presc_s23[1:3])),
  `Alpha, attribute (3)` = c(alpha_of(s1, items_presc_s1[4:6]),
                             alpha_of(s2, items_presc_s23[4:6]),
                             alpha_of(p,  items_presc_s23[4:6])),
  M  = c(mean(s1$presc), mean(s2$presc), mean(p$presc)),
  SD = c(sd(s1$presc),   sd(s2$presc),   sd(p$presc))
) %>%
  mutate(across(c(M, SD), ~ round(.x, 2))) %>%
  kable() %>% kable_styling(full_width = FALSE)
Study Alpha, 6-item prescriptive Alpha, distribution (3) Alpha, attribute (3) M SD
Study 1 0.79 0.61 0.81 5.76 0.75
Study 2 0.78 0.69 0.74 5.73 0.75
Study 3 pilot 0.87 0.79 0.82 5.70 0.94 
# How much does prescriptive SEB overlap with SZSB and the other controls?
overlap <- bind_rows(
  s1 %>% select(presc, all_of(controls)) %>% summarise(across(all_of(controls), ~ cor(presc, .x, use = "pair"))) %>% mutate(Study = "Study 1"),
  s2 %>% select(presc, all_of(controls)) %>% summarise(across(all_of(controls), ~ cor(presc, .x, use = "pair"))) %>% mutate(Study = "Study 2"),
  p  %>% select(presc, all_of(controls)) %>% summarise(across(all_of(controls), ~ cor(presc, .x, use = "pair"))) %>% mutate(Study = "Study 3 pilot")
) %>% select(Study, everything())

overlap %>% mutate(across(where(is.numeric), ~ round(.x, 2))) %>%
  kable(caption = "Correlation of prescriptive SEB with each control") %>%
  kable_styling(full_width = FALSE)
Correlation of prescriptive SEB with each control
Study szsb nfs sdo dom prest
Study 1 -0.23 0.13 -0.35 -0.13 0.14
Study 2 -0.23 0.13 -0.42 -0.33 0.16
Study 3 pilot -0.46 0.03 -0.43 -0.40 0.09 
redundancy <- function(d, label) {
  m <- lm(presc ~ szsb + nfs + sdo + dom + prest, data = d)
  r2 <- summary(m)$r.squared
  tibble(Study = label, `R2 (presc SEB ~ controls)` = r2, `VIF (presc SEB)` = 1 / (1 - r2))
}
bind_rows(redundancy(s1, "Study 1"), redundancy(s2, "Study 2"), redundancy(p, "Study 3 pilot")) %>%
  mutate(across(where(is.numeric), ~ round(.x, 2))) %>%
  kable(caption = "High values would mean prescriptive SEB is largely redundant with the controls") %>%
  kable_styling(full_width = FALSE)
High values would mean prescriptive SEB is largely redundant with the controls
Study R2 (presc SEB ~ controls) VIF (presc SEB)
Study 1 0.18 1.21
Study 2 0.26 1.35
Study 3 pilot 0.35 1.53

Study 1: Prescriptive SEB -> OCBI and UPB

Raw-scale models

s1_ocbi <- fit_specs(s1, "ocbi")
s1_upb  <- fit_specs(s1, "upb")

OCBI: preregistered model (full controls)

summary(s1_ocbi$full)
## 
## Call:
## lm(formula = fml, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.67091 -0.73883  0.03573  0.72075  2.59732 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.899227   0.560790   3.387 0.000781 ***
## presc        0.349552   0.079810   4.380 1.54e-05 ***
## szsb         0.061764   0.048160   1.282 0.200452    
## nfs          0.121520   0.084112   1.445 0.149349    
## sdo         -0.007658   0.042726  -0.179 0.857855    
## dom         -0.184551   0.059483  -3.103 0.002061 ** 
## prest        0.117087   0.089796   1.304 0.193044    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.076 on 383 degrees of freedom
## Multiple R-squared:  0.1179, Adjusted R-squared:  0.1041 
## F-statistic: 8.531 on 6 and 383 DF,  p-value: 1.033e-08

UPB: preregistered model (full controls)

summary(s1_upb$full)
## 
## Call:
## lm(formula = fml, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9460 -0.8824 -0.2573  0.6770  5.0760 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.95722    0.65570   2.985  0.00302 ** 
## presc       -0.18733    0.09332  -2.007  0.04540 *  
## szsb         0.04523    0.05631   0.803  0.42237    
## nfs         -0.07538    0.09835  -0.766  0.44389    
## sdo          0.10822    0.04996   2.166  0.03090 *  
## dom          0.30426    0.06955   4.375 1.57e-05 ***
## prest        0.15627    0.10499   1.488  0.13748    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.258 on 383 degrees of freedom
## Multiple R-squared:  0.1471, Adjusted R-squared:  0.1337 
## F-statistic: 11.01 on 6 and 383 DF,  p-value: 2.504e-11

Does prescriptive SEB add anything beyond SZSB?

bind_rows(
  incremental(s1_ocbi) %>% mutate(Outcome = "OCBI"),
  incremental(s1_upb)  %>% mutate(Outcome = "UPB")
) %>%
  select(Outcome, comparison, delta_R2, test, test_stat, p) %>%
  mutate(delta_R2 = round(delta_R2, 3), test_stat = round(test_stat, 2), p = fmt_p(p)) %>%
  kable() %>% kable_styling(full_width = FALSE)
Outcome comparison delta_R2 test test_stat p
OCBI SZSB -> SZSB + prescriptive SEB 0.074 F 30.94 <.001
OCBI All controls -> + prescriptive SEB 0.044 F 19.18 <.001
UPB SZSB -> SZSB + prescriptive SEB 0.022 F 8.87 .003
UPB All controls -> + prescriptive SEB 0.009 F 4.03 .045

Here, each row compares two regression models, one without prescriptive SEB and one with it. delta_R2 is the extra share of variance in the outcome that prescriptive SEB explains. The F test asks whether that gain is bigger than chance.

OCBI: Adding prescriptive SEB to a model with only SZSB raises R² by .074, about 7 percentage points more variance explained (F = 30.94, p < .001). Adding it to a model with all the controls (SZSB, need for status, SDO, dominance, prestige) still raises R² by .044 (p < .001). Decent effect.

UPB: Over SZSB alone, it adds .022 (p = .003). Over all controls, it adds only .009, under 1% of the variance (p = .045). Tiny effect.

Distribution vs. attribute prescriptive (which half carries the effect?)

sub_ocbi <- lm(ocbi ~ presc_dist + presc_attr + szsb + nfs + sdo + dom + prest, data = s1)
sub_upb  <- lm(upb  ~ presc_dist + presc_attr + szsb + nfs + sdo + dom + prest, data = s1)
summary(sub_ocbi)
## 
## Call:
## lm(formula = ocbi ~ presc_dist + presc_attr + szsb + nfs + sdo + 
##     dom + prest, data = s1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.75566 -0.71728  0.04801  0.74087  2.62404 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.92426    0.56170   3.426  0.00068 ***
## presc_dist   0.11749    0.07680   1.530  0.12687    
## presc_attr   0.23538    0.08007   2.940  0.00349 ** 
## szsb         0.05813    0.04835   1.202  0.23007    
## nfs          0.11954    0.08417   1.420  0.15635    
## sdo         -0.01120    0.04293  -0.261  0.79438    
## dom         -0.18508    0.05950  -3.110  0.00201 ** 
## prest        0.11119    0.09008   1.234  0.21783    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.076 on 382 degrees of freedom
## Multiple R-squared:  0.1196, Adjusted R-squared:  0.1035 
## F-statistic: 7.417 on 7 and 382 DF,  p-value: 2.275e-08
summary(sub_upb)
## 
## Call:
## lm(formula = upb ~ presc_dist + presc_attr + szsb + nfs + sdo + 
##     dom + prest, data = s1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9939 -0.8750 -0.2399  0.6759  5.0586 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.93012    0.65685   2.938   0.0035 ** 
## presc_dist  -0.03164    0.08981  -0.352   0.7248    
## presc_attr  -0.15929    0.09364  -1.701   0.0897 .  
## szsb         0.04917    0.05655   0.869   0.3851    
## nfs         -0.07323    0.09843  -0.744   0.4573    
## sdo          0.11205    0.05020   2.232   0.0262 *  
## dom          0.30484    0.06959   4.381 1.53e-05 ***
## prest        0.16265    0.10534   1.544   0.1234    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.258 on 382 degrees of freedom
## Multiple R-squared:  0.1486, Adjusted R-squared:  0.133 
## F-statistic: 9.521 on 7 and 382 DF,  p-value: 6.505e-11

Mediation: inclusivity (prescriptive SEB -> inclusivity -> OCBI)

Earlier Study 1 work found inclusivity mediated the full-scale SEB -> OCBI link. This re-tests that with prescriptive SEB only (bootstrapped indirect effect).

med_model <- '
  inclusivity ~ a*presc
  ocbi ~ cprime*presc + b*inclusivity
  indirect := a*b
  total := cprime + a*b
'
fit_med_s1 <- sem(med_model, data = s1, se = "bootstrap", bootstrap = 1000)
summary(fit_med_s1, standardized = TRUE, ci = TRUE)
## lavaan 0.7-2 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         5
## 
##   Number of observations                           390
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Parameter Estimates:
## 
##   Standard errors                            Bootstrap
##   Number of requested bootstrap draws             1000
##   Number of successful bootstrap draws            1000
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   inclusivity ~                                                         
##     presc      (a)    0.455    0.069    6.546    0.000    0.327    0.590
##   ocbi ~                                                                
##     presc   (cprm)    0.131    0.072    1.817    0.069   -0.010    0.271
##     inclsvt    (b)    0.616    0.071    8.691    0.000    0.485    0.769
##    Std.lv  Std.all
##                   
##     0.455    0.385
##                   
##     0.131    0.087
##     0.616    0.482
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .inclusivity       0.671    0.075    8.988    0.000    0.521    0.818
##    .ocbi              0.938    0.056   16.781    0.000    0.819    1.040
##    Std.lv  Std.all
##     0.671    0.852
##     0.938    0.728
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##     indirect          0.280    0.050    5.607    0.000    0.187    0.385
##     total             0.411    0.076    5.389    0.000    0.264    0.563
##    Std.lv  Std.all
##     0.280    0.186
##     0.411    0.272

Inclusivity accounted for roughly two-thirds of the association between prescriptive SEB and OCBI (indirect effect = .28, 95% CI [.19, .39]); the direct effect was no longer significant (b = .13, p = .069).

Study 2: Prescriptive SEB -> status affordance to subordinates

Each manager rated 3 subordinates, so ratings are nested within managers and analyzed with random intercepts (as preregistered).

s2_long <- s2 %>%
  mutate(
    aff_1 = rowMeans(across(c(affordance1_1, affordance1_2, affordance1_3)), na.rm = TRUE),
    aff_2 = rowMeans(across(c(affordance2_1, affordance2_2, affordance2_3)), na.rm = TRUE),
    aff_3 = rowMeans(across(c(affordance3_1, affordance3_2, affordance3_3)), na.rm = TRUE),
    presc_c = presc - mean(presc)          # grand-mean centered (manager level)
  ) %>%
  select(ResponseId, presc, presc_c, presc_dist, presc_attr, all_of(controls),
         aff_1, aff_2, aff_3) %>%
  pivot_longer(starts_with("aff_"), names_to = "slot", values_to = "affordance")

cat("Managers:", n_distinct(s2_long$ResponseId), " | Ratings:", nrow(s2_long))
## Managers: 157  | Ratings: 471
s2_mods <- fit_specs(s2_long, "affordance", mixed = TRUE)

Preregistered Model 1 (no controls)

summary(s2_mods$bivariate)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: fml
##    Data: data
## 
## REML criterion at convergence: 1276.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9932 -0.3320  0.0957  0.4486  2.5029 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  ResponseId (Intercept) 0.2980   0.5459  
##  Residual               0.6525   0.8078  
## Number of obs: 471, groups:  ResponseId, 157
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)   3.4166     0.4448 155.0000   7.682 1.66e-12 ***
## presc         0.3892     0.0770 155.0000   5.055 1.20e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       (Intr)
## presc -0.992

Preregistered Model 2 (all controls)

summary(s2_mods$full)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: fml
##    Data: data
## 
## REML criterion at convergence: 1279.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.0416 -0.3525  0.1164  0.4612  2.5472 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  ResponseId (Intercept) 0.2650   0.5148  
##  Residual               0.6525   0.8078  
## Number of obs: 471, groups:  ResponseId, 157
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)   3.34713    0.66598 149.99999   5.026 1.41e-06 ***
## presc         0.28811    0.08642 150.00000   3.334  0.00108 ** 
## szsb          0.13458    0.05875 150.00000   2.291  0.02338 *  
## nfs           0.27113    0.09519 150.00000   2.848  0.00501 ** 
## sdo          -0.08261    0.04749 150.00000  -1.739  0.08400 .  
## dom          -0.10756    0.06356 150.00000  -1.692  0.09268 .  
## prest        -0.10924    0.10813 149.99999  -1.010  0.31401    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##       (Intr) presc  szsb   nfs    sdo    dom   
## presc -0.749                                   
## szsb  -0.247  0.019                            
## nfs    0.055 -0.194  0.058                     
## sdo   -0.363  0.297 -0.093 -0.068              
## dom   -0.128  0.245 -0.365 -0.349 -0.254       
## prest -0.378  0.007  0.087 -0.661  0.130  0.025

Does prescriptive SEB add anything beyond SZSB?

incremental(s2_mods, mixed = TRUE) %>%
  select(comparison, test, test_stat, p) %>%
  mutate(test_stat = round(test_stat, 2), p = fmt_p(p)) %>%
  kable() %>% kable_styling(full_width = FALSE)
comparison test test_stat p
SZSB -> SZSB + prescriptive SEB LRT chi-sq 26.16 <.001
All controls -> + prescriptive SEB LRT chi-sq 11.22 <.001

Over SZSB alone (χ² = 26.16, p < .001): this is a large improvement in fit. Managers who endorse prescriptive SEB give more status to their subordinates, and SZSB doesn’t account for that. Over all controls (χ² = 11.22, p < .001): this is smaller, as expected, but still clearly significant. The controls (including need for status, which also predicts affordance) absorb some of the effect, but not all of it.

Distribution vs. attribute prescriptive

lmer(affordance ~ presc_dist + presc_attr + szsb + nfs + sdo + dom + prest + (1 | ResponseId),
     data = s2_long) %>% summary()
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: affordance ~ presc_dist + presc_attr + szsb + nfs + sdo + dom +  
##     prest + (1 | ResponseId)
##    Data: s2_long
## 
## REML criterion at convergence: 1281.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9798 -0.3538  0.1125  0.4846  2.5620 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  ResponseId (Intercept) 0.2650   0.5148  
##  Residual               0.6525   0.8078  
## Number of obs: 471, groups:  ResponseId, 157
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)   3.42017    0.66995 149.00000   5.105 9.95e-07 ***
## presc_dist    0.20701    0.07626 149.00000   2.715  0.00742 ** 
## presc_attr    0.05602    0.09792 149.00000   0.572  0.56809    
## szsb          0.12133    0.06022 149.00000   2.015  0.04575 *  
## nfs           0.29396    0.09788 149.00000   3.003  0.00313 ** 
## sdo          -0.07555    0.04801 149.00000  -1.574  0.11770    
## dom          -0.10680    0.06357 149.00000  -1.680  0.09503 .  
## prest        -0.10871    0.10813 149.00000  -1.005  0.31639    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) prsc_d prsc_t szsb   nfs    sdo    dom   
## presc_dist -0.332                                          
## presc_attr -0.426 -0.489                                   
## szsb       -0.263 -0.170  0.205                            
## nfs         0.078  0.085 -0.292  0.004                     
## sdo        -0.341  0.287 -0.002 -0.122 -0.031              
## dom        -0.126  0.149  0.098 -0.359 -0.336 -0.250       
## prest      -0.375  0.008 -0.001  0.084 -0.642  0.130  0.025

Study 3 pilot: Does the essay manipulation move prescriptive SEB?

pilot_dvs <- c(presc = "Prescriptive SEB", szsb = "SZSB", nfs = "Need for status", ocbi = "OCBI")

pilot_tbl <- map_dfr(names(pilot_dvs), function(v) {
  hi <- p[[v]][p$condition == "high"]; lo <- p[[v]][p$condition == "low"]
  tt <- t.test(hi, lo)
  sp <- sqrt(((length(hi) - 1) * var(hi) + (length(lo) - 1) * var(lo)) / (length(hi) + length(lo) - 2))
  tibble(DV = pilot_dvs[[v]],
         `M high SEB` = mean(hi), `M low SEB` = mean(lo),
         diff = mean(hi) - mean(lo), d = (mean(hi) - mean(lo)) / sp,
         t = unname(tt$statistic), p = tt$p.value)
})

pilot_tbl %>%
  mutate(across(where(is.numeric), ~ round(.x, 2)), p = fmt_p(p)) %>%
  kable(caption = "High vs. low SEB condition (positive = higher in high SEB)") %>%
  kable_styling(full_width = FALSE)
High vs. low SEB condition (positive = higher in high SEB)
DV M high SEB M low SEB diff d t p
Prescriptive SEB 6.00 5.41 0.59 0.65 3.24 <.001
SZSB 2.64 3.43 -0.79 -0.71 -3.53 <.001
Need for status 4.72 4.47 0.24 0.21 1.05 .290
OCBI 5.18 4.53 0.66 0.52 2.59 .010

The manipulation may move SZSB as well as prescriptive SEB. Here is the effect on prescriptive SEB with and without SZSB held constant, plus a test of whether prescriptive SEB carries the condition effect on OCBI.

lm(presc ~ condition, data = p) %>% summary()
## 
## Call:
## lm(formula = presc ~ condition, data = p)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.2467 -0.4133  0.0867  0.5867  1.5867 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     5.4133     0.1275  42.442  < 2e-16 ***
## conditionhigh   0.5867     0.1813   3.236  0.00166 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9019 on 97 degrees of freedom
## Multiple R-squared:  0.09743,    Adjusted R-squared:  0.08813 
## F-statistic: 10.47 on 1 and 97 DF,  p-value: 0.001659
lm(presc ~ condition + szsb + nfs + sdo + dom + prest, data = p) %>% summary()
## 
## Call:
## lm(formula = presc ~ condition + szsb + nfs + sdo + dom + prest, 
##     data = p)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.29881 -0.46964  0.07605  0.46710  1.48230 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    6.66495    0.49295  13.521  < 2e-16 ***
## conditionhigh  0.55049    0.16494   3.337 0.001221 ** 
## szsb          -0.12377    0.07849  -1.577 0.118231    
## nfs            0.17868    0.11997   1.489 0.139794    
## sdo           -0.22342    0.06085  -3.671 0.000404 ***
## dom           -0.22996    0.08367  -2.749 0.007205 ** 
## prest         -0.09894    0.15219  -0.650 0.517230    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7442 on 92 degrees of freedom
## Multiple R-squared:  0.4172, Adjusted R-squared:  0.3792 
## F-statistic: 10.98 on 6 and 92 DF,  p-value: 3.411e-09
med_pilot <- '
  presc ~ a*cond_high
  ocbi  ~ cprime*cond_high + b*presc
  indirect := a*b
  total := cprime + a*b
'
fit_med_p <- sem(med_pilot, data = p, se = "bootstrap", bootstrap = 1000)
summary(fit_med_p, standardized = TRUE, ci = TRUE)
## lavaan 0.7-2 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         5
## 
##   Number of observations                            99
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Parameter Estimates:
## 
##   Standard errors                            Bootstrap
##   Number of requested bootstrap draws             1000
##   Number of successful bootstrap draws             995
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   presc ~                                                               
##     cnd_hgh    (a)    0.587    0.183    3.203    0.001    0.213    0.946
##   ocbi ~                                                                
##     cnd_hgh (cprm)    0.478    0.244    1.963    0.050   -0.021    0.973
##     presc      (b)    0.307    0.146    2.097    0.036    0.014    0.571
##    Std.lv  Std.all
##                   
##     0.587    0.312
##                   
##     0.478    0.184
##     0.307    0.222
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .presc             0.797    0.206    3.872    0.000    0.458    1.253
##    .ocbi              1.500    0.209    7.159    0.000    1.079    1.900
##    Std.lv  Std.all
##     0.797    0.903
##     1.500    0.891
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##     indirect          0.180    0.105    1.717    0.086    0.004    0.402
##     total             0.659    0.252    2.609    0.009    0.123    1.168
##    Std.lv  Std.all
##     0.180    0.069
##     0.659    0.254

The high-SEB essay raised prescriptive SEB (a = 0.59, p = .001), which in turn predicted higher OCBI (b = 0.31, p = .036), producing a small indirect effect (0.18, 95% CI [0.004, 0.40]) that accounted for roughly a quarter of the total effect of condition on OCBI.

# Parallel mediation: prescriptive SEB and SZSB as competing mediators of condition -> OCBI
med_par <- '
  presc ~ a1*cond_high
  szsb  ~ a2*cond_high
  ocbi  ~ cprime*cond_high + b1*presc + b2*szsb
  presc ~~ szsb
  ind_presc := a1*b1
  ind_szsb  := a2*b2
'
fit_par <- sem(med_par, data = p, se = "bootstrap", bootstrap = 1000)
summary(fit_par, standardized = TRUE, ci = TRUE)
## lavaan 0.7-2 ended normally after 9 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         9
## 
##   Number of observations                            99
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Parameter Estimates:
## 
##   Standard errors                            Bootstrap
##   Number of requested bootstrap draws             1000
##   Number of successful bootstrap draws             989
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   presc ~                                                               
##     cnd_hgh   (a1)    0.587    0.184    3.193    0.001    0.214    0.951
##   szsb ~                                                                
##     cnd_hgh   (a2)   -0.792    0.223   -3.550    0.000   -1.222   -0.331
##   ocbi ~                                                                
##     cnd_hgh (cprm)    0.506    0.263    1.921    0.055   -0.025    1.036
##     presc     (b1)    0.334    0.159    2.097    0.036    0.018    0.625
##     szsb      (b2)    0.054    0.145    0.375    0.707   -0.213    0.356
##    Std.lv  Std.all
##                   
##     0.587    0.312
##                   
##    -0.792   -0.337
##                   
##     0.506    0.195
##     0.334    0.242
##     0.054    0.049
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##  .presc ~~                                                              
##    .szsb             -0.389    0.153   -2.550    0.011   -0.726   -0.115
##    Std.lv  Std.all
##                   
##    -0.389   -0.394
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .presc             0.797    0.205    3.887    0.000    0.462    1.251
##    .szsb              1.224    0.139    8.800    0.000    0.952    1.492
##    .ocbi              1.497    0.205    7.291    0.000    1.055    1.864
##    Std.lv  Std.all
##     0.797    0.903
##     1.224    0.886
##     1.497    0.889
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##     ind_presc         0.196    0.117    1.672    0.095    0.010    0.459
##     ind_szsb         -0.043    0.123   -0.351    0.726   -0.348    0.148
##    Std.lv  Std.all
##     0.196    0.075
##    -0.043   -0.017

With both mediators in the model, only prescriptive SEB carried the effect of condition on OCBI (indirect = 0.20, 95% CI [0.01, 0.46]), whereas SZSB did not (indirect = −0.04, 95% CI [−0.35, 0.15]), even though the essay lowered SZSB substantially (a = −0.79, p < .001).

To summarize: Prescriptive SEB partially mediated the effect of condition on OCBI (indirect effect = .18, 95% CI [.00, .40]), whereas SZSB did not (indirect effect = −.04, 95% CI [−.35, .15]). These results should be interpreted cautiously given the small sample.

Attribute-prescriptive only (distribution items removed)

Do attribute beliefs alone predict the status managers actually grant to subordinates? All variables are z-scored, so coefficients are standardized.

z2 <- zscore(s2_long, c("affordance", "presc_attr", "presc_dist", controls))

fit_attr <- function(rhs) {
  lmer(as.formula(paste("affordance ~", rhs, "+ (1 | ResponseId)")), data = z2)
}

attr_specs <- list(
  `Attribute alone`   = "presc_attr",
  `Plus SZSB`         = "presc_attr + szsb",
  `Plus all controls` = "presc_attr + szsb + nfs + sdo + dom + prest"
)
attr_mods <- map(attr_specs, fit_attr)

map_dfr(attr_mods, ~ get_coef(.x, "presc_attr"), .id = "Specification") %>%
  transmute(Specification,
            `std. b` = round(b, 2), SE = round(se, 2),
            `95% CI` = sprintf("[%.2f, %.2f]", b - 1.96 * se, b + 1.96 * se),
            p = fmt_p(p)) %>%
  kable(caption = "Attribute-prescriptive SEB -> status affordance") %>%
  kable_styling(full_width = FALSE)
Attribute-prescriptive SEB -> status affordance
Specification std. b SE 95% CI p
Attribute alone 0.22 0.06 [0.10, 0.33] <.001
Plus SZSB 0.24 0.06 [0.12, 0.36] <.001
Plus all controls 0.14 0.06 [0.01, 0.26] .034 
# Does attribute add beyond the controls? (likelihood ratio test)
m_ctrl <- fit_attr("szsb + nfs + sdo + dom + prest")
anova(m_ctrl, attr_mods[["Plus all controls"]])
## Data: z2
## Models:
## m_ctrl: as.formula(paste("affordance ~", rhs, "+ (1 | ResponseId)"))
## attr_mods[["Plus all controls"]]: as.formula(paste("affordance ~", rhs, "+ (1 | ResponseId)"))
##                                  npar    AIC    BIC  logLik -2*log(L)  Chisq Df
## m_ctrl                              8 1266.8 1300.0 -625.39    1250.8          
## attr_mods[["Plus all controls"]]    9 1264.1 1301.5 -623.04    1246.1 4.6969  1
##                                  Pr(>Chisq)  
## m_ctrl                                       
## attr_mods[["Plus all controls"]]    0.03022 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Attribute vs. distribution, head to head

cat("Correlation between attribute and distribution composites (managers):",
    round(cor(s2$presc_attr, s2$presc_dist, use = "pair"), 2))
## Correlation between attribute and distribution composites (managers): 0.53
cmp <- list(`Attribute only`    = "presc_attr",
            `Distribution only` = "presc_dist",
            `Both together`     = "presc_attr + presc_dist")

map_dfr(cmp, function(r) {
  cf <- summary(fit_attr(paste(r, "+ szsb + nfs + sdo + dom + prest")))$coefficients
  terms <- intersect(c("presc_attr", "presc_dist"), rownames(cf))
  tibble(Term = terms, b = cf[terms, "Estimate"], SE = cf[terms, "Std. Error"],
         p = cf[terms, ncol(cf)])
}, .id = "Model") %>%
  mutate(across(c(b, SE), ~ round(.x, 2)), p = fmt_p(p)) %>%
  kable(caption = "All models include SZSB, need for status, SDO, dominance, and prestige") %>%
  kable_styling(full_width = FALSE)
All models include SZSB, need for status, SDO, dominance, and prestige
Model Term b SE p
Attribute only presc_attr 0.14 0.06 .034
Distribution only presc_dist 0.21 0.06 <.001
Both together presc_attr 0.04 0.07 .568
Both together presc_dist 0.19 0.07 .007

Optional: how evenly status is distributed across subordinates

Affordance above is how much status managers grant on average. This checks whether attribute beliefs predict the spread (SD) of affordance across the three rated subordinates. Spread is noisy because it is based on only three randomly selected people, so treat it as exploratory.

s2_spread <- s2 %>%
  mutate(aff1 = rowMeans(across(c(affordance1_1, affordance1_2, affordance1_3))),
         aff2 = rowMeans(across(c(affordance2_1, affordance2_2, affordance2_3))),
         aff3 = rowMeans(across(c(affordance3_1, affordance3_2, affordance3_3))),
         aff_sd = apply(cbind(aff1, aff2, aff3), 1, sd)) %>%
  zscore(c("aff_sd", "presc_attr", "presc_dist", controls))

summary(lm(aff_sd ~ presc_attr + szsb + nfs + sdo + dom + prest, data = s2_spread))
## 
## Call:
## lm(formula = aff_sd ~ presc_attr + szsb + nfs + sdo + dom + prest, 
##     data = s2_spread)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.4263 -0.7377 -0.1501  0.3594  3.5264 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  1.218e-15  7.965e-02   0.000   1.0000  
## presc_attr  -3.058e-03  9.228e-02  -0.033   0.9736  
## szsb        -6.775e-02  9.193e-02  -0.737   0.4623  
## nfs         -8.297e-02  1.236e-01  -0.672   0.5029  
## sdo          1.926e-01  9.187e-02   2.097   0.0377 *
## dom          3.207e-02  1.055e-01   0.304   0.7616  
## prest        1.316e-01  1.132e-01   1.163   0.2465  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.998 on 150 degrees of freedom
## Multiple R-squared:  0.04231,    Adjusted R-squared:  0.004005 
## F-statistic: 1.105 on 6 and 150 DF,  p-value: 0.3624
summary(lm(aff_sd ~ presc_dist + szsb + nfs + sdo + dom + prest, data = s2_spread))
## 
## Call:
## lm(formula = aff_sd ~ presc_dist + szsb + nfs + sdo + dom + prest, 
##     data = s2_spread)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5950 -0.7360 -0.1752  0.3028  3.3967 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  1.476e-15  7.850e-02   0.000   1.0000  
## presc_dist  -1.886e-01  8.958e-02  -2.106   0.0369 *
## szsb        -5.184e-02  8.998e-02  -0.576   0.5654  
## nfs         -6.705e-02  1.169e-01  -0.574   0.5670  
## sdo          1.278e-01  9.453e-02   1.352   0.1785  
## dom         -1.717e-02  1.047e-01  -0.164   0.8699  
## prest        1.296e-01  1.115e-01   1.162   0.2471  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9836 on 150 degrees of freedom
## Multiple R-squared:  0.0698, Adjusted R-squared:  0.03259 
## F-statistic: 1.876 on 6 and 150 DF,  p-value: 0.0885

Study 3 pilot (continued): Dominance and prestige

The Study 3 pilot measured willingness to use dominance and prestige strategies (the 17-item scale from Andrews-Fearon & Davidai, 2023, Appendix B) after the manipulation. These are the same outcomes Andrews-Fearon and Davidai used, where manipulating zero-sum beliefs raised dominance but not prestige. The questions here, also raised in our email to Adam, are: (1) does the SEB manipulation change dominance and/or prestige, (2) does the effect survive accounting for SZSB, and (3) does SZSB (or prescriptive SEB) carry the effect? Note that SEB and SZSB in this dataset are the participant’s own scores (measured after the essay), not ratings of a manager’s beliefs.

dp_dvs <- c(dom = "Dominance (Cheng)", prest = "Prestige (Cheng)", nfs = "Need for status")

map_dfr(names(dp_dvs), function(v) {
  hi <- p[[v]][p$condition == "high"]; lo <- p[[v]][p$condition == "low"]
  tt <- t.test(hi, lo)
  sp <- sqrt(((length(hi) - 1) * var(hi) + (length(lo) - 1) * var(lo)) / (length(hi) + length(lo) - 2))
  tibble(DV = dp_dvs[[v]], `M high SEB` = mean(hi), `M low SEB` = mean(lo),
         diff = mean(hi) - mean(lo), d = (mean(hi) - mean(lo)) / sp,
         t = unname(tt$statistic), p = tt$p.value)
}) %>%
  mutate(across(where(is.numeric), ~ round(.x, 2)), p = fmt_p(p)) %>%
  kable(caption = "High vs. low SEB condition (positive = higher in high SEB)") %>%
  kable_styling(full_width = FALSE)
High vs. low SEB condition (positive = higher in high SEB)
DV M high SEB M low SEB diff d t p
Dominance (Cheng) 3.00 2.91 0.10 0.08 0.41 .680
Prestige (Cheng) 4.78 4.52 0.26 0.29 1.44 .150
Need for status 4.72 4.47 0.24 0.21 1.05 .290 
p %>% select(Dominance = dom, Prestige = prest, `Prescriptive SEB` = presc, SZSB = szsb) %>%
  cor(use = "pairwise.complete.obs") %>% round(2) %>%
  kable(caption = "Correlations in the pilot (both conditions pooled)") %>%
  kable_styling(full_width = FALSE)
Correlations in the pilot (both conditions pooled)
Dominance Prestige Prescriptive SEB SZSB
Dominance 1.00 0.30 -0.40 0.38
Prestige 0.30 1.00 0.09 -0.14
Prescriptive SEB -0.40 0.09 1.00 -0.46
SZSB 0.38 -0.14 -0.46 1.00

Condition x strategy interaction

Andrews-Fearon and Davidai test whether a manipulation moves dominance more than prestige with a mixed model (strategy type as a within-person factor, random intercept for participant). The same test here: a significant condition:strategy term means the essay affected the two strategies differently.

p_strat <- p %>%
  select(ResponseId, condition, dom, prest) %>%
  pivot_longer(c(dom, prest), names_to = "strategy", values_to = "willingness") %>%
  mutate(strategy = factor(strategy, levels = c("prest", "dom"), labels = c("Prestige", "Dominance")))

m_strat <- lmer(willingness ~ condition * strategy + (1 | ResponseId), data = p_strat)
summary(m_strat)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: willingness ~ condition * strategy + (1 | ResponseId)
##    Data: p_strat
## 
## REML criterion at convergence: 570.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.87837 -0.62362 -0.03265  0.59113  3.06041 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  ResponseId (Intercept) 0.3101   0.5569  
##  Residual               0.7575   0.8703  
## Number of obs: 198, groups:  ResponseId, 99
## 
## Fixed effects:
##                                 Estimate Std. Error       df t value Pr(>|t|)
## (Intercept)                       4.5222     0.1461 178.9047  30.948  < 2e-16
## conditionhigh                     0.2624     0.2077 178.9047   1.263    0.208
## strategyDominance                -1.6147     0.1741  97.0000  -9.276  4.9e-15
## conditionhigh:strategyDominance  -0.1673     0.2474  97.0000  -0.676    0.501
##                                    
## (Intercept)                     ***
## conditionhigh                      
## strategyDominance               ***
## conditionhigh:strategyDominance    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtnh strtgD
## conditinhgh -0.704              
## strtgyDmnnc -0.596  0.419       
## cndtnhgh:sD  0.419 -0.596 -0.704

The essay manipulation did not differentially affect dominance and prestige (condition × strategy interaction: b = −0.17, SE = 0.25, p = .50).

Does the condition effect on dominance survive SZSB / prescriptive SEB?

dom_total   <- lm(dom ~ condition,                    data = p)
dom_szsb    <- lm(dom ~ condition + szsb,             data = p)
dom_presc   <- lm(dom ~ condition + presc,            data = p)
dom_both    <- lm(dom ~ condition + presc + szsb,     data = p)

map_dfr(list(`Condition only` = dom_total, `+ SZSB` = dom_szsb,
             `+ prescriptive SEB` = dom_presc, `+ both` = dom_both),
        function(m) {
          cf <- summary(m)$coefficients
          tibble(`Condition (high - low)` = cf["conditionhigh", 1],
                 SE = cf["conditionhigh", 2], p = cf["conditionhigh", 4],
                 `SZSB b` = if ("szsb" %in% rownames(cf)) cf["szsb", 1] else NA,
                 `Prescriptive SEB b` = if ("presc" %in% rownames(cf)) cf["presc", 1] else NA,
                 R2 = summary(m)$r.squared)
        }, .id = "Model") %>%
  mutate(across(where(is.numeric), ~ round(.x, 2)), p = fmt_p(p)) %>%
  kable(caption = "Dependent variable: dominance") %>% kable_styling(full_width = FALSE)
Dependent variable: dominance
Model Condition (high - low) SE p SZSB b Prescriptive SEB b R2
Condition only 0.10 0.23 .680 NA NA 0.00
  • SZSB
0.44 0.22 .050 0.43 NA 0.18
  • prescriptive SEB
0.42 0.22 .060 NA -0.55 0.19
  • both
0.57 0.22 .010 0.30 -0.40 0.26 
prest_total <- lm(prest ~ condition,                  data = p)
prest_both  <- lm(prest ~ condition + presc + szsb,   data = p)
summary(prest_total)
## 
## Call:
## lm(formula = prest ~ condition, data = p)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8957 -0.7090 -0.0068  0.6599  2.2556 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     4.5222     0.1283  35.256   <2e-16 ***
## conditionhigh   0.2624     0.1823   1.439    0.153    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.907 on 97 degrees of freedom
## Multiple R-squared:  0.0209, Adjusted R-squared:  0.01081 
## F-statistic: 2.071 on 1 and 97 DF,  p-value: 0.1534
summary(prest_both)
## 
## Call:
## lm(formula = prest ~ condition + presc + szsb, data = p)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.87487 -0.71011  0.00277  0.61070  2.54045 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.70631    0.79012   5.956 4.34e-08 ***
## conditionhigh  0.19166    0.19820   0.967    0.336    
## presc          0.01531    0.11165   0.137    0.891    
## szsb          -0.07790    0.09010  -0.865    0.389    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9116 on 95 degrees of freedom
## Multiple R-squared:  0.03128,    Adjusted R-squared:  0.0006847 
## F-statistic: 1.022 on 3 and 95 DF,  p-value: 0.3863

Competing mediators: prescriptive SEB vs. SZSB

Both mediators are lowered/raised by the essay, and both correlate with dominance in the expected direction. Bootstrapped indirect effects test which one carries any condition effect. If the direct effect has the opposite sign of the indirect effects, this is inconsistent mediation (suppression), so a near-zero total effect does not mean nothing is happening.

med_dom <- '
  presc ~ a1*cond_high
  szsb  ~ a2*cond_high
  dom   ~ cprime*cond_high + b1*presc + b2*szsb
  presc ~~ szsb
  ind_presc := a1*b1
  ind_szsb  := a2*b2
  total     := cprime + a1*b1 + a2*b2
'
fit_med_dom <- sem(med_dom, data = p, se = "bootstrap", bootstrap = 1000)
summary(fit_med_dom, standardized = TRUE, ci = TRUE)
## lavaan 0.7-2 ended normally after 9 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         9
## 
##   Number of observations                            99
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Parameter Estimates:
## 
##   Standard errors                            Bootstrap
##   Number of requested bootstrap draws             1000
##   Number of successful bootstrap draws             994
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   presc ~                                                               
##     cnd_hgh   (a1)    0.587    0.184    3.186    0.001    0.213    0.950
##   szsb ~                                                                
##     cnd_hgh   (a2)   -0.792    0.223   -3.548    0.000   -1.222   -0.331
##   dom ~                                                                 
##     cnd_hgh (cprm)    0.569    0.214    2.662    0.008    0.136    0.979
##     presc     (b1)   -0.399    0.146   -2.740    0.006   -0.656   -0.082
##     szsb      (b2)    0.303    0.099    3.051    0.002    0.117    0.515
##    Std.lv  Std.all
##                   
##     0.587    0.312
##                   
##    -0.792   -0.337
##                   
##     0.569    0.251
##    -0.399   -0.330
##     0.303    0.314
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##  .presc ~~                                                              
##    .szsb             -0.389    0.152   -2.554    0.011   -0.726   -0.115
##    Std.lv  Std.all
##                   
##    -0.389   -0.394
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .presc             0.797    0.205    3.882    0.000    0.462    1.253
##    .szsb              1.224    0.139    8.825    0.000    0.951    1.491
##    .dom               0.953    0.121    7.894    0.000    0.689    1.164
##    Std.lv  Std.all
##     0.797    0.903
##     1.224    0.886
##     0.953    0.740
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##     ind_presc        -0.234    0.129   -1.807    0.071   -0.525   -0.026
##     ind_szsb         -0.240    0.103   -2.331    0.020   -0.471   -0.078
##     total             0.095    0.230    0.413    0.680   -0.372    0.538
##    Std.lv  Std.all
##    -0.234   -0.103
##    -0.240   -0.106
##     0.095    0.042
med_prest <- sub("dom   ~", "prest ~", med_dom, fixed = TRUE)
fit_med_prest <- sem(med_prest, data = p, se = "bootstrap", bootstrap = 1000)
summary(fit_med_prest, standardized = TRUE, ci = TRUE)
## lavaan 0.7-2 ended normally after 9 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         9
## 
##   Number of observations                            99
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Parameter Estimates:
## 
##   Standard errors                            Bootstrap
##   Number of requested bootstrap draws             1000
##   Number of successful bootstrap draws             990
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   presc ~                                                               
##     cnd_hgh   (a1)    0.587    0.184    3.184    0.001    0.214    0.951
##   szsb ~                                                                
##     cnd_hgh   (a2)   -0.792    0.224   -3.545    0.000   -1.222   -0.331
##   prest ~                                                               
##     cnd_hgh (cprm)    0.192    0.188    1.018    0.308   -0.184    0.571
##     presc     (b1)    0.015    0.184    0.083    0.934   -0.275    0.415
##     szsb      (b2)   -0.078    0.096   -0.808    0.419   -0.286    0.101
##    Std.lv  Std.all
##                   
##     0.587    0.312
##                   
##    -0.792   -0.337
##                   
##     0.192    0.106
##     0.015    0.016
##    -0.078   -0.101
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##  .presc ~~                                                              
##    .szsb             -0.389    0.153   -2.545    0.011   -0.726   -0.114
##    Std.lv  Std.all
##                   
##    -0.389   -0.394
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .presc             0.797    0.206    3.863    0.000    0.457    1.253
##    .szsb              1.224    0.138    8.842    0.000    0.952    1.492
##    .prest             0.797    0.105    7.584    0.000    0.554    0.957
##    Std.lv  Std.all
##     0.797    0.903
##     1.224    0.886
##     0.797    0.969
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##     ind_presc         0.009    0.113    0.079    0.937   -0.218    0.241
##     ind_szsb          0.062    0.083    0.739    0.460   -0.075    0.255
##     total             0.262    0.176    1.487    0.137   -0.086    0.609
##    Std.lv  Std.all
##     0.009    0.005
##     0.062    0.034
##     0.262    0.145

Integration across studies

Standardized (z-scored) coefficients for prescriptive SEB from every model, so all studies are on the same metric. The key comparison is how much the coefficient shrinks going from bivariate to + SZSB to full controls.

Study 3 pilot rows: the pilot manipulated SEB, so prescriptive SEB there is partly condition-driven. To keep these rows comparable to the correlational studies, condition (cond_high) is included as a covariate in every pilot model, so the coefficient reflects the within-condition association. When the outcome is dominance or prestige, that scale is dropped from the control set (it cannot be its own control).

z1 <- zscore(s1, c("ocbi", "upb", "presc", controls))
z2 <- zscore(s2_long, c("affordance", "presc", controls))
z3 <- zscore(p, c("ocbi", "dom", "prest", "presc", controls))

zm <- list(
  `Study 1: OCBI`                 = fit_specs(z1, "ocbi"),
  `Study 1: UPB`                  = fit_specs(z1, "upb"),
  `Study 2: Status affordance`    = fit_specs(z2, "affordance", mixed = TRUE),
  `Study 3 pilot: OCBI`           = fit_specs(z3, "ocbi", covar = "cond_high"),
  `Study 3 pilot: Dominance`      = fit_specs(z3, "dom", ctrl = setdiff(controls, "dom"), covar = "cond_high"),
  `Study 3 pilot: Prestige`       = fit_specs(z3, "prest", ctrl = setdiff(controls, "prest"), covar = "cond_high")
)

spec_labels <- c(bivariate = "Prescriptive SEB alone",
                 plus_szsb = "Plus SZSB",
                 full      = "Plus all controls")

cross <- imap_dfr(zm, function(mods, label) {
  map_dfr(names(spec_labels), function(s) {
    get_coef(mods[[s]]) %>% mutate(Outcome = label, Specification = spec_labels[[s]])
  })
}) %>%
  mutate(lo = b - 1.96 * se, hi = b + 1.96 * se,
         Specification = factor(Specification, levels = spec_labels),
         Outcome = factor(Outcome, levels = names(zm)))

cross %>%
  transmute(Outcome, Specification,
            `std. b` = round(b, 2), SE = round(se, 2),
            `95% CI` = sprintf("[%.2f, %.2f]", lo, hi), p = fmt_p(p)) %>%
  kable() %>% kable_styling(full_width = FALSE) %>%
  collapse_rows(columns = 1, valign = "top")
Outcome Specification std. b SE 95% CI p
Study 1: OCBI Prescriptive SEB alone 0.27 0.05 [0.18, 0.37] <.001
Plus SZSB 0.28 0.05 [0.18, 0.38] <.001
Plus all controls 0.23 0.05 [0.13, 0.34] <.001
Study 1: UPB Prescriptive SEB alone -0.18 0.05 [-0.28, -0.08] <.001
Plus SZSB -0.15 0.05 [-0.25, -0.05] .003
Plus all controls -0.10 0.05 [-0.21, -0.00] .045
Study 2: Status affordance Prescriptive SEB alone 0.29 0.06 [0.17, 0.40] <.001
Plus SZSB 0.31 0.06 [0.19, 0.42] <.001
Plus all controls 0.21 0.06 [0.09, 0.34] .001
Study 3 pilot: OCBI Prescriptive SEB alone 0.22 0.10 [0.02, 0.42] .031
Plus SZSB 0.24 0.11 [0.02, 0.46] .032
Plus all controls 0.28 0.13 [0.03, 0.53] .032
Study 3 pilot: Dominance Prescriptive SEB alone -0.45 0.10 [-0.64, -0.26] <.001
Plus SZSB -0.33 0.10 [-0.53, -0.13] .002
Plus all controls -0.27 0.10 [-0.47, -0.08] .007
Study 3 pilot: Prestige Prescriptive SEB alone 0.06 0.11 [-0.15, 0.26] .604
Plus SZSB 0.02 0.12 [-0.21, 0.24] .891
Plus all controls -0.05 0.07 [-0.19, 0.10] .517 
ggplot(cross, aes(x = b, y = Outcome, color = Specification)) +
  geom_vline(xintercept = 0, linetype = "dashed", color = "grey50") +
  geom_pointrange(aes(xmin = lo, xmax = hi), position = position_dodge(width = 0.6)) +
  scale_y_discrete(limits = rev) +
  labs(x = "Standardized coefficient for prescriptive SEB (95% CI)", y = NULL,
       title = "Prescriptive SEB effects across studies") +
  theme_minimal(base_size = 13) +
  theme(legend.position = "bottom", plot.title = element_text(face = "bold"))

# Incremental value over SZSB / controls, all outcomes in one table
bind_rows(
  incremental(fit_specs(s1, "ocbi")) %>% mutate(Outcome = "Study 1: OCBI"),
  incremental(fit_specs(s1, "upb"))  %>% mutate(Outcome = "Study 1: UPB"),
  incremental(s2_mods, mixed = TRUE) %>% mutate(Outcome = "Study 2: Status affordance"),
  incremental(fit_specs(p, "ocbi", covar = "cond_high")) %>% mutate(Outcome = "Study 3 pilot: OCBI"),
  incremental(fit_specs(p, "dom", ctrl = setdiff(controls, "dom"), covar = "cond_high")) %>%
    mutate(Outcome = "Study 3 pilot: Dominance"),
  incremental(fit_specs(p, "prest", ctrl = setdiff(controls, "prest"), covar = "cond_high")) %>%
    mutate(Outcome = "Study 3 pilot: Prestige")
) %>%
  transmute(Outcome, comparison, test,
            delta_R2 = ifelse(is.na(delta_R2), "-", sprintf("%.3f", delta_R2)),
            stat = round(test_stat, 2), p = fmt_p(p)) %>%
  kable() %>% kable_styling(full_width = FALSE) %>%
  collapse_rows(columns = 1, valign = "top")
Outcome comparison test delta_R2 stat p
Study 1: OCBI SZSB -> SZSB + prescriptive SEB F 0.074 30.94 <.001
All controls -> + prescriptive SEB F 0.044 19.18 <.001
Study 1: UPB SZSB -> SZSB + prescriptive SEB F 0.022 8.87 .003
All controls -> + prescriptive SEB F 0.009 4.03 .045
Study 2: Status affordance SZSB -> SZSB + prescriptive SEB LRT chi-sq
26.16 <.001
All controls -> + prescriptive SEB LRT chi-sq
11.22 <.001
Study 3 pilot: OCBI SZSB -> SZSB + prescriptive SEB F 0.045 4.76 .032
All controls -> + prescriptive SEB F 0.045 4.76 .032
Study 3 pilot: Dominance SZSB -> SZSB + prescriptive SEB F 0.083 10.67 .002
All controls -> + prescriptive SEB F 0.047 7.55 .007
Study 3 pilot: Prestige SZSB -> SZSB + prescriptive SEB F 0.000 0.02 .891
All controls -> + prescriptive SEB F 0.001 0.42 .517

Pooled OCBI model: Study 1 + Study 3 pilot

OCBI is the one outcome measured in both Study 1 and the pilot. Variables are z-scored within study; study_pilot shifts the intercept and presc:study_pilot tests whether the prescriptive SEB slope differs in the pilot. Condition is included as a covariate (coded 0 for all Study 1 participants).

vars_pool <- c("ocbi", "presc", controls)

pooled <- bind_rows(
  s1 %>% transmute(study = "Study 1", cond_high = 0, ocbi, presc, szsb, nfs, sdo, dom, prest),
  p  %>% transmute(study = "Study 3 pilot", cond_high, ocbi, presc, szsb, nfs, sdo, dom, prest)
) %>%
  group_by(study) %>%
  mutate(across(all_of(vars_pool), ~ as.numeric(scale(.x)))) %>%
  ungroup() %>%
  mutate(study = factor(study, levels = c("Study 1", "Study 3 pilot")))

m_pool <- lm(ocbi ~ presc * study + szsb + nfs + sdo + dom + prest + cond_high, data = pooled)
summary(m_pool)
## 
## Call:
## lm(formula = ocbi ~ presc * study + szsb + nfs + sdo + dom + 
##     prest + cond_high, data = pooled)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.74334 -0.65360  0.03586  0.64733  2.27157 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               2.100e-16  4.793e-02   0.000  1.00000    
## presc                     2.423e-01  5.200e-02   4.659 4.13e-06 ***
## studyStudy 3 pilot       -1.990e-01  1.466e-01  -1.357  0.17544    
## szsb                      6.713e-02  4.720e-02   1.422  0.15560    
## nfs                       1.111e-01  7.115e-02   1.561  0.11920    
## sdo                       1.102e-02  4.989e-02   0.221  0.82521    
## dom                      -1.638e-01  5.270e-02  -3.109  0.00199 ** 
## prest                     9.536e-02  6.889e-02   1.384  0.16694    
## cond_high                 4.020e-01  2.036e-01   1.975  0.04888 *  
## presc:studyStudy 3 pilot -6.693e-02  1.125e-01  -0.595  0.55207    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9466 on 479 degrees of freedom
## Multiple R-squared:  0.1187, Adjusted R-squared:  0.1022 
## F-statistic:  7.17 on 9 and 479 DF,  p-value: 8.704e-10

Key takeaways

  1. Prescriptive SEB holds up beyond SZSB in the correlational data. In Studies 1 and 2 and the Study 3 pilot, prescriptive SEB predicts its outcomes (OCBI, UPB, status affordance, dominance) after accounting for SZSB, and it adds unique variance (e.g., Study 1 OCBI ΔR² = .074; Study 2 affordance LRT χ² = 26.2; pilot dominance ΔR² = .083). It overlaps only modestly with SZSB (r = -.23 in Studies 1 and 2), so the two are distinct constructs in these samples. This supports the pivot to prescriptive SEBs only.

  2. Effects are small to moderate, and the evidence is uneven. Standardized coefficients are about .2 to .3 (about -.1 for UPB). Study 1 OCBI and Study 2 affordance are the sturdiest results; UPB only just survives full controls (p = .045).

  3. The manipulation is the weak point. The essay lowers SZSB more than it raises prescriptive SEB (d = -.71 vs. .65), and the two are more entangled in the pilot (r = -.46). A causal study will need either a cleaner SEB manipulation or SZSB measured as a competing mediator.

  4. Dominance is promising but not yet supported experimentally.

    • Prescriptive SEB predicts lower willingness to use dominance (β = -.27 with all controls) and adds beyond SZSB, but only correlationally. Prestige is unrelated, matching the pattern in Andrews-Fearon and Davidai (2023).
    • The pilot does not reproduce the paper’s dominance-versus-prestige difference under manipulation (condition x strategy p = .50). The null total effect on dominance reflects suppression: a positive direct effect (+.57) offsets negative paths through prescriptive SEB (-.23) and SZSB (-.24).
    • The direct test of the proposed model (manager’s SEB -> subordinate dominance tactics) is the separate email-paradigm pilot, which is not analyzed here.

  5. Two issues

    • SZSB_7R is scored without reversal because the source paper’s appendix appears to mislabel it. This changes some results slightly (e.g., SZSB now modestly predicts Study 2 affordance), so it is worth confirming with the authors.
    • Study 1 used different distribution-prescriptive wording than Studies 2 and 3, and the driving subscale flips across outcomes (attribute for Study 1 OCBI; distribution for Study 2 affordance and pilot dominance). Present prescriptive SEB as one construct, but expect questions about it.

Session info

sessionInfo()
## R version 4.6.0 (2026-04-24)
## Platform: aarch64-apple-darwin23
## Running under: macOS Ventura 13.3
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/New_York
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] kableExtra_1.4.0 knitr_1.51       lavaan_0.7-2     car_3.1-5       
##  [5] carData_3.0-6    psych_2.6.5      lmerTest_3.2-1   lme4_2.0-1      
##  [9] Matrix_1.7-5     qualtRics_3.3.0  lubridate_1.9.5  forcats_1.0.1   
## [13] stringr_1.6.0    dplyr_1.2.1      purrr_1.2.2      readr_2.2.0     
## [17] tidyr_1.3.2      tibble_3.3.1     ggplot2_4.0.3    tidyverse_2.0.0 
## 
## loaded via a namespace (and not attached):
##  [1] sjlabelled_1.2.0    tidyselect_1.2.1    viridisLite_0.4.3  
##  [4] farver_2.1.2        S7_0.2.2            fastmap_1.2.0      
##  [7] digest_0.6.39       timechange_0.4.0    lifecycle_1.0.5    
## [10] magrittr_2.0.5      compiler_4.6.0      rlang_1.2.0        
## [13] sass_0.4.10         tools_4.6.0         yaml_2.3.12        
## [16] labeling_0.4.3      bit_4.6.0           mnormt_2.1.2       
## [19] xml2_1.5.2          RColorBrewer_1.1-3  abind_1.4-8        
## [22] withr_3.0.2         numDeriv_2016.8-1.1 grid_4.6.0         
## [25] stats4_4.6.0        scales_1.4.0        MASS_7.3-66        
## [28] insight_1.5.1       cli_3.6.6           rmarkdown_2.31     
## [31] crayon_1.5.3        reformulas_0.4.4    generics_0.1.4     
## [34] otel_0.2.0          rstudioapi_0.19.0   tzdb_0.5.0         
## [37] minqa_1.2.8         cachem_1.1.0        splines_4.6.0      
## [40] parallel_4.6.0      vctrs_0.7.3         boot_1.3-32        
## [43] jsonlite_2.0.0      hms_1.1.4           bit64_4.8.2        
## [46] Formula_1.2-5       systemfonts_1.3.2   jquerylib_0.1.4    
## [49] glue_1.8.1          nloptr_2.2.1        stringi_1.8.7      
## [52] gtable_0.3.6        quadprog_1.5-8      pillar_1.11.1      
## [55] htmltools_0.5.9     R6_2.6.1            textshaping_1.0.5  
## [58] Rdpack_2.6.6        vroom_1.7.1         evaluate_1.0.5     
## [61] pbivnorm_0.6.0      lattice_0.22-9      rbibutils_2.4.1    
## [64] bslib_0.11.0        Rcpp_1.1.1-1.1      svglite_2.2.2      
## [67] nlme_3.1-169        xfun_0.58           pkgconfig_2.0.3