Kindness, stability, strength: Trivialization of racism mediates the relationship between values and belonging among White engineering students

Poster Text & References

Introduction

One explanation for prejudice and discrimination is that – similar to stereotype threat – the fear of being perceived as biased can actually increase bias (Goff et al., 2008; Richeson & Shelton, 2007). Values affirmation interventions (VAI; Cohen et al., 2009), commonly employed to counter stereotype threat, may thus reduce prejudice in specific contexts (Sherman & Cohen, 2002). Although findings are mixed, there have been promising results (Adams et al., 2006; Badea, Tavani, Rubin, & Meyer, 2017; Unzueta & Lowery, 2008; Lehmiller et al., 2010; Čehajić-Clancy et al., 2011; Lesick & Zell, 2021). Some studies suggest that the values being affirmed also influence outcomes (Lehmiller et al., 2010; Badea, Tavani, Rubin, & Meyer, 2017), suggesting non-self-affirmational mechanisms.

A previous study of 231 engineering students examined the impact of a VAI on students’ engineering identity, belonging, and anti-racist attitudes (using the Propensity to Make Attributions to Prejudice scale; Miller & Saucier, 2018). Results indicated reduced trivialization of racism among women of Color and increased vigilance against racism among men of Color, with no impact on White students (Perkins et al., 2023). The current analysis focused on White students, exploring the relationship between endorsed values, anti-racist attitudes, and belonging in engineering. We hypothesized that communal or social values would associate with less trivialization, more vigilance, and lower belonging. Mediation analysis probed values’ role in trivialization, vigilance, and belonging.

Method

Participants (n = 102) completed a pre-test survey that measured several constructs including belonging and expectancy regarding engineering (Scheidt et al., 2018). Two weeks after the start of the semester, students completed the values affirmation online, in which they selected at least three very important and three somewhat important values from a list of 13 (derived from Schwartz’ theory of basic values; Schwartz, 2012). Afterwards, they picked one of their very important values and completed two short writing prompts. At the end of the semester, they completed the pre-test survey measures again as well as two subscales from the Propensity to Make Attributions to Prejudice scale (PMAPS; Miller & Saucier, 2018).

This study analyzes the White subsample’s (n = 62) responses to the values prompt, their belonging and expectancy, and their trivialization of and vigilance against racism. Factor analysis was used to identify the latent values underlying the 13 specific values used in the intervention: kindness (benevolence, universalism, and collectivism); stability (face, security, and conformity); and strength (achievement, power). Participants’ responses to the belonging and expectancy scales were also combined into a single item to measure their current feelings of belonging and their anticipated place in engineering (referred to as belonging from this point forward). One outlier (detected using Mahalanobis’ distance) was dropped.

Results

Our analysis consisted of three mediation analyses using the mediate() function from the psych package in R.

• There was a significant total effect of kindness on belonging (b = -.44, p < .001), which was completely mediated when considering the effects of trivialization (b = -.12, p = .362). A bias-corrected bootstrap for the indirect effect (b = -.33) was calculated with 1,000 samples and the confidence interval was below zero (-.51 to -.18; Figure 1).

• There was a significant total effect of stability on belonging (b = .30, p = .017), which was also completely mediated by trivialization (b = .09, p = .410). Once again, the bias-corrected bootstrap for the indirect effect (b = .21) was calculated with 1,000 samples and the confidence interval was above zero (.09 to .37; Figure 2)

• There was a significant total effect of strength on belonging (b = .35, p = .005) that was completely mediated by trivialization (b = .05, p = .686), and the confidence interval of the bias-corrected bootstrap for the indirect effect (b = .30) was above zero (.17 to .45; Figure 3).

References

Badea, C., Tavani, J.-L., Rubin, M., & Meyer, T. (2017). Self-affirmation, political value congruence, and support for refugees. Journal of Applied Social Psychology, 47(7), 355–365. https://doi.org/10.1111/jasp.12441

Čehajić-Clancy, S., Effron, D. A., Halperin, E., Liberman, V., & Ross, L. D. (2011). Affirmation, acknowledgment of in-group responsibility, group-based guilt, and support for reparative measures. Journal of Personality and Social Psychology, 101(2), 256–270. https://doi.org/10.1037/a0023936

Cohen, G. L., Garcia, J., Purdie-Vaughns, V., Apfel, N., & Brzustoski, P. (2009). Recursive Processes in Self-Affirmation: Intervening to Close the Minority Achievement Gap. Science, 324(5925), 400–403. https://doi.org/10.1126/science.1170769

Goff, P. A., Steele, C. M., & Davies, P. G. (2008). The space between us: Stereotype threat and distance in interracial contexts. Journal of Personality and Social Psychology, 94, 91–107. https://doi.org/10.1037/0022-3514.94.1.91

Lehmiller, J. J., Law, A. T., & Tormala, T. T. (2010). The effect of self-affirmation on sexual prejudice. Journal of Experimental Social Psychology, 46(2), 276–285. https://doi.org/10.1016/j.jesp.2009.11.009

Lesick, T. l., & Zell, E. (2021). Is Affirmation the Cure? Self-Affirmation and European-Americans’ Perception of Systemic Racism. Basic and Applied Social Psychology, 43(1), 1–13. https://doi.org/10.1080/01973533.2020.1811092

Miller, S. S., & Saucier, D. A. (2018). Individual differences in the propensity to make attributions to prejudice. Group Processes & Intergroup Relations, 21(2), 280–301. https://doi.org/10.1177/1368430216674342

Perkins, H., Major, J., Chen, J., Berger, E., & Godwin, A. (2023). Using a values affirmation to increase engineering students’ awareness and acknowledgement of racism. 2023 American Psychological Association Conference.

Richeson, J. A., & Shelton, J. N. (2007). Negotiating Interracial Interactions: Costs, Consequences, and Possibilities. Current Directions in Psychological Science, 16(6), 316–320. https://doi.org/10.1111/j.1467-8721.2007.00528.x

Scheidt, M., Godwin, A., Senkpeil, R. R., Ge, J. S., Chen, J., Self, B. P., Widmann, J. M., & Berger, E. J. (2018, June 23). Validity Evidence for the SUCCESS Survey: Measuring Non-Cognitive and Affective Traits of Engineering and Computing Students. 2018 ASEE Annual Conference & Exposition. https://peer.asee.org/validity-evidence-for-the-success-survey-measuring-non-cognitive-and-affective-traits-of-engineering-and-computing-students

Schwartz, S. H. (2012). An Overview of the Schwartz Theory of Basic Values. Online Readings in Psychology and Culture, 2(1). https://doi.org/10.9707/2307-0919.1116

Sherman, D., K., & Cohen, G., L. (2002). Accepting Threatening Information: Self–Affirmation and the Reduction of Defensive Biases. Current Directions in Psychological Science, 11(4), 115–149.

Step 1: Load Data & Libraries

Things done in this section: load libraries, import data, separate into pre, post, and follow-up dataframes, and create race_minority and gender_minority variables from participant responses.

Little’s MCAR was used earlier to check if data is missing completely at random. Test is not significant for full dataset (X2 (192, N = 258) = 203.92, p = .264) or for dataset with unit nonresponders dropped (X2 (127, N = 204) = 118.52, p = .692). Data is missing completely at random and we’re okay to proceed with analysis.

library(psych)
library(ggplot2)
library(rstatix)
library(expss) #for cross_cases()
library(dplyr)
library(kableExtra)
library(nFactors)
library(corrplot)
library(sjPlot)
library(viridis)

# import file
import <- read.csv(file="data/final data 10-29-22.csv", header = T)

pre <- subset(import, select=c(UID, grep("pre", colnames(import))))
post <- subset(import, select=c(UID, grep("post", colnames(import))))
follow <- subset(import, select=c(UID, grep("follow", colnames(import))))
pmaps <- subset(import, select=c(UID, grep("pmaps", colnames(import))))
act <- subset(import, select=c(UID, grep("act", colnames(import))))
demo <- subset(import, select=c(UID, 129:162))

m1 <- merge(act, follow, by = "UID")
m2 <- merge(m1, pmaps, by = "UID")
df <- merge(m2, demo, by = "UID")

# m3 <- na.omit(merge(pre, post, by = "UID"))
# act$con[!is.na(act$Q5_1_act)] <- "chall"
# act$con[!is.na(act$Q15_1_act)] <- "val"
# act$con[!is.na(act$Q4_act)] <- "con"
# m4 <- merge(m3, na.omit(subset(act, select=c(UID,con))), by = "UID", all.y = T)
# subset(data.frame(table(m4$UID)), Freq > 1)
# m4 <- subset(m4, UID != "ENHLY4123X")

rm(pre, post, follow, act, pmaps, demo, import, m1, m2)

Recode Values Data

# 8 = not important, 5 = somewhat important, 1 = very important

val <- subset(df, select=c(UID, grep("Q15", colnames(df)), Q17_act, Q19_act))
val2 <- subset(val, select=c(2:14))

# Recode values in multiple columns
recode_values <- function(x) {
  case_when(
    x == "Very Important" ~ "1",
    x == "Somewhat Important" ~ "0",
    x == "Not Important" ~ "-1",
    TRUE ~ x
  )
}

val3 <- val2 %>%
  mutate_at(vars(starts_with("Q15")), recode_values)

# Recode values in multiple columns
recode_values <- function(x) {
  case_when(
    x == "5" ~ "0",
    x == "8" ~ "-1",
    TRUE ~ x
  )
}

val4 <- val3 %>%
  mutate_at(vars(starts_with("Q15")), recode_values)

str(val4)

## 'data.frame':    694 obs. of  13 variables:
##  $ Q15_1_act : chr  NA NA NA "1" ...
##  $ Q15_2_act : chr  NA NA NA "1" ...
##  $ Q15_3_act : chr  NA NA NA "1" ...
##  $ Q15_4_act : chr  NA NA NA "1" ...
##  $ Q15_5_act : chr  NA NA NA "0" ...
##  $ Q15_6_act : chr  NA NA NA "0" ...
##  $ Q15_7_act : chr  NA NA NA "1" ...
##  $ Q15_8_act : chr  NA NA NA "0" ...
##  $ Q15_9_act : chr  NA NA NA "0" ...
##  $ Q15_10_act: chr  NA NA NA "1" ...
##  $ Q15_11_act: chr  NA NA NA "0" ...
##  $ Q15_12_act: chr  NA NA NA "0" ...
##  $ Q15_13_act: chr  NA NA NA "-1" ...

val5 <- val4 %>%
  mutate_if(is.character, as.numeric)
str(val5)

## 'data.frame':    694 obs. of  13 variables:
##  $ Q15_1_act : num  NA NA NA 1 NA 0 NA NA 0 NA ...
##  $ Q15_2_act : num  NA NA NA 1 NA 0 NA NA 1 NA ...
##  $ Q15_3_act : num  NA NA NA 1 NA -1 NA NA 1 NA ...
##  $ Q15_4_act : num  NA NA NA 1 NA 1 NA NA 1 NA ...
##  $ Q15_5_act : num  NA NA NA 0 NA 1 NA NA 0 NA ...
##  $ Q15_6_act : num  NA NA NA 0 NA -1 NA NA 1 NA ...
##  $ Q15_7_act : num  NA NA NA 1 NA 1 NA NA 1 NA ...
##  $ Q15_8_act : num  NA NA NA 0 NA -1 NA NA 0 NA ...
##  $ Q15_9_act : num  NA NA NA 0 NA -1 NA NA -1 NA ...
##  $ Q15_10_act: num  NA NA NA 1 NA 1 NA NA 0 NA ...
##  $ Q15_11_act: num  NA NA NA 0 NA 0 NA NA 1 NA ...
##  $ Q15_12_act: num  NA NA NA 0 NA 0 NA NA 1 NA ...
##  $ Q15_13_act: num  NA NA NA -1 NA -1 NA NA -1 NA ...

df2 <- cbind.data.frame(df[1],val5[1:12],df[36:105])

rm(val,val2,val3,val4,val5)

Step 2: Create Composites & Check Descriptives

Things done in this section: create composite variables from timepoint 3 (follow-up), check univariate normality, visualize data. Created variable belexp that combines belonging (current feelings of belonging) and expectancy (anticipated future belonging).

ggplot(gather(subset(df2, select=c(14:49))), aes(value)) + 
  geom_histogram(bins = 7) + 
  facet_wrap(~key)

## Warning: Removed 9369 rows containing non-finite values (`stat_bin()`).

attach(df2)
df2$bel <- (Q2_1_follow + Q2_2_follow + Q2_3_follow + Q2_4_follow)/4
df2$rec <- (Q2_5_follow + Q2_6_follow + Q2_7_follow + Q2_8_follow)/4
df2$int <- (Q2_9_follow + Q2_10_follow + Q2_11_follow)/3
df2$ftpins <- (Q3_1_follow + Q3_2_follow + Q3_3_follow)/3
df2$pof <- (Q3_4_follow + Q3_5_follow + Q3_6_follow + Q3_7_follow)/4
df2$exp <- (Q3_8_follow + Q3_9_follow + Q3_10_follow + Q3_11_follow + Q3_12_follow)/5
df2$anx <- (Q4_1_follow + Q4_2_follow + Q4_3_follow + Q4_4_follow + Q4_5_follow)/5
df2$triv <- (Q47_1_pmaps + Q47_2_pmaps + Q47_3_pmaps + Q47_4_pmaps)/4
df2$vig <- (Q47_5_pmaps + Q47_6_pmaps + Q47_7_pmaps + Q47_8_pmaps)/4
df2$belexp <- (Q2_1_follow + Q2_2_follow + Q2_3_follow + Q2_4_follow +
                 Q3_8_follow + Q3_9_follow + Q3_10_follow + Q3_11_follow + Q3_12_follow)/9
detach(df2)

df2$rec <- as.vector(scale(df2$rec, center=T, scale=T))
df2$int <- as.vector(scale(df2$int, center=T, scale=T))
df2$ftpins <- as.vector(scale(df2$ftpins, center=T, scale=T)) 
df2$pof <- as.vector(scale(df2$pof, center=T, scale=T))
df2$anx <- as.vector(scale(df2$anx, center=T, scale=T))
df2$triv <- as.vector(scale(df2$triv, center=T, scale=T))
df2$vig <- as.vector(scale(df2$vig, center=T, scale=T))
df2$belexp <- as.vector(scale(df2$belexp, center=T, scale=T))

Univariate Normality

Issues with kurtosis for many of the variables at follow-up. Belonging has ok skew but high kurtosis (2.67) while belexp better (kurtosis = 2.01). Trivialization and vigilance are ok.

desc <- describe(subset(df2, select=c(bel, rec, int, ftpins, pof, exp, anx, triv, vig, belexp)))

kbl(round(desc, digits = 2)) %>%
  kable_styling() %>%
  row_spec(which(desc$kurtosis > 2), bold = T) %>%
  row_spec(which(desc$kurtosis < -2), bold = T) %>%
  row_spec(which(desc$skew > 2), italic = T) %>%
  row_spec(which(desc$skew < -2), italic = T)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
bel	1	435	5.86	1.05	6.00	6.00	1.11	1.00	7.00	6.00	-1.28	2.67	0.05
rec	2	435	0.00	1.00	0.17	0.11	1.12	-4.86	1.18	6.04	-1.34	3.17	0.05
int	3	435	0.00	1.00	0.14	0.17	0.96	-5.02	0.78	5.80	-1.96	5.15	0.05
ftpins	4	434	0.00	1.00	0.22	0.14	1.04	-5.41	0.93	6.34	-1.71	5.22	0.05
pof	5	434	0.00	1.00	0.30	0.15	1.03	-4.56	0.99	5.55	-1.46	2.92	0.05
exp	6	434	5.76	0.99	6.00	5.85	0.89	1.00	7.00	6.00	-0.92	1.46	0.05
anx	7	434	0.00	1.00	-0.02	0.01	1.14	-2.07	1.78	3.85	-0.09	-0.73	0.05
triv	8	431	0.00	1.00	-0.29	-0.11	1.11	-1.19	2.41	3.59	0.73	-0.25	0.05
vig	9	432	0.00	1.00	0.02	0.03	0.90	-3.01	1.84	4.85	-0.36	0.22	0.05
belexp	10	434	0.00	1.00	0.09	0.09	0.89	-5.21	1.29	6.51	-1.00	2.01	0.05

Look @ Data: Anti-racist Attitudes & Race

ggplot(aes(x=triv, fill=re_white), data=subset(df2, !is.na(re_white))) +
  geom_density(color="#e9ecef", alpha=0.6, position = 'identity') +
  scale_fill_manual(values=c("#69b3a2", "#404080")) +
  labs(fill="White")

## Warning: Removed 224 rows containing non-finite values (`stat_density()`).

ggplot(aes(x=vig, fill=re_white), data=subset(df2, !is.na(re_white))) +
  geom_density(color="#e9ecef", alpha=0.6, position = 'identity') +
  scale_fill_manual(values=c("#69b3a2", "#404080")) +
  labs(fill="White")

## Warning: Removed 223 rows containing non-finite values (`stat_density()`).

Look @ Data: Anti-racist Attitudes & Gender

ggplot(aes(x=triv, fill=ge_w), data=subset(df2, !is.na(ge_w))) +
  geom_density(color="#e9ecef", alpha=0.6, position = 'identity') +
  scale_fill_manual(values=c("#69b3a2", "#404080")) +
  labs(fill="Women")

## Warning: Removed 224 rows containing non-finite values (`stat_density()`).

ggplot(aes(x=vig, fill=ge_w), data=subset(df2, !is.na(ge_w))) +
  geom_density(color="#e9ecef", alpha=0.6, position = 'identity') +
  scale_fill_manual(values=c("#69b3a2", "#404080")) +
  labs(fill="Women")

## Warning: Removed 223 rows containing non-finite values (`stat_density()`).

Step 3: Code Values Data

Things done in this section: code participants’ responses to the values affirmation activity to understand their values. Students were asked to rate at least three values from the list below. Ratings were not-important (-1), somewhat-important (0), or very-important (+1). Factor analysis used to identify latent variables underlying the larger list of values (FA used instead of PCA due to focus on underlying, latent factors instead of dimension reduction). Once latent factors identified, averages were created. Higher score indicates greater importance. Score below zero indicates not important.

• Self-direction: I value independence and self-direction when solving engineering problems.
• Stimulation: I value novel engineering challenges, new experiences, and creative problem-solving.
• Hedonism: I value the personal gratification of solving technical problems or helping to address real-world issues.
• Achievement: I value persistence in the face of difficulty and demonstrating competence and success in engineering.
• Power: I value leadership and the ability to make decisions and control resources in group efforts.
• Face: I value the prestige that an engineering degree offers.
• Security: I value security and stability (for example, financial security or access to clean water) for myself and others.
• Conformity: I value adhering to an objective engineering process and the ability to maintain a stable working environment.
• Tradition: I value the knowledge and understanding that traditional culture or religion provide when seeking engineering solutions.
• Benevolence: I value the welfare of people, such as the safety of my co-workers/classmates, and the wellbeing of my community.
• Universalism: I value understanding and appreciating all people and all of nature, seeking kindness and justice in my engineering work.
• Collectivism: I value collaboration and teamwork when working to achieve engineering goals.
• Other

Values Descriptives & Univariate Normality

colnames(df2)[2:13] <- c("Self-direction",
                          "Stimulation",
                          "Hedonism",
                          "Achievement",
                          "Power",
                          "Face",
                          "Security",
                          "Conformity",
                          "Tradition",
                          "Benevolence",
                          "Universalism",
                          "Collectivism")
desc <- describe(subset(df2, select=c(2:13)))

kbl(round(desc, digits = 2)) %>%
  kable_styling() %>%
  row_spec(which(desc$kurtosis > 2), bold = T) %>%
  row_spec(which(desc$kurtosis < -2), bold = T) %>%
  row_spec(which(desc$skew > 2), italic = T) %>%
  row_spec(which(desc$skew < -2), italic = T)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
Self-direction	1	102	0.53	0.54	1	0.56	0.00	-1	1	2	-0.49	-1.02	0.05
Stimulation	2	102	0.63	0.53	1	0.68	0.00	-1	1	2	-0.92	-0.35	0.05
Hedonism	3	102	0.62	0.63	1	0.74	0.00	-1	1	2	-1.38	0.71	0.06
Achievement	4	102	0.80	0.49	1	0.93	0.00	-1	1	2	-2.45	5.19	0.05
Power	5	102	0.41	0.62	0	0.48	1.48	-1	1	2	-0.53	-0.66	0.06
Face	6	102	0.25	0.78	0	0.32	1.48	-1	1	2	-0.47	-1.23	0.08
Security	7	102	0.70	0.52	1	0.78	0.00	-1	1	2	-1.44	1.12	0.05
Conformity	8	102	-0.06	0.67	0	-0.07	0.00	-1	1	2	0.07	-0.81	0.07
Tradition	9	102	-0.25	0.82	0	-0.32	1.48	-1	1	2	0.49	-1.35	0.08
Benevolence	10	102	0.56	0.62	1	0.66	0.00	-1	1	2	-1.07	0.05	0.06
Universalism	11	102	0.25	0.79	0	0.32	1.48	-1	1	2	-0.48	-1.27	0.08
Collectivism	12	102	0.49	0.73	1	0.61	0.00	-1	1	2	-1.03	-0.39	0.07

long_df <- df2 %>%
  gather(variable, value, 2:13)
long_df <- long_df[, c("UID", "variable", "value")]

long_df %>%
  ggplot( aes(x=value, color=variable, fill=variable)) +
    geom_histogram(bins=3) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    theme(
      legend.position="none",
      panel.spacing = unit(0.1, "lines"),
      strip.text.x = element_text(size = 8)
    ) +
    facet_wrap(~variable) +
  xlab("Ratings (Very Important; Somewhat Important; Not Important)") +
  ylab("Frequency")

## Warning: Removed 7104 rows containing non-finite values (`stat_bin()`).

Values Correlations

d <- subset(df2, select=c(2:13))

out <- corr.test(d)

corrplot(out$r, type="upper", method = "color", tl.col = "black", tl.cex = .75,
         p.mat = out$p,
         sig.level = c(.001, .01, .05), pch.cex = .9,
         insig = "label_sig", pch.col = "white",
         order = "hclust")

Values Factor Analysis

ev <- eigen(cor(na.omit(d))) # get eigenvalues
ap <- parallel(subject = nrow(na.omit(d)), var = ncol(na.omit(d)),
               rep = 100,cent = .05)
nS <- nScree(x = ev$values, aparallel = ap$eigen$qevpea)
plotnScree(nS)

fit <- factanal(na.omit(d), 3, rotation="promax") 
print(fit, digits = 3, cutoff = 0.3, sort = TRUE) 

## 
## Call:
## factanal(x = na.omit(d), factors = 3, rotation = "promax")
## 
## Uniquenesses:
## Self-direction    Stimulation       Hedonism    Achievement          Power 
##          0.859          0.668          0.822          0.215          0.666 
##           Face       Security     Conformity      Tradition    Benevolence 
##          0.590          0.606          0.298          0.432          0.438 
##   Universalism   Collectivism 
##          0.160          0.657 
## 
## Loadings:
##                Factor1 Factor2 Factor3
## Stimulation     0.543                 
## Tradition       0.682   0.408         
## Benevolence     0.687                 
## Universalism    0.923                 
## Collectivism    0.535                 
## Face                    0.573         
## Security                0.630         
## Conformity      0.329   0.795         
## Achievement                     0.863 
## Self-direction -0.311                 
## Hedonism                0.334         
## Power                           0.473 
## 
##                Factor1 Factor2 Factor3
## SS loadings      2.785   1.692   1.175
## Proportion Var   0.232   0.141   0.098
## Cumulative Var   0.232   0.373   0.471
## 
## Factor Correlations:
##         Factor1 Factor2 Factor3
## Factor1   1.000  0.1025  0.1012
## Factor2   0.102  1.0000 -0.0999
## Factor3   0.101 -0.0999  1.0000
## 
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 41.25 on 33 degrees of freedom.
## The p-value is 0.153

fit <- factanal(na.omit(d), 4, rotation="promax") 
print(fit, digits = 3, cutoff = 0.3, sort = TRUE) 

## 
## Call:
## factanal(x = na.omit(d), factors = 4, rotation = "promax")
## 
## Uniquenesses:
## Self-direction    Stimulation       Hedonism    Achievement          Power 
##          0.854          0.670          0.512          0.324          0.631 
##           Face       Security     Conformity      Tradition    Benevolence 
##          0.585          0.605          0.266          0.380          0.381 
##   Universalism   Collectivism 
##          0.177          0.506 
## 
## Loadings:
##                Factor1 Factor2 Factor3 Factor4
## Stimulation     0.509                         
## Benevolence     0.813                         
## Universalism    0.712                         
## Collectivism    0.825                   0.303 
## Security                0.526                 
## Conformity              0.834                 
## Tradition       0.351   0.569                 
## Achievement     0.347           0.797         
## Power                           0.543         
## Hedonism                                0.762 
## Self-direction                                
## Face                    0.422           0.315 
## 
##                Factor1 Factor2 Factor3 Factor4
## SS loadings      2.538   1.556   1.156   0.956
## Proportion Var   0.212   0.130   0.096   0.080
## Cumulative Var   0.212   0.341   0.437   0.517
## 
## Factor Correlations:
##         Factor1 Factor2 Factor3 Factor4
## Factor1   1.000 -0.1937 -0.1733   0.475
## Factor2  -0.194  1.0000 -0.0371   0.242
## Factor3  -0.173 -0.0371  1.0000  -0.220
## Factor4   0.475  0.2423 -0.2203   1.000
## 
## Test of the hypothesis that 4 factors are sufficient.
## The chi square statistic is 25.96 on 24 degrees of freedom.
## The p-value is 0.355

fit <- factanal(na.omit(d), 5, rotation="promax") 
print(fit, digits = 3, cutoff = 0.3, sort = TRUE) 

## 
## Call:
## factanal(x = na.omit(d), factors = 5, rotation = "promax")
## 
## Uniquenesses:
## Self-direction    Stimulation       Hedonism    Achievement          Power 
##          0.645          0.652          0.494          0.439          0.005 
##           Face       Security     Conformity      Tradition    Benevolence 
##          0.585          0.601          0.278          0.361          0.357 
##   Universalism   Collectivism 
##          0.198          0.500 
## 
## Loadings:
##                Factor1 Factor2 Factor3 Factor4 Factor5
## Benevolence     0.827                                 
## Universalism    0.585                                 
## Collectivism    0.821                                 
## Security                0.526                         
## Conformity              0.828                         
## Tradition               0.596                         
## Power                           1.061                 
## Hedonism                                0.799         
## Self-direction                                  0.660 
## Achievement     0.467                           0.515 
## Stimulation     0.460                                 
## Face                    0.428           0.329         
## 
##                Factor1 Factor2 Factor3 Factor4 Factor5
## SS loadings      2.337   1.572   1.290   1.056   0.852
## Proportion Var   0.195   0.131   0.107   0.088   0.071
## Cumulative Var   0.195   0.326   0.433   0.521   0.592
## 
## Factor Correlations:
##         Factor1 Factor2 Factor3 Factor4 Factor5
## Factor1  1.0000 -0.0285 -0.0251   0.490  -0.259
## Factor2 -0.0285  1.0000 -0.2443  -0.180   0.470
## Factor3 -0.0251 -0.2443  1.0000   0.132   0.167
## Factor4  0.4895 -0.1798  0.1321   1.000  -0.293
## Factor5 -0.2593  0.4697  0.1670  -0.293   1.000
## 
## Test of the hypothesis that 5 factors are sufficient.
## The chi square statistic is 13.5 on 16 degrees of freedom.
## The p-value is 0.636

Results

Three factor identified three factors but one item (tradition) cross-loaded. Four-factor model resolved the cross-loading. Five factor model did produce a loading for self-direction, which loaded on a two-item factor with achievement. The four factor model does have a weak fourth factor (only two items, one of which is loading very weakly).

Consistent across all models:

• benevolence, universalism, collectivism, stimulation
• face, security, conformity

Consistent across 3/4 models:

• achievement, power

Consistent across 4/5 models:

• face, security, conformity, tradition

Based on performance across all three models, sticking with the three-factor model but including tradition with face/security/conformity (currently cross-loading).

Dropping hedonism. Item may have been double- or triple-barreled and loads weakly and inconsistently.

Dropping self-direction. Either loads on its own factor or not at all.

d <- subset(df2, select=c(3, 5:13))

ev <- eigen(cor(na.omit(d))) # get eigenvalues
ap <- parallel(subject = nrow(na.omit(d)), var = ncol(na.omit(d)),
               rep = 100,cent = .05)
nS <- nScree(x = ev$values, aparallel = ap$eigen$qevpea)
plotnScree(nS)

fit <- factanal(na.omit(d), 3, rotation="promax") 
print(fit, digits = 3, cutoff = 0.3, sort = TRUE) 

## 
## Call:
## factanal(x = na.omit(d), factors = 3, rotation = "promax")
## 
## Uniquenesses:
##  Stimulation  Achievement        Power         Face     Security   Conformity 
##        0.659        0.374        0.590        0.631        0.639        0.260 
##    Tradition  Benevolence Universalism Collectivism 
##        0.416        0.404        0.191        0.616 
## 
## Loadings:
##              Factor1 Factor2 Factor3
## Stimulation   0.563                 
## Tradition     0.647   0.445         
## Benevolence   0.691                 
## Universalism  0.911                 
## Collectivism  0.544                 
## Face                  0.530         
## Security              0.597         
## Conformity            0.819         
## Achievement                   0.766 
## Power        -0.352           0.553 
## 
##                Factor1 Factor2 Factor3
## SS loadings      2.614   1.563   1.058
## Proportion Var   0.261   0.156   0.106
## Cumulative Var   0.261   0.418   0.523
## 
## Factor Correlations:
##         Factor1 Factor2 Factor3
## Factor1  1.0000  0.0191   0.179
## Factor2  0.0191  1.0000  -0.123
## Factor3  0.1792 -0.1230   1.000
## 
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 14.8 on 18 degrees of freedom.
## The p-value is 0.675

Tradition is still cross-loading and stimulation doesn’t fit the emerging factor – drop?

d <- subset(df2, select=c(5:9, 11:13))

ev <- eigen(cor(na.omit(d))) # get eigenvalues
ap <- parallel(subject = nrow(na.omit(d)), var = ncol(na.omit(d)),
               rep = 100,cent = .05)
nS <- nScree(x = ev$values, aparallel = ap$eigen$qevpea)
plotnScree(nS)

fit <- factanal(na.omit(d), 3, rotation="promax") 
print(fit, digits = 3, cutoff = 0.3, sort = TRUE) 

## 
## Call:
## factanal(x = na.omit(d), factors = 3, rotation = "promax")
## 
## Uniquenesses:
##  Achievement        Power         Face     Security   Conformity  Benevolence 
##        0.364        0.587        0.605        0.603        0.347        0.387 
## Universalism Collectivism 
##        0.202        0.600 
## 
## Loadings:
##              Factor1 Factor2 Factor3
## Benevolence   0.722                 
## Universalism  0.906                 
## Collectivism  0.576                 
## Face                  0.554         
## Security              0.632         
## Conformity            0.774         
## Achievement                   0.769 
## Power        -0.326           0.558 
## 
##                Factor1 Factor2 Factor3
## SS loadings      1.946   1.352   1.049
## Proportion Var   0.243   0.169   0.131
## Cumulative Var   0.243   0.412   0.543
## 
## Factor Correlations:
##         Factor1 Factor2 Factor3
## Factor1  1.0000 -0.0715  -0.164
## Factor2 -0.0715  1.0000  -0.191
## Factor3 -0.1640 -0.1914   1.000
## 
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 6.5 on 7 degrees of freedom.
## The p-value is 0.483

Final Values Factors

• kindness: benevolence, universalism, collectivism - https://freeicons.io/entrepreneur-18/compassionate-kind-kindly-merciful-icon-926886
• stability: face, security, conformity - https://freeicons.io/law-icon-set/lock-safe-secure-icon-699010
• strength: achievement, power - https://freeicons.io/healthy-lifestyle/muscle-strong-strength-bodybuilding-fitness-icon-491787

Create Values Composites

colnames(df2)[2:13] <- tolower(colnames(df2)[2:13])
df2$kindness <- (df2$benevolence + df2$universalism + df2$collectivism)/3
df2$stability <- (df2$face + df2$security + df2$conformity)/3
df2$strength <- (df2$achievement + df2$power)/2

df2$kindness <- as.vector(scale(df2$kindness, center=T, scale=T))
df2$stability <- as.vector(scale(df2$stability, center=T, scale=T))
df2$strength <- as.vector(scale(df2$strength, center=T, scale=T))

desc <- describe(subset(df2, select=c(kindness, stability, strength)))

kbl(round(desc, digits = 2)) %>%
  kable_styling() %>%
  row_spec(which(desc$kurtosis > 2), bold = T) %>%
  row_spec(which(desc$kurtosis < -2), bold = T) %>%
  row_spec(which(desc$skew > 2), italic = T) %>%
  row_spec(which(desc$skew < -2), italic = T)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
kindness	1	102	0	1	0.39	0.13	0.83	-2.42	0.95	3.37	-0.88	-0.35	0.1
stability	2	102	0	1	0.07	0.05	0.97	-1.89	1.38	3.27	-0.51	-1.02	0.1
strength	3	102	0	1	-0.23	0.18	1.61	-3.50	0.85	4.35	-1.42	2.05	0.1

corr.test(subset(df2, select=c(kindness, stability, strength)))

## Call:corr.test(x = subset(df2, select = c(kindness, stability, strength)))
## Correlation matrix 
##           kindness stability strength
## kindness      1.00      0.04     0.02
## stability     0.04      1.00     0.17
## strength      0.02      0.17     1.00
## Sample Size 
## [1] 102
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##           kindness stability strength
## kindness      0.00      1.00     1.00
## stability     0.71      0.00     0.25
## strength      0.84      0.08     0.00
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

long_df <- df2 %>%
  gather(variable, value, 94:96)
long_df <- long_df[, c("UID", "variable", "value")]

long_df$variable[long_df$variable == "kindness"] <- "Kindness"
long_df$variable[long_df$variable == "stability"] <- "Stability"
long_df$variable[long_df$variable == "strength"] <- "Strength"

long_df %>%
  ggplot( aes(x=value, color=variable, fill=variable)) +
    geom_histogram(bins=5) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    theme(
      legend.position="none",
      panel.spacing = unit(0.1, "lines"),
      strip.text.x = element_text(size = 8)
    ) +
    facet_wrap(~variable) +
  xlab("Standardized Ratings") + ylab("Frequency")

## Warning: Removed 1776 rows containing non-finite values (`stat_bin()`).

Step 4: Check for and Drop Outliers

Using Mahalanobis’ distance. One outlier dropped.

d <- na.omit(subset(df2, select=c(1,85:88,90:96)))

m_dist <- mahalanobis(d[-1], colMeans(d[-1]), cov(d[-1]))
d$MD <- round(m_dist, 1)
plot(d$MD)
describe(m_dist)

##    vars  n  mean   sd median trimmed  mad  min   max range skew kurtosis  se
## X1    1 87 10.87 7.47   9.38    9.79 4.69 3.58 57.67 54.08 3.18    15.84 0.8

cut <- qchisq(.999, df=(ncol(d)-1))
abline(a=cut, b=0, col="red")

d$outlier <- F
d$outlier[d$MD > cut] <- T
table(d$outlier)

## 
## FALSE  TRUE 
##    86     1

outs <- subset(d, select=c(UID, outlier), outlier == T)
df3 <- subset(df2, !(UID %in% outs$UID))

Step 5: Check Values & Variables Normality and Correlations

Add the new value variables and check all univariate normality and correlations. Strength kurtosis is a bit high (2.02) but ok, probably because of influence from achievement which was highly rated by most students.

desc <- describe(subset(df3, select=c(85:88,90:96)))

kbl(round(desc, digits = 2)) %>%
  kable_styling() %>%
  row_spec(which(desc$kurtosis > 2), bold = T) %>%
  row_spec(which(desc$kurtosis < -2), bold = T) %>%
  row_spec(which(desc$skew > 2), italic = T) %>%
  row_spec(which(desc$skew < -2), italic = T)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
rec	1	434	0.01	0.99	0.17	0.11	1.12	-4.86	1.18	6.04	-1.34	3.27	0.05
int	2	434	0.01	0.98	0.14	0.18	0.96	-5.02	0.78	5.80	-1.92	5.07	0.05
ftpins	3	433	0.01	0.97	0.22	0.14	1.04	-5.41	0.93	6.34	-1.53	4.25	0.05
pof	4	433	0.01	0.99	0.30	0.15	1.03	-4.56	0.99	5.55	-1.47	3.02	0.05
anx	5	433	0.00	1.00	-0.02	0.01	1.14	-2.07	1.78	3.85	-0.10	-0.73	0.05
triv	6	430	0.00	1.00	-0.29	-0.11	1.11	-1.19	2.41	3.59	0.73	-0.25	0.05
vig	7	431	0.00	1.00	0.02	0.03	0.90	-3.01	1.84	4.85	-0.36	0.21	0.05
belexp	8	433	0.01	0.99	0.09	0.10	0.89	-5.21	1.29	6.51	-0.98	2.02	0.05
kindness	9	101	0.01	1.00	0.39	0.14	0.83	-2.42	0.95	3.37	-0.90	-0.32	0.10
stability	10	101	0.00	1.00	0.07	0.05	0.97	-1.89	1.38	3.27	-0.51	-1.04	0.10
strength	11	101	-0.01	1.00	-0.23	0.17	1.61	-3.50	0.85	4.35	-1.41	2.02	0.10

orig <- colnames(df3)
colnames(df3)[85:96] <- c("Engineering Recognition", "Engineering Interest", "Future Time Perspective: Instrumentality", "Future Time Perspective: Perceptions of Future", "exp", "Test Anxiety", "Trivialization of Racism", "Vigilance Against Racism", "Engineering Belonging", "Value: Kindness", "Value: Stability", "Value: Strength")

out <- corr.test(subset(df3, select=c("Engineering Recognition", "Engineering Interest", "Future Time Perspective: Instrumentality", "Future Time Perspective: Perceptions of Future", "Test Anxiety", "Trivialization of Racism", "Vigilance Against Racism", "Engineering Belonging", "Value: Kindness", "Value: Stability", "Value: Strength")))

corrplot(out$r, type="upper", method = "color", tl.col = "black", tl.cex = .75,
         p.mat = out$p,
         sig.level = c(.001, .01, .05), pch.cex = .9,
         insig = "label_sig", pch.col = "white",
         order = "hclust")

colnames(df3) <- orig

Step 6: Exploratory Analyses

Things done in this section: examine the relationships between the variables independently. Calculated corrected p-values and report them in the comments in the code.

Note the small sample size! 48 white men and 14 white women.

df4 <- na.omit(subset(df3, select=c(kindness, stability, strength, triv, vig, re_white, ge_m, belexp)))
cross_cases(df4, re_white, ge_m)

	ge_m
	FALSE	TRUE
re_white
FALSE	4	19
TRUE	14	48
#Total cases	18	67

# white men = 48
# white women = 14

df5 <- subset(df4, re_white == T)

triv <- lm(data = df5, triv ~ kindness + stability + strength)
summary(triv)

## 
## Call:
## lm(formula = triv ~ kindness + stability + strength, data = df5)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.96596 -0.56427  0.06294  0.54870  1.64159 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.1822     0.1117   1.631   0.1084    
## kindness     -0.7312     0.1052  -6.954 3.51e-09 ***
## stability     0.2766     0.1150   2.405   0.0194 *  
## strength      0.5312     0.1050   5.061 4.50e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8468 on 58 degrees of freedom
## Multiple R-squared:  0.6219, Adjusted R-squared:  0.6024 
## F-statistic:  31.8 on 3 and 58 DF,  p-value: 2.755e-12

# (Intercept)   kindness    stability   strength
# 0.135       0.000     0.029       0.000
plot_model(triv, type = "diag")

## [[1]]

## 
## [[2]]

## `geom_smooth()` using formula = 'y ~ x'

## 
## [[3]]

## 
## [[4]]

## `geom_smooth()` using formula = 'y ~ x'

# plot_model(triv, type = "pred")

vig <- lm(data = df5, vig ~ kindness + stability + strength)
summary(vig)

## 
## Call:
## lm(formula = vig ~ kindness + stability + strength, data = df5)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7435 -0.3100  0.1038  0.3802  1.9802 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.03959    0.10391  -0.381 0.704591    
## kindness     0.27738    0.09781   2.836 0.006284 ** 
## stability   -0.43338    0.10695  -4.052 0.000153 ***
## strength    -0.02782    0.09764  -0.285 0.776725    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7876 on 58 degrees of freedom
## Multiple R-squared:  0.3296, Adjusted R-squared:  0.2949 
## F-statistic: 9.505 on 3 and 58 DF,  p-value: 3.359e-05

# (Intercept)   kindness    stability   strength
# 0.755       0.012     0.001       0.777
plot_model(vig, type = "diag")

## [[1]]

## 
## [[2]]

## `geom_smooth()` using formula = 'y ~ x'

## 
## [[3]]

## 
## [[4]]

## `geom_smooth()` using formula = 'y ~ x'

# plot_model(vig, type = "pred")

belxp <- lm(data = df5, belexp ~ kindness + stability + strength)
summary(belxp)

## 
## Call:
## lm(formula = belexp ~ kindness + stability + strength, data = df5)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.06840 -0.32243  0.01255  0.38740  1.23516 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.36097    0.09027   3.999 0.000183 ***
## kindness    -0.33339    0.08497  -3.924 0.000234 ***
## stability    0.16369    0.09291   1.762 0.083374 .  
## strength     0.21298    0.08482   2.511 0.014850 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6842 on 58 degrees of freedom
## Multiple R-squared:  0.3424, Adjusted R-squared:  0.3084 
## F-statistic: 10.07 on 3 and 58 DF,  p-value: 1.954e-05

# (Intercept)   kindness    stability   strength
# 0.001       0.001     0.114       0.025
plot_model(belxp, type = "diag")

## [[1]]

## 
## [[2]]

## `geom_smooth()` using formula = 'y ~ x'

## 
## [[3]]

## 
## [[4]]

## `geom_smooth()` using formula = 'y ~ x'

# plot_model(belxp, type = "pred")

belxp2 <- lm(data = df5, belexp ~ triv + vig)
# (Intercept) triv      vig
# 0.002       0.000     0.479
summary(belxp2)

## 
## Call:
## lm(formula = belexp ~ triv + vig, data = df5)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3638 -0.3479  0.1230  0.2792  1.3405 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.30443    0.08589   3.545 0.000777 ***
## triv         0.35492    0.06968   5.093 3.87e-06 ***
## vig         -0.08193    0.09976  -0.821 0.414787    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6516 on 59 degrees of freedom
## Multiple R-squared:  0.3933, Adjusted R-squared:  0.3727 
## F-statistic: 19.12 on 2 and 59 DF,  p-value: 3.959e-07

pvals = c(summary(triv)$coefficients[,4],
          summary(vig)$coefficients[,4],
          summary(belxp)$coefficients[,4],
          summary(belxp2)$coefficients[,4])
round(p.adjust(pvals, "BH"), digits=3)

## (Intercept)    kindness   stability    strength (Intercept)    kindness 
##       0.135       0.000       0.029       0.000       0.755       0.012 
##   stability    strength (Intercept)    kindness   stability    strength 
##       0.001       0.777       0.001       0.001       0.114       0.025 
## (Intercept)        triv         vig 
##       0.002       0.000       0.479

Results

• Based on these exploratory analyses, values inform both antiracist beliefs/attitudes and belonging/expectancy
• Is the effect of values on belonging/expectancy mediated by acceptance of racism?
• We see that participants who value kindness report lower belonging. How much of that effect is due to increased acceptance of racism?

Step 7: Mediation Analysis

Note - uses ordinary least squares approach.

set.seed(100)
options(scipen = 999)

bel_kind <- mediate(y = "belexp", x = "kindness", m = c("triv"), data = df5, n.iter = 1000, std = T)

bel_kind

## 
## Mediation/Moderation Analysis 
## Call: mediate(y = "belexp", x = "kindness", m = c("triv"), data = df5, 
##     n.iter = 1000, std = T)
## 
## The DV (Y) was  belexp . The IV (X) was  kindness . The mediating variable(s) =  triv .
## 
## Total effect(c) of  kindness  on  belexp  =  -0.44   S.E. =  0.12  t  =  -3.85  df=  60   with p =  0.00029
## Direct effect (c') of  kindness  on  belexp  removing  triv  =  -0.12   S.E. =  0.13  t  =  -0.92  df=  59   with p =  0.36
## Indirect effect (ab) of  kindness  on  belexp  through  triv   =  -0.33 
## Mean bootstrapped indirect effect =  -0.33  with standard error =  0.08  Lower CI =  -0.48    Upper CI =  -0.18
## R = 0.63 R2 = 0.4   F = 19.26 on 2 and 59 DF   p-value:  0.00000000793 
## 
##  To see the longer output, specify short = FALSE in the print statement or ask for the summary

summary(bel_kind)

## Call: mediate(y = "belexp", x = "kindness", m = c("triv"), data = df5, 
##     n.iter = 1000, std = T)
## 
## Direct effect estimates (traditional regression)    (c') X + M on Y 
##           belexp   se     t df      Prob
## Intercept   0.00 0.10  0.00 59 1.0000000
## kindness   -0.12 0.13 -0.92 59 0.3620000
## triv        0.55 0.13  4.38 59 0.0000487
## 
## R = 0.63 R2 = 0.4   F = 19.26 on 2 and 59 DF   p-value:  0.000000364 
## 
##  Total effect estimates (c) (X on Y) 
##           belexp   se     t df     Prob
## Intercept   0.00 0.12  0.00 60 1.000000
## kindness   -0.44 0.12 -3.85 60 0.000291
## 
##  'a'  effect estimates (X on M) 
##           triv  se     t df        Prob
## Intercept  0.0 0.1  0.00 60 1.000000000
## kindness  -0.6 0.1 -5.74 60 0.000000328
## 
##  'b'  effect estimates (M on Y controlling for X) 
##      belexp   se    t df      Prob
## triv   0.55 0.13 4.38 59 0.0000487
## 
##  'ab'  effect estimates (through all  mediators)
##          belexp  boot   sd lower upper
## kindness  -0.33 -0.33 0.08 -0.48 -0.18

bel_stab <- mediate(y = "belexp", x = "stability", m = c("triv"), data = df5, n.iter = 1000, std = T)

bel_stab

## 
## Mediation/Moderation Analysis 
## Call: mediate(y = "belexp", x = "stability", m = c("triv"), data = df5, 
##     n.iter = 1000, std = T)
## 
## The DV (Y) was  belexp . The IV (X) was  stability . The mediating variable(s) =  triv .
## 
## Total effect(c) of  stability  on  belexp  =  0.3   S.E. =  0.12  t  =  2.45  df=  60   with p =  0.017
## Direct effect (c') of  stability  on  belexp  removing  triv  =  0.09   S.E. =  0.11  t  =  0.83  df=  59   with p =  0.41
## Indirect effect (ab) of  stability  on  belexp  through  triv   =  0.21 
## Mean bootstrapped indirect effect =  0.22  with standard error =  0.07  Lower CI =  0.09    Upper CI =  0.38
## R = 0.63 R2 = 0.39   F = 19.14 on 2 and 59 DF   p-value:  0.00000000871 
## 
##  To see the longer output, specify short = FALSE in the print statement or ask for the summary

summary(bel_stab)

## Call: mediate(y = "belexp", x = "stability", m = c("triv"), data = df5, 
##     n.iter = 1000, std = T)
## 
## Direct effect estimates (traditional regression)    (c') X + M on Y 
##           belexp   se    t df       Prob
## Intercept   0.00 0.10 0.00 59 1.00000000
## stability   0.09 0.11 0.83 59 0.41000000
## triv        0.59 0.11 5.42 59 0.00000115
## 
## R = 0.63 R2 = 0.39   F = 19.14 on 2 and 59 DF   p-value:  0.000000393 
## 
##  Total effect estimates (c) (X on Y) 
##           belexp   se    t df  Prob
## Intercept    0.0 0.12 0.00 60 1.000
## stability    0.3 0.12 2.45 60 0.017
## 
##  'a'  effect estimates (X on M) 
##           triv   se    t df    Prob
## Intercept 0.00 0.12 0.00 60 1.00000
## stability 0.36 0.12 2.99 60 0.00409
## 
##  'b'  effect estimates (M on Y controlling for X) 
##      belexp   se    t df       Prob
## triv   0.59 0.11 5.42 59 0.00000115
## 
##  'ab'  effect estimates (through all  mediators)
##           belexp boot   sd lower upper
## stability   0.21 0.22 0.07  0.09  0.38

bel_stre <- mediate(y = "belexp", x = "strength", m = c("triv"), data = df5, n.iter = 1000, std = T)

bel_stre

## 
## Mediation/Moderation Analysis 
## Call: mediate(y = "belexp", x = "strength", m = c("triv"), data = df5, 
##     n.iter = 1000, std = T)
## 
## The DV (Y) was  belexp . The IV (X) was  strength . The mediating variable(s) =  triv .
## 
## Total effect(c) of  strength  on  belexp  =  0.35   S.E. =  0.12  t  =  2.88  df=  60   with p =  0.0055
## Direct effect (c') of  strength  on  belexp  removing  triv  =  0.05   S.E. =  0.12  t  =  0.41  df=  59   with p =  0.69
## Indirect effect (ab) of  strength  on  belexp  through  triv   =  0.3 
## Mean bootstrapped indirect effect =  0.3  with standard error =  0.07  Lower CI =  0.17    Upper CI =  0.47
## R = 0.62 R2 = 0.39   F = 18.71 on 2 and 59 DF   p-value:  0.000000012 
## 
##  To see the longer output, specify short = FALSE in the print statement or ask for the summary

summary(bel_stre)

## Call: mediate(y = "belexp", x = "strength", m = c("triv"), data = df5, 
##     n.iter = 1000, std = T)
## 
## Direct effect estimates (traditional regression)    (c') X + M on Y 
##           belexp   se    t df       Prob
## Intercept   0.00 0.10 0.00 59 1.00000000
## strength    0.05 0.12 0.41 59 0.68600000
## triv        0.60 0.12 5.07 59 0.00000423
## 
## R = 0.62 R2 = 0.39   F = 18.71 on 2 and 59 DF   p-value:  0.00000051 
## 
##  Total effect estimates (c) (X on Y) 
##           belexp   se    t df    Prob
## Intercept   0.00 0.12 0.00 60 1.00000
## strength    0.35 0.12 2.88 60 0.00549
## 
##  'a'  effect estimates (X on M) 
##           triv   se    t df      Prob
## Intercept  0.0 0.11 0.00 60 1.0000000
## strength   0.5 0.11 4.51 60 0.0000306
## 
##  'b'  effect estimates (M on Y controlling for X) 
##      belexp   se    t df       Prob
## triv    0.6 0.12 5.07 59 0.00000423
## 
##  'ab'  effect estimates (through all  mediators)
##          belexp boot   sd lower upper
## strength    0.3  0.3 0.07  0.17  0.47

options(scipen = 0)

Results

• Increased valuing of kindness in early semester is associated with decreased belonging/expectancy at end of semester

• Kindness negatively associated with triv

• Kindness and bel/exp relationship mediated by end-of-semester trivialization

• Increased valuing of stability in early semester is associated with increased belonging/expectancy at end of semester

• Stability positively associated with triv

• Stability and bel/exp relationship mediated by end of semester trivialization

• Increased valuing of strength in early semester is associated with increased belonging/expectancy at end of semester

• Strength positively associated with triv

• Strength and bel/exp relationship mediated by end of semester trivialization

Summary: * Among White engineering students, three latent factors emerge from a collection of 12 values: kindness, stability, and strength * A series of multiple linear regressions suggests that students who value kindness more report lower belonging/expectancy, but also less trivialization and more vigilance. Those who value strength report more trivialization and belonging/expectancy, and those who value stability report less vigilance. Lastly, higher trivialization is associated with increased belonging/expectancy. * A series of mediation analyses suggests that the relationships between values and belonging/expectancy are mediated by trivialization.