Spoiling the party. Experimental evidence on the willingness to transmit inconvenient ethical information
Jantsje Mol, Ivan Soraperra & Joël van der Weele
April 2024
Tables
Table 1: Descriptive statistics by treatment
df.table1 <- df %>%
mutate(time_in_minutes = time_seconds/60) %>%
mutate(gender_ = case_when(gender == "Non-binary" ~ "Non-binary/not say",
gender == "Rather not say" ~ "Non-binary/not say",
TRUE ~ gender))
table1 <- table1(~ gender_ + age + income + identify_charity +
browser + as.factor(dana_reveal) + as.factor(test_button_click) | treatment, data=df.table1) %>%
as.data.frame()
table1 <- rbind(table1[1:5,], table1[7,], table1[9:15,], table1[17,], table1[20,], table1[25,], table1[28,])
table1 <- rbind(table1[-1,], table1[1,]) # move nr of observations to bottom row
table1 <- table1[,2:5]
p_gender <- round(chisq.test(df.table1$gender_, df.table1$treatment)$p.value,3)
p_age <- round(as.data.frame(summary(aov(age ~ treatment, data = df.table1))[[1]])[1,5],3)
p_income <- round(chisq.test(df.table1$income, df.table1$treatment)$p.value,3)
p_identify <- round(as.data.frame(summary(aov(identify_charity ~ treatment, data = df.table1))[[1]])[1,5],3)
p_browser <- round(chisq.test(df.table1$browser, df.table1$treatment)$p.value,3)
p_dana_reveal <- round(chisq.test(df.table1$dana_reveal, df.table1$treatment)$p.value,3)
p_test_button_click <- round(chisq.test(df.table1$test_button_click, df.table1$treatment)$p.value,3)
p_values <- rbind(p_gender, " ", " ", " ",
p_age, p_income, " ", " ", " ", " ", " ", " ",
p_identify, p_browser, p_dana_reveal, p_test_button_click, " ") %>%
as.data.frame()
names(p_values) <- "p-value"
table1 <- cbind(table1, p_values)
rownames(table1) <- c("Gender (%)",
"Female","Male", "Non-binary/not say",
"Age in years (SD)",
"Monthly income (%)",
"less than 999",
"1000-1999",
"2000-2999",
"3000-3999",
"more than 4000",
"Rather not say",
"Identify with charity (SD)(a)",
"Browser type Desktop (%)",
"Reveal in DWK (%)",
"Press btn in the test round (%)",
"Observations")
kable(table1, format = "html", linesep = "",
caption = "Descriptive statistics by treatment", align = "c",
label = "descriptives") %>%
add_indent(c(2:4, 7:12)) %>%
footnote(general = "The table reports the means for the continuous and the counts for the categorical variables with, respectively, SD and percentages in parentheses. The column p-value reports the results of a test comparing the different treatments. A Chi-squared test is used for categorical variables and an Anova for the continuous variables.") %>%
add_footnote("Response to the question *How much do you identify with the charity Red Cross?* ranging from -5 = not at all to 5 = very much.", notation = "alphabet")| Baseline | Request | Request + Punishment | Overall | p-value | |
|---|---|---|---|---|---|
| Gender (%) | 0.054 | ||||
| Female | 136 (45.0%) | 316 (51.8%) | 323 (53.8%) | 775 (51.3%) | |
| Male | 161 (53.3%) | 291 (47.7%) | 273 (45.5%) | 725 (47.9%) | |
| Non-binary/not say | 5 (1.7%) | 3 (0.5%) | 4 (0.7%) | 12 (0.8%) | |
| Age in years (SD) | 39.5 (12.9) | 39.1 (13.0) | 39.0 (13.0) | 39.1 (13.0) | 0.825 |
| Monthly income (%) | 0.209 | ||||
| less than 999 | 29 (9.6%) | 55 (9.0%) | 47 (7.8%) | 131 (8.7%) | |
| 1000-1999 | 68 (22.5%) | 156 (25.6%) | 130 (21.7%) | 354 (23.4%) | |
| 2000-2999 | 80 (26.5%) | 175 (28.7%) | 162 (27.0%) | 417 (27.6%) | |
| 3000-3999 | 61 (20.2%) | 103 (16.9%) | 123 (20.5%) | 287 (19.0%) | |
| more than 4000 | 51 (16.9%) | 88 (14.4%) | 88 (14.7%) | 227 (15.0%) | |
| Rather not say | 13 (4.3%) | 33 (5.4%) | 50 (8.3%) | 96 (6.3%) | |
| Identify with charity (SD)(a) | 0.185 (2.94) | 0.210 (2.74) | 0.157 (2.80) | 0.184 (2.81) | 0.947 |
| Browser type Desktop (%) | 281 (93.0%) | 566 (92.8%) | 517 (86.2%) | 1364 (90.2%) | 0.001 |
| Reveal in DWK (%) | 119 (39.4%) | 256 (42.0%) | 223 (37.2%) | 598 (39.6%) | 0.232 |
| Press btn in the test round (%) | 292 (96.7%) | 579 (94.9%) | 572 (95.3%) | 1443 (95.4%) | 0.477 |
| Observations | (N=302) | (N=610) | (N=600) | (N=1512) | |
| a Response to the question How much do you identify with the charity Red Cross? ranging from -5 = not at all to 5 = very much. | |||||
| Note: | |||||
| The table reports the means for the continuous and the counts for the categorical variables with, respectively, SD and percentages in parentheses. The column p-value reports the results of a test comparing the different treatments. A Chi-squared test is used for categorical variables and an Anova for the continuous variables. |
Table 3: Ordered probit regressions of Sender-index
df2 <- df %>%
mutate(group = case_when(request == "request_no_info" & treatment == "Request + Punishment" ~ 1,
request == "request_no_info" & treatment == "Request"~ 2,
treatment == "Baseline" ~ 3,
request == "request_info" & treatment == "Request" ~ 4,
request == "request_info" & treatment == "Request + Punishment" ~ 5
),
h2_request_info = case_when(group > 3 ~ 1, TRUE ~ 0),
h2_request_ignorance = case_when(group < 3 ~ 1, TRUE ~ 0),
group = ordered(group, levels = c(1,2,3,4,5), labels = c("Request No Info + Pun", "Request No Info", "Baseline", "Request Info", "Request Info + Pun"))) %>%
group_by(group) %>%
arrange(sender_index,.by_group = TRUE)
oprob4 <- polr(sender_index_f ~ I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) +
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, treatment == "Baseline" | treatment == "Request"), Hess=TRUE, method="probit")
McFadden.oprob4 <- round(pR2(oprob4)["McFadden"],3)
LL.oprob4 <- round(pR2(oprob4)["llh"],1)
# HC robust standard errors (for ordered probit you need CL)
cov_robust4 <- vcovCL(oprob4, type = "HC1") # HC1 reproduces STATA default
robust_se4 <- sqrt(diag(cov_robust4))
# Model with Baseline and Request data + controls IVAN-----------------------------------------------------------------
oprob4a <- polr(sender_index_f ~ I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) +
identify_charity +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, dana_reveal == 0 & treatment !="Request + Punishment"), Hess=TRUE, method="probit")
McFadden.oprob4a <- round(pR2(oprob4a)["McFadden"],3)
LL.oprob4a <- round(pR2(oprob4a)["llh"],1)
# HC robust standard errors (for ordered probit you need CL)
cov_robust4a <- vcovCL(oprob4a, type = "HC1") # HC1 reproduces STATA default
robust_se4a <- sqrt(diag(cov_robust4a))
# Model with Baseline and Request data + controls IVAN-----------------------------------------------------------------
oprob4b <- polr(sender_index_f ~ I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) +
identify_charity +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, dana_reveal == 1 & treatment !="Request + Punishment"), Hess=TRUE, method="probit")
McFadden.oprob4b <- round(pR2(oprob4b)["McFadden"],3)
LL.oprob4b <- round(pR2(oprob4b)["llh"],1)
# HC robust standard errors (for ordered probit you need CL)
cov_robust4b <- vcovCL(oprob4b, type = "HC1") # HC1 reproduces STATA default
robust_se4b <- sqrt(diag(cov_robust4b))
# Model with All data + controls -----------------------------------------------------------------
oprob6 <- polr(sender_index_f ~ I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")) +
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=df2, Hess=TRUE, method="probit")
McFadden.oprob6 <- round(pR2(oprob6)["McFadden"],3)
LL.oprob6 <- round(pR2(oprob6)["llh"],1)
# HC robust standard errors (for ordered probit you need CL)
cov_robust6 <- vcovCL(oprob6, type = "HC1") # HC1 reproduces STATA default
robust_se6 <- sqrt(diag(cov_robust6))
# Model with All data + controls IVAN-----------------------------------------------------------------
oprob6a <- polr(sender_index_f ~ I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")) +
identify_charity +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, dana_reveal == 0), Hess=TRUE, method="probit")
McFadden.oprob6a <- round(pR2(oprob6a)["McFadden"],3)
LL.oprob6a <- round(pR2(oprob6a)["llh"],1)
# HC robust standard errors (for ordered probit you need CL)
cov_robust6a <- vcovCL(oprob6a, type = "HC1") # HC1 reproduces STATA default
robust_se6a <- sqrt(diag(cov_robust6a))
# Model with All data + controls IVAN-----------------------------------------------------------------
oprob6b <- polr(sender_index_f ~ I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")) +
identify_charity +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, dana_reveal == 1), Hess=TRUE, method="probit")
McFadden.oprob6b <- round(pR2(oprob6b)["McFadden"],3)
LL.oprob6b <- round(pR2(oprob6b)["llh"],1)
# HC robust standard errors (for ordered probit you need CL)
cov_robust6b <- vcovCL(oprob6b, type = "HC1") # HC1 reproduces STATA default
robust_se6b <- sqrt(diag(cov_robust6b))regression <- stargazer(oprob4, oprob4a, oprob4b, oprob6,oprob6a, oprob6b,
type = "html",
# report=('vc*p'), # if you want to check the p-values
se = list(robust_se4, robust_se4a, robust_se4b, robust_se6, robust_se6a, robust_se6b),
keep.stat = c("rsq", "n"),
star.cutoffs=c(0.05,0.01,0.001),
star.char = c("*", "**", "***"),
notes.append = FALSE,
omit.stat=c("f"),
font.size = "scriptsize",
table.placement = "H",
label="reg:senders_index_oprobit",
dep.var.caption = "\\textit{Dependent variable}: Sender-index",
dep.var.labels.include = FALSE,
title = "Ordered probit regressions of Sender-index",
ord.intercepts = TRUE,
omit = c("gender_f", "age", "income_c", "browser", "uq_wrong_button"),
order = c(2,3,1,4,5,6),
covariate.labels = c("Information preference - Request info",
" Request ignorance",
" Request info under punishment threat",
" Request ignorance under punishment threat",
"Control variables - Identify with charity",
" Revealed in DWK",
"Cutoff point 1",
"Cutoff point 2",
"Cutoff point 3"),
add.lines = list(c("Log likelihood",
LL.oprob4, LL.oprob4a, LL.oprob4b, LL.oprob6, LL.oprob6a, LL.oprob6b),
c("Pseudo $R^2$ (McFadden)",
McFadden.oprob4, McFadden.oprob4a, McFadden.oprob4b, McFadden.oprob6,
McFadden.oprob6a, McFadden.oprob6b),
c("Covariates", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes"),
c("Revealed in DWK", "", "No", "Yes", "", "No", "Yes")
),
notes.align = "l",
notes = "Ordinal probit model of the Sender-index. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Model 1, 2 and 3 include all participants in the Request treatment. Model 4, 5 and 6 include all participants in the Request and Request + Punishment treatment. Robust standard errors in parentheses.")| Dependent variable: Sender-index | ||||||
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Information preference - Request info | -0.011 | -0.111 | 0.085 | -0.028 | -0.072 | 0.023 |
| (0.092) | (0.121) | (0.148) | (0.082) | (0.107) | (0.132) | |
| Request ignorance | -0.130* | -0.255*** | 0.023 | -0.150*** | -0.232*** | -0.063 |
| (0.053) | (0.065) | (0.101) | (0.035) | (0.041) | (0.072) | |
| Request info under punishment threat | 0.096 | -0.048 | 0.356* | |||
| (0.087) | (0.107) | (0.153) | ||||
| Request ignorance under punishment threat | 0.083 | 0.097 | -0.008 | |||
| (0.053) | (0.072) | (0.083) | ||||
| Control variables - Identify with charity | 0.099*** | 0.123*** | 0.076* | 0.073*** | 0.088*** | 0.055* |
| (0.021) | (0.027) | (0.036) | (0.017) | (0.021) | (0.028) | |
| Revealed in DWK | 0.257* | 0.323*** | ||||
| (0.119) | (0.093) | |||||
| Cutoff point 1 | -0.227*** | -0.113*** | -0.580*** | -0.135*** | -0.153*** | -0.271*** |
| (0.017) | (0.023) | (0.032) | (0.017) | (0.023) | (0.027) | |
| Cutoff point 2 | 0.221*** | 0.362*** | -0.150 | 0.304*** | 0.322*** | 0.119 |
| (0.061) | (0.080) | (0.101) | (0.048) | (0.062) | (0.080) | |
| Cutoff point 3 | 0.714*** | 0.913*** | 0.282* | 0.768*** | 0.816*** | 0.553*** |
| (0.078) | (0.105) | (0.123) | (0.060) | (0.079) | (0.097) | |
| Log likelihood | -522 | -312.5 | -203.6 | -842.8 | -523.1 | -311.9 |
| Pseudo R(McFadden) | 0.038 | 0.048 | 0.028 | 0.029 | 0.028 | 0.026 |
| Covariates | Yes | Yes | Yes | Yes | Yes | Yes |
| Revealed in DWK | No | Yes | No | Yes | ||
| Observations | 412 | 244 | 168 | 667 | 402 | 265 |
| Note: | Ordinal probit model of the Sender-index. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Model 1, 2 and 3 include all participants in the Request treatment. Model 4, 5 and 6 include all participants in the Request and Request + Punishment treatment. Robust standard errors in parentheses. | |||||
Figures
Figure 3: Percentage of Senders by sender-index in the Baseline treatment
library(cowplot) # for plot_grid
df.switching <- df %>%
filter(!is.na(sender_index)) %>%
filter(button_role == "Sender") %>%
select(starts_with("message_minus"), pp_id, sender_index) %>%
mutate(message_minus0.5 = case_when(message_minus0.5 == "True" ~ 1, message_minus0.5 == "False" ~ 0),
message_minus1.0 = case_when(message_minus1.0 == "True" ~ 1, message_minus1.0 == "False" ~ 0),
message_minus2.5 = case_when(message_minus2.5 == "True" ~ 1, message_minus2.5 == "False" ~ 0),
switching = paste0(message_minus2.5, message_minus1.0, message_minus0.5),
) %>%
pivot_longer(starts_with("message_"),
names_sep = "_", names_to = c("variable", "message"), values_to = "value") %>%
mutate(message = case_when(message == "minus2.5" ~ "-2.5",
message == "minus1.0" ~ "-1.0",
message == "minus0.5" ~ "-0.5"),
message = factor(message, levels = c("-0.5", "-1.0", "-2.5")))
df.switching.sum <- df.switching %>%
select(pp_id, switching) %>%
distinct(.keep_all = TRUE) %>%
group_by(switching) %>%
tally() %>%
mutate(pct = n / sum(n),
pct_label =scales::percent(n / sum(n), accuracy = 0.1, trim = FALSE))
top.fig <- ggplot(df.switching.sum, aes(c(1,1,1,1), pct, fill = switching)) +
geom_col(width = 0.6, col = "black") +
labs(fill = "", y = "% of Senders", x = "") +
theme_ridges(center_axis_labels = TRUE) +
theme(legend.position = "none", axis.text.x = element_blank(), strip.text.x = element_blank()) +
geom_text(aes(label = pct_label), vjust = -0.5, nudge_x = 0) +
facet_wrap(~switching, nrow = 1, strip.position = "bottom") +
scale_fill_manual(values = c("#fef0d9", "#fdcc8a", "#fc8d59", "#d7301f")) +
scale_y_continuous(breaks = c(seq(0,1, by = 0.1)), limits=c(0,0.5), labels = c(seq(0,1, by = 0.1))*100)
bottom.fig <- ggplot(df.switching, aes(message, value, group = 1)) +
geom_line(size=1) + geom_point() +
facet_wrap(~switching, nrow = 1, strip.position = "bottom",
labeller = labeller(switching =
c("000" = "\n0",
"100" = "\n1",
"110" = "\n2",
"111" = "\n3"))) +
labs(y = "Choice", x = "\nSender-index") +
scale_y_continuous(breaks = c(seq(0,1, by = 1)), limits=c(0,1), labels = c("hide", "share")) +
theme_ridges(center_axis_labels = TRUE) +
theme(legend.position = "none",
strip.background = element_blank(),
strip.placement = "outside",
axis.text.x = element_text(size= 8)
)
plot_grid(top.fig, bottom.fig, ncol=1, align = "v", rel_heights = c(3, 2.2))
Figure 4: Percentage of Senders by sender-index and treatment
h4 <- df %>%
filter(button_role == "Sender") %>%
mutate(consequence = paste0(substr(consequence, 0,1), substr(consequence, 3,6)),
consequence = as.numeric(consequence),
group_h4 = case_when(treatment == "Request + Punishment" & request == "request_info" ~ "Punishment\n Information\n requested",
treatment == "Request" & request == "request_info" ~ "Request\n Information\n requested",
treatment == "Request + Punishment" & request == "request_no_info" ~ "Punishment\n Ignorance\n requested",
treatment == "Request" & request == "request_no_info" ~ "Request\n Ignorance\n requested",
treatment == "Baseline" ~ "Baseline"),
group_h4 = ordered(group_h4, levels=c("Punishment\n Ignorance\n requested",
"Request\n Ignorance\n requested",
"Baseline",
"Request\n Information\n requested",
"Punishment\n Information\n requested")),
dummy_req = case_when(request == "request_info" ~ 1, TRUE ~ 0),
dummy_pun = case_when(treatment == "Request + Punishment" ~ 1, TRUE ~ 0))
five_bars <- h4 %>%
filter(!is.na(sender_index)) %>%
select(sender_index, group_h4) %>%
group_by(group_h4, sender_index) %>%
tally() %>%
mutate(pct = n / sum(n),
pct_label =scales::percent(n / sum(n), accuracy = 0.1, trim = FALSE),
pct_label_plus_n = paste0(pct_label, " (n = ", n, ")")) %>%
mutate(sender_index_f = as.factor(sender_index))
ggplot(five_bars, aes(y=pct, x = sender_index, fill = sender_index_f)) +
geom_bar(stat="identity", position = position_dodge(),color="black") +
scale_y_continuous(labels = scales::percent_format(accuracy = 1L)) +
labs(y = "% of Senders", fill = "", x = "\nSender-index"
# , title = "Percentage of Senders by sender-index, treatment and request"
) +
theme_bw() + theme(legend.position = "none") + facet_wrap(~group_h4, nrow = 1) +
scale_fill_manual(values = c("#fef0d9", "#fdcc8a", "#fc8d59", "#d7301f")) 
Figure 5: Self-reported motivations to send, by sender-index
ra <- read.xlsx(here('input', "ra_coding_agreed_coded.xlsx"), 1) %>%
select(pp_id, send_motivation1_cat1, second.motivation) %>%
rename(send_motivation1_cat = send_motivation1_cat1,
send_motivation1_cat2 = second.motivation) %>%
mutate(send_motivation1_cat = case_when(send_motivation1_cat == "procedural " ~ "procedural",
send_motivation1_cat == "help the other player to be selfish " ~ "help the other player to be selfish",
send_motivation1_cat == "unconditional charity help " ~ "unconditional charity help",
send_motivation1_cat == "outcome-based" ~ "conditional charity help",
TRUE ~ send_motivation1_cat),
# merged conditional charity help and outcome-based, as they are the same
send_motivation1_cat2 = case_when(send_motivation1_cat2 == "outcome-based" ~ "conditional charity help",
TRUE ~ send_motivation1_cat2),
send_motivation1_cat = ordered(send_motivation1_cat, levels = rev(c("unconditional charity help","conditional charity help",
"procedural", "requested", "no explanation", "help the other player to be selfish",
"help all parties", "other"))))
ra2 <- read.xlsx(here('input', "ra_coding_agreed_coded2.xlsx"), 1) %>%
select(pp_id, send_motivation1_cat1, send_motivation1_cat1_secondmotivation) %>%
rename(send_motivation2_cat = send_motivation1_cat1,
send_motivation2_cat2 = send_motivation1_cat1_secondmotivation)
df <- merge(df, ra, by = "pp_id", all.x = T)
df <- merge(df, ra2, by = "pp_id", all.x = T)
rm(ra, ra2)
df5 <- df %>%
mutate(send_motivation1_cat_ = case_when(send_motivation1_cat == "help all parties" ~ "other",
send_motivation1_cat == "help the other player to be selfish" ~ "other",
TRUE ~ as.character(send_motivation1_cat)),
send_motivation1_cat_ = ordered(send_motivation1_cat, levels = c("unconditional charity help",
"conditional charity help",
"procedural",
"requested",
"other")))
strategies <- df5 %>%
filter(button_role == "Sender" & sender_index > 0
& !is.na(send_motivation1_cat_)) %>%
select(send_motivation1_cat_, sender_index) %>%
group_by(send_motivation1_cat_, sender_index) %>%
tally() %>%
# complete(send_motivation1_cat_, fill = list(n = 0)) %>%
# ungroup() %>%
group_by(sender_index) %>%
mutate(pct_strategy = prop.table(n))
ggplot(data = strategies, aes(x=sender_index, y = pct_strategy, fill = send_motivation1_cat_)) +
geom_bar(stat = "identity")+
labs(x = "Sender-index", y = "", fill = "") +
theme_bw() +
scale_y_continuous(labels = scales::percent)
Figure 6: Consequence for the Charity. Average transfer of the Receiver
# bar graph means and se
df1 <- df %>%
filter(button_role == "Sender") %>%
mutate( consequence = paste0(substr(consequence, 0,1), substr(consequence, 3,6)),
consequence = as.numeric(consequence)) %>%
select(group_id,consequence)
df2 <- df %>%
filter(button_role == "Receiver") %>%
select(-consequence)
df2 <- left_join(df2, df1, by = "group_id") %>%
mutate( charity_outcome = consequence*button_click,
group_5 = case_when(treatment == "Request + Punishment" & request == "request_info" ~ "Req. + Pun.\nInformation\nrequested",
treatment == "Request" & request == "request_info" ~ "Request\nInformation\nrequested",
treatment == "Request + Punishment" & request == "request_no_info" ~ "Req. + Pun.\nIgnorance\nrequested",
treatment == "Request" & request == "request_no_info" ~ "Request\nIgnorance\nrequested",
treatment == "Baseline" ~ "Baseline"),
group_5 = ordered(group_5, levels=c("Baseline",
"Request\nInformation\nrequested",
"Request\nIgnorance\nrequested",
"Req. + Pun.\nInformation\nrequested",
"Req. + Pun.\nIgnorance\nrequested"
)),
treatment = ordered(treatment, levels=c("Baseline",
"Request",
"Request + Punishment")))
df2_for_appendix <- df2
bar1 <- df2 %>%
group_by(treatment) %>%
summarise(
n=n(),
mean=mean(charity_outcome),
sd=sd(charity_outcome)
) %>%
mutate( se=sd/sqrt(n)) %>%
ggplot(aes(x=treatment, y = mean)) + geom_point(aes(colour=treatment, fill=treatment),pch=c(21,22,23),size=4) +
geom_errorbar(aes(ymin = mean - se, ymax = mean + se,colour=treatment),width=0.2,lwd=0.7) +
labs(x="", y = "Average earnings for charity \n") +
scale_y_continuous(limits = c(-1, -0.3)) + labs(y = "Consequences for the Red Cross (in Pounds)\n", fill = "", x = "\nTreatment") +
scale_x_discrete(labels = c("Baseline", "Request", "Req. +\nPun.")) +
theme_bw() + theme(legend.position = "none") +
scale_fill_manual(values = c("#fdcc8a", "#fc8d59", "#d7301f")) +
scale_colour_manual(values = c("#fdcc8a", "#fc8d59", "#d7301f"))
# bar graph means
bar2 <- df2 %>%
group_by(group_5) %>%
summarise(
n=n(),
mean=mean(charity_outcome),
sd=sd(charity_outcome),
treatment = unique(treatment)
) %>%
mutate( se=sd/sqrt(n)) %>%
ggplot(aes(x=group_5, y = mean)) + geom_point(aes(colour=treatment,fill=treatment),pch=c(19,24,25,24,25),size=4) +
geom_errorbar(aes(ymin = mean - se, ymax = mean + se,colour=treatment),width=0.2,lwd=0.7) + scale_y_continuous(limits = c(-1, -0.3)) +
labs(y = "", fill = "", x = "\nTreatment and request") +
theme_bw() + theme(legend.position = "none", axis.text.y = element_blank(), strip.text.y = element_blank()) +
scale_fill_manual(values = c("#fdcc8a", "#fc8d59", "#d7301f")) +
scale_colour_manual(values = c("#fdcc8a", "#fc8d59", "#d7301f"))
plot_grid(bar1, bar2, ncol=2, align = "h", rel_widths = c(1, 2))
In-text statistics and footnotes
3.1 Preliminaries
click_pct <-round(addmargins(table(df$button_click))["1"]/addmargins(table(df$button_role))["Receiver"]*100,1)
# to get the n of people who received each message:
# table(subset(df, button_role == "Receiver")$message)
df.buttonclicks <- df %>%
select(button_click, message, button_role) %>%
filter(button_role == "Receiver") %>%
mutate(message = ordered(message, levels = c("-2.50", "-1.00", "-0.50", "+0.50", "no message"),
labels = c("-2.50 \n (n=112)", "-1.00 \n (n=112)", "-0.50 \n (n=107)", "+0.50 \n (n=61)", "??? \n (n=364)"))) %>%
group_by(message, button_click) %>%
tally() %>%
mutate(pct = n / sum(n), # n gives the number of people who clicked
pct_label =scales::percent(n / sum(n), accuracy = 0.1, trim = FALSE),
pct_label_plus_n = paste0(pct_label, " (n = ", n, ")")) %>%
filter(button_click == 1)Indeed, almost all Receivers press the button when uninformed (96.4%%; n = 364) across all treatments. Moreover, all 61 Receivers that saw good news — i.e.,saw that the button increased the donation by an additional £0.5 — pressed the button. Finally, we observed that the likelihood of pressing the button decreases with the severity of the negative consequence for the charity: 73.8%% (n = 107) of the informed Receivers clicked the button when the consequences were -0.5 pounds, 66.1%% (n = 112) when they were -1.0 pounds, and 51.8%% (n = 112) when they were -2.5 pounds.
uninf_pct <- round(mean(df$belief_uninformed, na.rm = T),1)
uninf_sd <- round(sd(df$belief_uninformed, na.rm = T),1)On average, Senders believe that 80% (SD = 18.1) of the Receivers press the button when not informed about the consequences. ### 3.2 Information Sharing in the Baseline Treatment
df.messages <- df %>%
filter(button_role == "Sender") %>%
select(starts_with("message_")) %>%
pivot_longer(everything(),names_sep = "_", names_to = c("variable", "message"), values_to = "value") %>%
mutate(message = case_when(message == "plus0.5" ~ "+0.5",
message == "minus2.5" ~ "-2.5",
message == "minus1.0" ~ "-1.0",
message == "minus0.5" ~ "-0.5"),
message = factor(message, levels = rev(c("+0.5", "-0.5", "-1.0", "-2.5")))) %>%
group_by(message, value) %>%
tally() %>%
mutate(pct = n / sum(n),
pct_label =scales::percent(n / sum(n), accuracy = 0.1, trim = FALSE)) %>%
filter(value == "True")A positive consequence of £0.5 is shared by 38.6%% of Senders. Negative consequences of -0.5, -1.0 and -2.5 pounds are shared by 44.6%%, 58.3%%and 71.8%% of Senders, respectively.
invalid_num <- df %>%
filter(button_role == "Sender" & is.na(sender_index)) %>%
tally()Note that the index is not well-defined if a Sender decides to share information for less serious consequences and not to share information for more serious ones. Empirically, this is the case for only 40 out of 756 Senders which, following the preregistration protocol, are excluded from the main analysis.
sender_index0 <- round(table(subset(df, button_role == "Sender")$sender_index)["0"]/table(df$button_role)["Sender"]*100,0)
sender_index3 <- round(table(subset(df, button_role == "Sender")$sender_index)["3"]/table(df$button_role)["Sender"]*100,0)On the one hand, one forth (24of the Senders never share information with the Receiver (sender-index = 0), another 40% of Senders always share information about the consequences (sender-index = 3).
3.3 The Effect of Requests
df2 <- df %>%
mutate(group = case_when(request == "request_no_info" & treatment == "Request + Punishment" ~ 1,
request == "request_no_info" & treatment == "Request"~ 2,
treatment == "Baseline" ~ 3,
request == "request_info" & treatment == "Request" ~ 4,
request == "request_info" & treatment == "Request + Punishment" ~ 5
),
h2_request_info = case_when(group > 3 ~ 1, TRUE ~ 0),
h2_request_ignorance = case_when(group < 3 ~ 1, TRUE ~ 0),
group = ordered(group, levels = c(1,2,3,4,5), labels = c("Request No Info + Pun", "Request No Info", "Baseline", "Request Info", "Request Info + Pun"))) %>%
group_by(group) %>%
arrange(sender_index,.by_group = TRUE)
h2_trend <- df2 %>%
filter(button_role == "Sender") %>%
select(sender_index, group, treatment) %>%
filter(treatment == "Baseline" | treatment == "Request")
# https://www.rdocumentation.org/packages/PMCMRplus/versions/1.9.6/topics/jonckheereTest
jt <- jonckheereTest(h2_trend$sender_index, h2_trend$group, alternative = c("greater"), nperm=NULL)
# sender-index averages
sender_index_average <- df %>%
filter((treatment == "Baseline" | treatment == "Request") & !is.na(sender_index)) %>%
select(request, sender_index, treatment) %>%
group_by(request, treatment) %>%
summarise(average = mean(sender_index))
# even more strict comparison: a chi-square test
footnote6_chi <- chisq.test(table(h2_trend$sender_index, h2_trend$group,exclude = c("Request No Info + Pun","Request Info + Pun",NA)))
# percentages request
request <- df %>%
filter(treatment == "Request" & button_role == "Sender") %>%
group_by(request) %>%
tally() %>%
mutate(pct = round(n / sum(n) * 100, 1))Indeed, a non-parametric Jonckheere-Terpstra trend test fails to reject the hypothesis of no difference in the sender-index across different requests (z = 0.31, p = 0.377).
The average sender-index gives a similar picture, with an average of 1.73 when information is requested, of 1.65 when ignorance is requested, and of 1.71 when the request was not present.
Footnote 6 Also testing the more general assumption of a difference across distributions does not support the idea that the request has an effect on the decision to share information. A \(\chi^2\) test cannot reject the null hypothesis of no differences in the distribution of the sender index (\(\chi^2\)(6) = 2.38, p = 0.882)
A majority of Senders (225; 73.8%) received a Request for information,while the rest (80; 26.2%) received a request for ignorance.
3.4 The Role of Punishment
# descriptives about requests and punishment
request_pun <- df %>%
filter(treatment == "Request + Punishment" & button_role == "Sender") %>%
group_by(request) %>%
tally() %>%
mutate(pct = round(n / sum(n) * 100, 1))
pun_pct <- round(prop.table(table((df$punishment)))["1"] * 100, 1)
follow_request <- df %>%
filter(treatment == "Request + Punishment" & button_role == "Sender") %>%
select(punished, selected_message, request) %>%
mutate(message_informative = case_when(selected_message == "no message" ~ "No \nmessage", TRUE ~ "Informative \nmessage"),
punished_f = as.factor(case_when(punished == 0 ~ "No", TRUE ~ "Yes"))) %>%
group_by(message_informative, request) %>%
tally()
punishment <- df %>%
filter(treatment == "Request + Punishment" & button_role == "Sender") %>%
select(punished, selected_message, request) %>%
mutate(message_informative = case_when(selected_message == "no message" ~ "No \nmessage", TRUE ~ "Informative \nmessage"),
punished_f = as.factor(case_when(punished == 0 ~ "No", TRUE ~ "Yes"))) %>%
group_by(message_informative, request, punished_f) %>%
tally() %>%
complete(punished_f, fill = list(n = 0)) %>%
mutate(pct_punished = prop.table(n)) %>%
filter(punished_f == "Yes")Footnote 7 The distribution of requests observed in the punishment treatment is similar to the one observed in the treatment without punishment. In Request + Punishment treatment, 206 Senders (68.7%) received a request for information and 94 (31.3%) received a request for ignorance. 52 (17.3%) of the 300 Receivers punished the Sender for (not) responding to their request.
Information requests were followed by 113 Senders and ignored by 93 Senders, of which 30 were punished (32.3%). Conversely 48 Senders sent information when ignorance was requested, but only 7 of those were punished (14.6%). In a few cases, Receivers were punished when following the request for information (6 cases) or ignorance (9 cases).
# non-parametric Request Info Punishment > Request info
h3_request_info <- df %>%
filter(treatment == "Request" | treatment == "Request + Punishment",
request == "request_info",
button_role == "Sender") %>%
select(treatment, request, sender_index)
test_info <- wilcox.test(h3_request_info$sender_index ~ h3_request_info$treatment, alternative = "less")
# non-parametric Request Ignorance Punishment < Request Ignorance
h3_request_ignorance <- df %>%
filter(treatment == "Request" | treatment == "Request + Punishment",
request == "request_no_info",
button_role == "Sender") %>%
select(treatment, request, sender_index)
test_no_info <- wilcox.test(h3_request_ignorance$sender_index ~ h3_request_ignorance$treatment, alternative = "greater") Indeed, a one-sided Wilcoxon rank-sum test fails to reject the null hypothesis that punishment has no effect on the sender-index both when ignorance is requested (p = 0.865) and when information is requested (p = 0.164).
h3_trend <- df2 %>%
filter(button_role == "Sender") %>%
select(sender_index, group, treatment)
footnote8_jt <- jonckheereTest(h3_trend$sender_index, h3_trend$group, alternative = c("greater"), nperm=NULL)
footnote8_chisq <- chisq.test(table(h3_trend$sender_index, h3_trend$group,exclude = c(NA)))Footnote 8 A Jonckheere-Terpstra trend test using all 5 combinations of treatments and requests does not reject the null hypothesis that the sender-index is not increasing in the pressure to follow the request (z = 0.38, p = 0.352). Similarly, a \(\chi^2\) test cannot reject the null hypothesis of no differences in the distributions of the sender-index across all 5 combinations of requests and treatments (\(\chi^2\) (12) = 7.58, p = 0.817).
3.5 Motives for sharing information
# motives for sharing
share_positive_pct <- df %>%
filter(button_role == "Sender") %>%
group_by(message_plus0.5) %>%
tally() %>%
mutate(pct = round(prop.table(n) *100,1))
df.motivations <- df %>%
filter(button_role == "Sender" & sender_index >0 & !is.na(send_motivation1_cat)) %>%
select(send_motivation1_cat, sender_index) %>%
group_by(send_motivation1_cat) %>%
tally() %>%
mutate(pct = n / sum(n),
pct_label =scales::percent(n / sum(n), accuracy = 0.1, trim = FALSE),
pct_label_plus_n = paste0(pct_label, " (n = ", n, ")")) Indeed, the questionnaire reveals that the main motivations to send are a wish to help the charity either unconditionally (30.3%% “I wanted Red Cross to get as much money as possible”), or conditional on the impact not being too negative (30.1%% “when the consequence was too large”).
For instance, 38.6% of Senders share even when the externality is positive, and information does not change the Receiver’s decision. Indeed, we find that a large number of Senders mention such procedural concerns (28.8%% “it is the right thing to do”), Indeed, a few Senders mention helping the other player explicitly in the questionnaire ( 1.3%% “probably they would be happy to be informed, instead of feeling bad”). At the same time, some Senders appear to be doing the opposite, and use information as a way to make Receivers feel bad about pressing the button ( 0.4%% “to make them feel guilty”)
# motives for not sharing
strategies_notsend <- df %>%
filter(button_role == "Sender" #& sender_index > 0
& !is.na(send_motivation2_cat)) %>%
select(send_motivation2_cat, sender_index) %>%
mutate(send_motivation2_cat = case_when(send_motivation2_cat == "no explanation" ~ "other",
send_motivation2_cat == "other" ~ "other",
TRUE ~ as.character(send_motivation2_cat))) %>%
group_by(send_motivation2_cat, sender_index) %>%
tally() %>%
# complete(send_motivation2_cat, fill = list(n = 0)) %>% # only necessary if a category is empty
# ungroup() %>%
group_by(sender_index) %>%
mutate(pct_strategy = round(prop.table(n) *100,1))
strategies_notsend1 <- strategies_notsend %>% mutate(sender_index = 1, n = 0, pct_strategy = 0)
strategies_notsend2 <- strategies_notsend %>% mutate(sender_index = 2, n = 0, pct_strategy = 0)
strategies_notsend3 <- strategies_notsend %>% mutate(sender_index = 3, n = 0, pct_strategy = 0)
strategies_notsend <- rbind(strategies_notsend, strategies_notsend1, strategies_notsend2, strategies_notsend3) %>%
mutate(send_motivation2_cat = ordered(send_motivation2_cat, levels = c("own interest",
"help the other player to be selfish",
"indifference",
"procedural",
"requested",
"other"),
labels = c("own interest",
"help the other player to be\n selfish",
"indifference",
"procedural",
"requested",
"other")))Furthermore, we asked the 156 respondents with a sender-index of 0 why they did not send at all. Their main motivations are a request for ignorance (30.1%) and the cost of sending (29.5%, ‘I wanted to maximise my return’), followed by procedural motivations (14.7%, to see what they would do’) and indifference (14.1%, the other person would be just as likely to press the button’). Nine participants (5.8%) indicated that they wanted to help the other person to be selfish, and another 5.8% indicated various other reasons.
3.6 Consequences for the charity
df1 <- df %>%
filter(button_role == "Sender") %>%
mutate( consequence = paste0(substr(consequence, 0,1), substr(consequence, 3,6)),
consequence = as.numeric(consequence)) %>%
select(group_id,consequence)
df2 <- df %>%
filter(button_role == "Receiver") %>%
select(-consequence)
df2 <- left_join(df2, df1, by = "group_id") %>%
mutate( charity_outcome = consequence*button_click,
group_5 = case_when(treatment == "Request + Punishment" & request == "request_info" ~ "Req. + Pun.\nInformation\nrequested",
treatment == "Request" & request == "request_info" ~ "Request\nInformation\nrequested",
treatment == "Request + Punishment" & request == "request_no_info" ~ "Req. + Pun.\nIgnorance\nrequested",
treatment == "Request" & request == "request_no_info" ~ "Request\nIgnorance\nrequested",
treatment == "Baseline" ~ "Baseline"),
group_5 = ordered(group_5, levels=c("Req. + Pun.\nIgnorance\nrequested",
"Request\nIgnorance\nrequested",
"Baseline",
"Request\nInformation\nrequested",
"Req. + Pun.\nInformation\nrequested"))
)
rm(df1)
# Different outcomes by tmt
payoff_charity_model <- lm(df2$charity_outcome~df2$treatment)
payoff_charity <- summary(payoff_charity_model)
footnote9 <- chisq.test(table(df2$charity_outcome,df2$treatment))
overall_p <- function(my_model) {
f <- summary(my_model)$fstatistic
p <- pf(f[1],f[2],f[3],lower.tail=F)
attributes(p) <- NULL
return(p)
}
payoff_charity_p <- round(overall_p(payoff_charity_model),3)The results show no difference in the average payoff of the Red Cross, and therefore we cannot reject the null hypothesis that the aggregated outcome is the same across the three treatments (F(2,753) = 0.87, p = 0.419)
Footnote 9 Comparing the distribution of payoffs leads to the same conclusion (\(\chi^2\)(8) = 4.55, p = 0.804).
# # Different outcomes by tmt and request
payoff_charity5_model <- lm(df2$charity_outcome~relevel(factor(df2$group_5,ordered=F),ref="Baseline"))
payoff_charity5 <- summary(payoff_charity5_model)
footnote10 <- chisq.test(table(df2$charity_outcome,df2$group_5))
payoff_charity5_p <- round(overall_p(payoff_charity5_model),3)However, a Wald test comparing the means across the five groups gives a non-significant result (F(4,751) = 1.7, p = 0.148).
Footnote 10 Comparing the distributions, instead, shows a significant difference in the outcomes for the charity (\(\chi^2\)(16) = 34.13, p = 0.005), but this test is not the most suitable as some cells have less than 5 observations.
Appendix
Figure A1: Percentage of Senders by switching structure
weird <- df %>%
filter(button_role == "Sender") %>%
select(starts_with("message_"), -message_sent_selected, pp_id) %>%
mutate(message_minus0.5 = case_when(message_minus0.5 == "True" ~ 1, message_minus0.5 == "False" ~ 0),
message_minus1.0 = case_when(message_minus1.0 == "True" ~ 1, message_minus1.0 == "False" ~ 0),
message_minus2.5 = case_when(message_minus2.5 == "True" ~ 1, message_minus2.5 == "False" ~ 0),
message_plus0.5 = case_when(message_plus0.5 == "True" ~ 1, message_plus0.5 == "False" ~ 0),
index = paste0(message_minus2.5, message_minus1.0, message_minus0.5, message_plus0.5)) %>%
pivot_longer(starts_with("message_"),
names_sep = "_", names_to = c("variable", "message"), values_to = "value") %>%
mutate(message = case_when(message == "minus2.5" ~ "-2.5",
message == "minus1.0" ~ "-1.0",
message == "minus0.5" ~ "-0.5",
message == "plus0.5" ~ "+0.5"),
message = factor(message, levels = c("+0.5", "-0.5", "-1.0", "-2.5")))
weird.sum <- weird %>%
select(index, pp_id) %>%
group_by(index, pp_id) %>%
distinct() %>%
group_by(index) %>%
tally() %>%
mutate(pct = n / sum(n),
pct_label =scales::percent(n / sum(n), accuracy = 0.1, trim = FALSE),
valid = case_when(index == "0000" ~ "0",
index == "0001" ~ "0",
index == "1001" ~ "1",
index == "1000" ~ "1",
index == "1100" ~ "2",
index == "1101" ~ "2",
index == "1110" ~ "3",
index == "1111" ~ "3",
TRUE ~ "invalid"),
index = rev(index))
right.fig <- ggplot(weird.sum, aes(index, pct, fill = valid)) +
geom_col(width = 0.7) +
labs(fill = "Sender-index", x = "", y = "") +
theme_ridges(center_axis_labels = TRUE) +
theme(legend.position = "right",
legend.title = element_text(size=11),
legend.text = element_text(size=9),
axis.text.y = element_blank(),
axis.text.x = element_blank(),
axis.title.x = element_text(color="white")) +
geom_text(aes(label = pct_label), hjust = -0.5, nudge_y = 0) +
scale_y_continuous(breaks = c(seq(0,1, by = 0.1)), limits=c(0,0.35)) + coord_flip() +
scale_fill_manual(values = c("#fef0d9", "#fdcc8a", "#fc8d59", "#d7301f", "grey"))
left.fig <- ggplot(weird, aes(message, value, group = 1)) +
geom_line(size=1) + geom_point() +
facet_wrap(~index, ncol = 1, strip.position = "left") +
labs(y = "", x = "") +
scale_y_continuous(breaks = c(seq(0,1, by = 1)), limits=c(0,1), labels = c("hide", "share")) +
theme_ridges(center_axis_labels = TRUE) + theme(legend.position = "none",
strip.background = element_blank(),
strip.placement = "outside",
strip.text = element_blank(),
axis.text.x = element_text(size=7),
axis.text.y = element_text(size=5))
grid.arrange(left.fig, right.fig, ncol = 2, widths = c(2,5))
Table B1: OLS regressions of Sender-index
############################ Table B1 (= Table 3 as OLS) for Robustness checks (as preregistered)
############################
df2 <- df %>%
mutate(group = case_when(request == "request_no_info" & treatment == "Request + Punishment" ~ 1,
request == "request_no_info" & treatment == "Request"~ 2,
treatment == "Baseline" ~ 3,
request == "request_info" & treatment == "Request" ~ 4,
request == "request_info" & treatment == "Request + Punishment" ~ 5
),
h2_request_info = case_when(group > 3 ~ 1, TRUE ~ 0),
h2_request_ignorance = case_when(group < 3 ~ 1, TRUE ~ 0),
group = ordered(group, levels = c(1,2,3,4,5), labels = c("Request No Info + Pun", "Request No Info", "Baseline", "Request Info", "Request Info + Pun"))) %>%
group_by(group) %>%
arrange(sender_index,.by_group = TRUE)
# Baseline data model 2 -----------------------------------------------------------------
m1 <- lm(sender_index ~
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, treatment == "Baseline"))
# Model with Baseline and Request data -----------------------------------------------------------------
m2 <- lm(sender_index ~ I(h2_request_info*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request")),
data=subset(df2, treatment == "Baseline" | treatment == "Request"))
# Model with Baseline and Request data + controls -----------------------------------------------------------------
m3 <- lm(sender_index ~ I(h2_request_info*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request")) +
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, treatment == "Baseline" | treatment == "Request"))
# Model with All data -----------------------------------------------------------------
m4 <- lm(sender_index ~ I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")),
data=df2)
# Model with All data + controls -----------------------------------------------------------------
m5 <- lm(sender_index ~I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")) +
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=df2) stargazer(m1, m2, m3, m4, m5,
type = 'html',
keep.stat = c("rsq", "n"),
star.cutoffs=c(0.1,0.05,0.01,0.001),
star.char = c("\\circ", "*", "**", "***"),
notes.append = FALSE,
omit.stat=c("f"),
font.size = "scriptsize",
table.placement = "H",
label="reg:senders_index_ols",
intercept.bottom = FALSE,
dep.var.caption = "\\textit{Dependent variable}: Sender-index",
dep.var.labels.include = FALSE,
title = "OLS regressions of Sender-index",
order = c(1,10,11,9,12,2:8,13:15),
omit = c("gender_f", "age", "income_c", "browser", "uq_wrong_button"),
covariate.labels = c("Constant",
"**Information preference** Request Info",
" Request Ignorance",
" Request Info under punishment threat",
" Request Ignorance under punishment threat",
"**Control variables** Identify with charity",
" Revealed in DWK"),
notes.align = "l",
notes = "OLS model of the Sender-index. Model 1 includes observations in the Baseline treatment. Models 2 and 3 include observations in the Baseline and Request treatments. Models 4 and 5 include all observations. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Robust standard errors in parentheses.")| Dependent variable: Sender-index | |||||
| (1) | (2) | (3) | (4) | (5) | |
| Constant | 1.252** | 1.714*** | 1.225*** | 1.714*** | 1.164*** |
| (0.395) | (0.102) | (0.248) | (0.103) | (0.209) | |
| Information preference Request Info | 0.015 | -0.010 | 0.015 | -0.030 | |
| (0.133) | (0.133) | (0.133) | (0.133) | ||
| Request Ignorance | -0.065 | -0.166 | -0.065 | -0.190 | |
| (0.175) | (0.176) | (0.175) | (0.176) | ||
| Request Info under punishment threat | 0.122 | 0.086 | |||
| (0.137) | (0.140) | ||||
| Request Ignorance under punishment threat | 0.162 | 0.076 | |||
| (0.167) | (0.169) | ||||
| Control variables Identify with charity | 0.104** | 0.105*** | 0.079*** | ||
| (0.036) | (0.021) | (0.017) | |||
| Revealed in DWK | 0.162 | 0.251* | 0.330*** | ||
| (0.215) | (0.124) | (0.097) | |||
| Observations | 140 | 438 | 412 | 716 | 667 |
| R2 | 0.129 | 0.001 | 0.099 | 0.003 | 0.074 |
| Note: | OLS model of the Sender-index. Model 1 includes observations in the Baseline treatment. Models 2 and 3 include observations in the Baseline and Request treatments. Models 4 and 5 include all observations. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Robust standard errors in parentheses. | ||||
Table B2: Tobit regressions of Sender-index
# following https://rdrr.io/cran/AER/man/tobit.html
# Baseline data model 2 -----------------------------------------------------------------
m1 <- tobit(sender_index ~ identify_charity + dana_reveal + gender_f + age + income_c + I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, treatment == "Baseline"), left=0)
# Model with Baseline and Request data -----------------------------------------------------------------
m2 <- tobit(sender_index ~ I(h2_request_info*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request")),
data=subset(df2, treatment == "Baseline" | treatment == "Request"), left=0)
# Model with Baseline and Request data + controls -----------------------------------------------------------------
m3 <- tobit(sender_index ~ I(h2_request_info*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request")) +
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, treatment == "Baseline" | treatment == "Request"), left=0)
# Model with All data -----------------------------------------------------------------
m4 <- tobit(sender_index ~ I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")),
data=df2, left=0)
# Model with All data + controls -----------------------------------------------------------------
m5 <- tobit(sender_index ~I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")) +
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=df2, left=0)stargazer(m1, m2, m3, m4, m5, type = 'html',
keep.stat = c("rsq", "n"),
star.cutoffs=c(0.1,0.05,0.01,0.001),
star.char = c("\\circ", "*", "**", "***"),
notes.append = FALSE,
omit.stat=c("f"),
font.size = "scriptsize",
table.placement = "H",
label="reg:senders_index_tobit",
intercept.bottom = FALSE,
dep.var.caption = "\\textit{Dependent variable}: Sender-index",
dep.var.labels.include = FALSE,
title = "Tobit regressions of Sender-index",
order = c(1,10,11,9,12,2:8,13:15),
omit = c("gender_f", "age", "income_c", "browser", "uq_wrong_button"),
covariate.labels = c("Constant",
"**Information preference** Request Info",
" Request Ignorance",
" Request Info under punishment threat",
" Request Ignorance under punishment threat",
"**Control variables** Identify with charity",
" Revealed in DWK"),
notes.align = "l",
notes = "Tobit model of the Sender-index (left = 0). Model 1 includes observations in the Baseline treatment. Models 2 and 3 include observations in the Baseline and Request treatments. Models 4 and 5 include all observations. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Robust standard errors in parentheses.")| Dependent variable: Sender-index | |||||
| (1) | (2) | (3) | (4) | (5) | |
| Constant | 0.846 | 1.480*** | 0.842* | 1.483*** | 0.771** |
| (0.518) | (0.139) | (0.334) | (0.137) | (0.277) | |
| Information preference Request Info | 0.028 | -0.017 | 0.027 | -0.042 | |
| (0.179) | (0.177) | (0.177) | (0.176) | ||
| Request Ignorance | -0.114 | -0.247 | -0.113 | -0.277 | |
| (0.236) | (0.235) | (0.234) | (0.233) | ||
| Request Info under punishment threat | 0.157 | 0.117 | |||
| (0.182) | (0.184) | ||||
| Request Ignorance under punishment threat | 0.177 | 0.071 | |||
| (0.222) | (0.222) | ||||
| Control variables Identify with charity | 0.130** | 0.142*** | 0.104*** | ||
| (0.047) | (0.029) | (0.023) | |||
| Revealed in DWK | 0.260 | 0.322* | 0.410** | ||
| (0.276) | (0.164) | (0.128) | |||
| Observations | 140 | 438 | 412 | 716 | 667 |
| Note: | Tobit model of the Sender-index (left = 0). Model 1 includes observations in the Baseline treatment. Models 2 and 3 include observations in the Baseline and Request treatments. Models 4 and 5 include all observations. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Robust standard errors in parentheses. | ||||
Table B3: Probit regressions of Sender-index
# preregistration Q8 "We will do robustness checks with an alternative sender-index,
# which is 1 if the sender sends information for the worst outcome, and zero otherwise."
# note that we now do consider the 40 'weird' cases
df2 <- df2 %>%
mutate(sender_index_binary = case_when(message_minus2.5 == "True" ~ 1,
button_role == "Receiver" ~ NA_real_,
TRUE ~ 0))
# Baseline data model 1 -----------------------------------------------------------------
prob1 <- glm(sender_index_binary ~ dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, treatment == "Baseline"), family = binomial(link = "probit"))
McFadden.prob1 <- round(pR2(prob1)["McFadden"],3)
LL.prob1 <- round(pR2(prob1)["llh"],1)
cov_robust1 <- vcovCL(prob1, type = "HC1") # HC1 reproduces STATA default
robust_se1 <- sqrt(diag(cov_robust1))
# Baseline data model 2 -----------------------------------------------------------------
prob2 <- glm(sender_index_binary ~
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, treatment == "Baseline"), family = binomial(link = "probit"))
McFadden.prob2 <- round(pR2(prob2)["McFadden"],3)
LL.prob2 <- round(pR2(prob2)["llh"],1)
cov_robust2 <- vcovCL(prob2, type = "HC1") # HC1 reproduces STATA default
robust_se2 <- sqrt(diag(cov_robust2))
# Model with Baseline and Request data -----------------------------------------------------------------
prob3 <- glm(sender_index_binary ~ I(h2_request_info*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request")),
data=subset(df2, treatment == "Baseline" | treatment == "Request"), family = binomial(link = "probit"))
McFadden.prob3 <- round(pR2(prob3)["McFadden"],3)
LL.prob3 <- round(pR2(prob3)["llh"],1)
cov_robust3 <- vcovCL(prob3, type = "HC1") # HC1 reproduces STATA default
robust_se3 <- sqrt(diag(cov_robust3))
# Model with Baseline and Request data + controls -----------------------------------------------------------------
prob4 <- glm(sender_index_f ~ I(h2_request_info*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request")) +
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=subset(df2, treatment == "Baseline" | treatment == "Request"), family = binomial(link = "probit"))
McFadden.prob4 <- round(pR2(prob4)["McFadden"],3)
LL.prob4 <- round(pR2(prob4)["llh"],1)
cov_robust4 <- vcovCL(prob4, type = "HC1") # HC1 reproduces STATA default
robust_se4 <- sqrt(diag(cov_robust4))
# Model with All data -----------------------------------------------------------------
prob5 <- glm(sender_index_binary ~ I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")),
data=df2, family = binomial(link = "probit"))
McFadden.prob5 <- round(pR2(prob5)["McFadden"],3)
LL.prob5 <- round(pR2(prob5)["llh"],1)
cov_robust5 <- vcovCL(prob5, type = "HC1") # HC1 reproduces STATA default
robust_se5 <- sqrt(diag(cov_robust5))
# Model with All data + controls -----------------------------------------------------------------
prob6 <- glm(sender_index_binary ~ I(h2_request_info*(treatment == "Request + Punishment")) + I(h2_request_info*(treatment == "Request")) +
I(h2_request_ignorance*(treatment == "Request")) + I(h2_request_ignorance*(treatment == "Request + Punishment")) +
identify_charity + dana_reveal +
gender_f + age + income_c +
I(browser!="Desktop") + uq_wrong_button,
data=df2, family = binomial(link = "probit"))
McFadden.prob6 <- round(pR2(prob6)["McFadden"],3)
LL.prob6 <- round(pR2(prob6)["llh"],1)
cov_robust6 <- vcovCL(prob6, type = "HC1") # HC1 reproduces STATA default
robust_se6 <- sqrt(diag(cov_robust6))stargazer(prob2, prob3, prob4, prob5, prob6,
intercept.bottom = FALSE,
type = "html",
se = list(robust_se2, robust_se3, robust_se4, robust_se5, robust_se6),
keep.stat = c("rsq", "n"),
star.cutoffs=c(0.1,0.05,0.01,0.001),
star.char = c("\\circ", "*", "**", "***"),
model.names = FALSE,
omit.stat=c("f"),
font.size = "scriptsize",
table.placement = "H",
label="reg:senders_index_binary",
title = "Probit regressions of binary Sender-index",
omit = c("gender_f", "age", "income_c", "browser", "uq_wrong_button"),
order = c(1,10,11,9,12,2:3),
dep.var.caption = "\\textit{Dependent variable}: Sender-index binary",
dep.var.labels.include = FALSE,
covariate.labels = c("Constant",
"**Information preference** Request Info",
" Request Ignorance",
" Request Info under punishment threat",
" Request Ignorance under punishment threat",
"**Control variables** Identify with charity",
" Revealed in DWK"),
add.lines = list(c("Log likelihood",
LL.prob2, LL.prob3, LL.prob4, LL.prob5, LL.prob5),
c("Pseudo $R^2$ (McFadden)",
McFadden.prob2, McFadden.prob3, McFadden.prob4, McFadden.prob5, McFadden.prob6),
c("Covariates", "Yes", "Yes", "Yes", "Yes", "Yes")
),
notes.align = "l",
notes = "Probit model of binary Sender-index (1 if sender sends worst outcome, 0 otherwise) - note that this includes the 40 responses which were considered invalid for the regular sender-index. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Model 1 includes observations in the Baseline treatment. Models 2 and 3 include observations in the Baseline and Request treatments. Models 4 and 5 include all observations. Robust standard errors in parentheses."
)| Dependent variable: Sender-index binary | |||||
| (1) | (2) | (3) | (4) | (5) | |
| Constant | 0.216 | 0.569*** | 0.307 | 0.569*** | 0.102 |
| (0.479) | (0.109) | (0.291) | (0.109) | (0.233) | |
| Information preference Request Info | 0.027 | -0.030 | 0.027 | -0.056 | |
| (0.141) | (0.154) | (0.141) | (0.148) | ||
| Request Ignorance | -0.115 | -0.253 | -0.115 | -0.253 | |
| (0.182) | (0.200) | (0.182) | (0.191) | ||
| Request Info under punishment threat | 0.039 | 0.021 | |||
| (0.143) | (0.156) | ||||
| Request Ignorance under punishment threat | 0.024 | -0.066 | |||
| (0.176) | (0.192) | ||||
| Control variables Identify with charity | 0.082 | 0.096*** | 0.059** | ||
| (0.043) | (0.025) | (0.019) | |||
| Revealed in DWK | 0.190 | 0.188 | 0.242* | ||
| (0.260) | (0.144) | (0.109) | |||
| Log likelihood | -78.8 | -273.1 | -226.6 | -449.1 | -449.1 |
| Pseudo R(McFadden) | 0.06 | 0.001 | 0.056 | 0.001 | 0.033 |
| Covariates | Yes | Yes | Yes | Yes | Yes |
| Observations | 143 | 456 | 412 | 756 | 703 |
| Note: | p<0.1; p<0.05; p<0.01 | ||||
| Probit model of binary Sender-index (1 if sender sends worst outcome, 0 otherwise) - note that this includes the 40 responses which were considered invalid for the regular sender-index. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Model 1 includes observations in the Baseline treatment. Models 2 and 3 include observations in the Baseline and Request treatments. Models 4 and 5 include all observations. Robust standard errors in parentheses. | |||||
Table C1: OLS regression of the outcome for the charity
df2 <- df2_for_appendix
outcome.lm1<-lm(charity_outcome~relevel(factor(df2$group_5,ordered=F),ref="Baseline")
,data=df2)
robust_se1 <- coeftest(outcome.lm1, vcov.=function(x) vcovHC(x, "HC1")) #stata like robust SE
summary(outcome.lm1)
outcome.lm2<-lm(charity_outcome~relevel(factor(df2$group_5,ordered=F),ref="Baseline") +
identify_charity + dana_reveal+ gender_f + age + income_c +
I(browser!="Desktop"),data=df2)
robust_se2 <- coeftest(outcome.lm2, vcov.=function(x) vcovHC(x, "HC1")) #stata like robust SE
summary(outcome.lm2)stargazer(outcome.lm1, outcome.lm2,
type = 'html',
se = list(robust_se1[,2], robust_se2[,2]),
keep.stat = c("rsq", "n", "adj.rsq"),
star.cutoffs=c(0.1,0.05,0.01,0.001),
star.char = c("\\circ", "*", "**", "***"),
omit.stat=c("f"),
font.size = "scriptsize",
table.placement = "H",
label="reg:charity_outcomes",
dep.var.caption = "\\textit{Dependent variable}: Charity outcome in pound",
dep.var.labels.include = FALSE,
title = "OLS regression of the outcome for the charity",
order = c(1,3,4,2,5,6:12),
omit = c("gender_f", "age", "income_c", "browser", "uq_wrong_button"),
intercept.bottom = FALSE,
covariate.labels = c("Constant",
"**Information preference** Request Info",
" Request Ignorance",
" Request Info under punishment threat",
" Request Ignorance under punishment threat",
"**Control variables** Identify with charity",
" Revealed in DWK"),
notes = "OLS regression of the outcome for the charity. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Robust standard errors in parentheses.",
notes.align = "l")| Dependent variable: Charity outcome in pound | ||
| (1) | (2) | |
| Constant | -0.477*** | -0.661*** |
| (0.068) | (0.148) | |
| Information preference Request Info | -0.254 | -0.207 |
| (0.134) | (0.137) | |
| Request Ignorance | -0.084 | -0.119 |
| (0.096) | (0.098) | |
| Request Info under punishment threat | -0.017 | -0.055 |
| (0.089) | (0.090) | |
| Request Ignorance under punishment threat | -0.204 | -0.175 |
| (0.117) | (0.127) | |
| Control variables Identify with charity | 0.031* | |
| (0.012) | ||
| Revealed in DWK | 0.186* | |
| (0.073) | ||
| Observations | 756 | 713 |
| R2 | 0.009 | 0.036 |
| Adjusted R2 | 0.004 | 0.022 |
| Note: | p<0.1; p<0.05; p<0.01 | |
| OLS regression of the outcome for the charity. Covariates suppressed for brevity: gender, age, income, browser type, comprehension questions. Robust standard errors in parentheses. | ||
Figure D1: Differences in beliefs
df1 <- df %>%
select(starts_with("belief_pun"), starts_with("belief_push"), pp_id, request, sender_index, treatment,gender_f,age,income_c,browser) %>%
#filter(belief_pun0 != "") %>%
pivot_longer(starts_with("belief_"),names_sep = "_", names_to = c("variable", "consequence"), values_to = "value") %>%
mutate(belief_type = case_when(grepl("pun", consequence) ~ "Punishment",
grepl("push", consequence) ~ "Push the button"),
consequence = case_when(grepl("0", consequence) ~ "???",
grepl("1", consequence) ~ "-2.5",
grepl("2", consequence) ~ "-1.0",
grepl("3", consequence) ~ "-0.5",
grepl("4", consequence) ~ "+0.5"),
consequence = factor(consequence, levels = rev(c("???", "+0.5", "-0.5", "-1.0", "-2.5"))),
request = case_when(request == "request_no_info" ~ "Ignorance requested",
request == "request_info" ~ "Information requested")
)
df2 <- df %>%
select(starts_with("message_minus"), starts_with("message_plus"), pp_id, belief_pun0, belief_push0,treatment) %>%
#filter(belief_pun0 != "") %>%
pivot_longer(starts_with("message_"),names_sep = "_", names_to = c("variable", "consequence"), values_to = "value") %>%
mutate(consequence = case_when(grepl("minus2.5", consequence) ~ "-2.5",
grepl("minus1.0", consequence) ~ "-1.0",
grepl("minus0.5", consequence) ~ "-0.5",
grepl("plus0.5", consequence) ~ "+0.5"),
consequence = factor(consequence, levels = rev(c("???", "+0.5", "-0.5", "-1.0", "-2.5")))
)
df.beliefspun <- left_join(df1, df2, by = c("pp_id","consequence")) %>%
select(!c("variable.x","variable.y","treatment.x")) %>%
rename(belief = value.x,
share = value.y,
treatment = treatment.y
)
# Figure with averages of belief differences
#---------------------------------------------------------------------------------------------------------------
g0 <- df.beliefspun %>%
filter(belief_type == "Push the button" & treatment != "Baseline" & !is.na(sender_index) & consequence != "+0.5") %>%
group_by(belief_type,request,treatment,consequence) %>%
summarise(
n=n(),
mean=mean(belief-belief_push0),
sd=sd(belief-belief_push0)
) %>%
mutate( se=sd/sqrt(n)) %>%
ggplot(aes(x=consequence, y = mean, col=request, shape = request)) +
geom_point(size=4,position=position_dodge(width = 0.4)) +
geom_errorbar(aes(ymin = mean - se, ymax = mean + se),width=0.2,lwd=0.7,position=position_dodge(width = 0.4)) +
scale_color_manual(labels = c("Ignorance", "Information"),
values = c("#a6611a", "#018571")) +
geom_hline(yintercept = 0,lty=3) +
theme_bw() + facet_wrap(~treatment, nrow=1) +
scale_y_continuous(breaks = c(seq(-50,50, by = 20)), limits=c(-50,10)) +
labs(y = "Pushing the button more when... \n\n <- hiding info ---------------- sharing info ->\n",
fill = "", x = "\nConsequences",
title="Pressing the button") +
theme(legend.position = "none",
axis.title.y = element_text(size= 10),
plot.title = element_text(hjust = 0.5))
g1 <- df.beliefspun %>%
filter(belief_type == "Punishment" & treatment == "Request + Punishment" & !is.na(sender_index) & consequence != "+0.5") %>%
group_by(belief_type,request,treatment,consequence) %>%
summarise(
n=n(),
mean=mean(belief-belief_pun0),
sd=sd(belief-belief_pun0)
) %>%
mutate( se=sd/sqrt(n)) %>%
ggplot(aes(x=consequence, y = mean, col=request, shape=request)) +
geom_point(size=4,position=position_dodge(width = 0.4)) +
geom_errorbar(aes(ymin = mean - se, ymax = mean + se, col = request), width=0.2,lwd=0.7,position=position_dodge(width = 0.4)) +
scale_color_manual(labels = c("Ignorance", "Information"),
values = c("#a6611a", "#018571")) +
geom_hline(yintercept = 0,lty=3) +
theme_bw() +
facet_wrap(~"Request + Punishment", nrow=1) +
scale_y_continuous(breaks = c(seq(-50,50, by = 20)), limits=c(-50,10)) +
labs(y = "Expect more punishment when... \n\n <- hiding info ---------------- sharing info ->\n",
fill = "", x = "\nConsequences",
title="Punishment") +
theme(legend.position = "none",
axis.title.y = element_text(size= 10),
plot.title = element_text(hjust = 0.5))
f <- plot_grid(g0, g1, ncol=2, align = "h", rel_widths = c(1.8, 1))
# function to extract legend from plot
get_only_legend <- function(plot) {
plot_table <- ggplot_gtable(ggplot_build(plot))
legend_plot <- which(sapply(plot_table$grobs, function(x) x$name) == "guide-box")
legend <- plot_table$grobs[[legend_plot]]
return(legend)
}
plot1_legend <- df.beliefspun %>%
group_by(belief_type,sender_index,request,treatment,consequence) %>%
summarise(
n=n(),
mean=mean(belief-belief_pun0),
sd=sd(belief-belief_pun0)
) %>%
mutate( se=sd/sqrt(n),
sender_index = factor(sender_index),
request = case_when(request == "Ignorance requested" ~ "Ignorance",
request == "Information requested" ~ "Information")
) %>%
filter(belief_type == "Punishment" & treatment == "Request + Punishment" & !is.na(sender_index) & consequence != "+0.5") %>%
ggplot(aes(x=consequence, y = mean, fill=request, col=request, shape = request)) +
geom_point(size=4,position=position_dodge(width = 0.4)) +
geom_errorbar(aes(ymin = mean - se, ymax = mean + se, col = request),width=0.2,lwd=0.7,position=position_dodge(width = 0.4)) +
geom_hline(yintercept = 0,lty=3) +
scale_color_manual(labels = c("Ignorance", "Information"),
values = c("#a6611a", "#018571")) +
theme_bw() + facet_wrap(~sender_index, nrow=1) +
scale_y_continuous(breaks = c(seq(-50,50, by = 20)), limits=c(-45,15)) +
labs(fill = "Request received",
col = "Request received",
shape = "Request received") +
theme(legend.position = "bottom")
# extract legend from plot1 using above function
legend <- get_only_legend(plot1_legend)
plot_grid(f, legend, ncol=1, rel_heights = c(10,1))
SessionInfo
sessionInfo()## R version 4.3.3 (2024-02-29 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 11 x64 (build 22631)
##
## Matrix products: default
##
##
## locale:
## [1] LC_COLLATE=English_Netherlands.utf8 LC_CTYPE=English_Netherlands.utf8
## [3] LC_MONETARY=English_Netherlands.utf8 LC_NUMERIC=C
## [5] LC_TIME=English_Netherlands.utf8
##
## time zone: Europe/Amsterdam
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] cowplot_1.1.3 AER_1.2-12 survival_3.5-8 car_3.1-2
## [5] carData_3.0-5 lmtest_0.9-40 zoo_1.8-12 sandwich_3.1-0
## [9] pscl_1.5.9 multiwayvcov_1.2.3 MASS_7.3-60.0.1 kableExtra_1.4.0
## [13] ggsignif_0.6.4 plm_2.6-3 stargazer_5.2.3 PMCMRplus_1.9.10
## [17] gridExtra_2.3 knitr_1.45 table1_1.4.3 ggridges_0.5.6
## [21] anytime_0.3.9 numbers_0.8-5 openxlsx_4.2.5.2 here_1.0.1
## [25] lubridate_1.9.3 forcats_1.0.0 stringr_1.5.1 dplyr_1.1.4
## [29] purrr_1.0.2 readr_2.1.5 tidyr_1.3.1 tibble_3.2.1
## [33] ggplot2_3.5.0 tidyverse_2.0.0
##
## loaded via a namespace (and not attached):
## [1] tidyselect_1.2.0 viridisLite_0.4.2 farver_2.1.1
## [4] Rmpfr_0.9-5 fastmap_1.1.1 digest_0.6.34
## [7] timechange_0.3.0 lifecycle_1.0.4 multcompView_0.1-10
## [10] magrittr_2.0.3 compiler_4.3.3 rlang_1.1.3
## [13] sass_0.4.8 tools_4.3.3 utf8_1.2.4
## [16] yaml_2.3.8 collapse_2.0.10 labeling_0.4.3
## [19] xml2_1.3.6 SuppDists_1.1-9.7 abind_1.4-5
## [22] withr_3.0.0 grid_4.3.3 fansi_1.0.6
## [25] colorspace_2.1-0 scales_1.3.0 cli_3.6.2
## [28] mvtnorm_1.2-4 rmarkdown_2.26 miscTools_0.6-28
## [31] generics_0.1.3 rstudioapi_0.15.0 tzdb_0.4.0
## [34] bdsmatrix_1.3-7 cachem_1.0.8 splines_4.3.3
## [37] parallel_4.3.3 vctrs_0.6.5 Matrix_1.6-5
## [40] boot_1.3-29 jsonlite_1.8.8 hms_1.1.3
## [43] Formula_1.2-5 systemfonts_1.0.6 BWStest_0.2.3
## [46] jquerylib_0.1.4 glue_1.7.0 stringi_1.8.3
## [49] gtable_0.3.4 gmp_0.7-4 munsell_0.5.0
## [52] pillar_1.9.0 htmltools_0.5.7 R6_2.5.1
## [55] maxLik_1.5-2 Rdpack_2.6 rprojroot_2.0.4
## [58] evaluate_0.23 lattice_0.22-5 highr_0.10
## [61] rbibutils_2.2.16 memoise_2.0.1 bslib_0.6.1
## [64] Rcpp_1.0.12 zip_2.3.1 svglite_2.1.3
## [67] nlme_3.1-164 xfun_0.42 kSamples_1.2-10
## [70] pkgconfig_2.0.3