knitr::opts_chunk$set(message = FALSE, warning = FALSE)Regression Analyses
Overview
This documents presents the statistical analyses from our “Benevolent Sexism and the Gender Gap in Startup Evaluation” study published in 2023 in the journal Entrepreneurship: Theory and Practice. We wanted to know whether startup evaluators’ benevolent sexist attitudes impacts how viable they believe startups are, depending on the gender of the founder. To find out, we set up three experimental studies where we randomly assigned participants to evaluate startups led either by men or women, while also measuring their endorsement of benevolent sexism.
Key variables
- Entrepreneur gender (
Condition): coded as 0 for men-led startups, 1 for women-led startups. - Evaluator gender (
sex): coded as 0 for men evaluators, 1 for women evaluators. - Evaluator benevolent sexism (
BS_c): measured on a 1-6 scale. - Evaluator hostile sexism (
HS_c): measured on a 1-6 scale. - Evaluator perceptions of startup viability (
viable): measured on a 1-7 scale. - Evaluator funding allocations (
Invest): ranging from 0 to 100,000 dollars.
Main analysis
Our main analysis examines the two-way interaction between evaluators’ benevolent sexism and the gender of the entrepreneur. This will tell us whether the gender of a startup’s founder influences how an evaluator’s benevolent sexist attitudes affect their judgment of the startup’s potential.
Exploratory analysis
We also conduct some exploratory analyses:
- A three-way interaction between evaluator benevolent sexism, entrepreneur gender, and evaluator gender. This analysis sheds light on if men and women evaluators behave differently based on their benevolent sexist attitudes.
- A moderated mediation model examining how benevolent sexism and entrepreneur gender indirectly affect funding decisions through influencing perceptions of startup viability. This model helps us understand a potential pathway through which evaluator benevolent sexism might translate into financial outcomes for startups.
We start by performing these analyses for study 1. Then, to maintain consistency and enhance efficiency, we write a function to automate these analyses for Studies 2 and 3.
Data Loading and Preprocessing
# Load the necessary libraries
library(tidyverse)
library(interactions)
# Load the data for Study 1
study_1 <- readRDS("/Users/mac/Library/CloudStorage/OneDrive-McGillUniversity/Work/Projects/BS in entre/Data/Main studies/Study 1/Data/R data/study_1.rds")
study_2 <- readRDS("~/Library/CloudStorage/OneDrive-McGillUniversity/Work/Projects/BS in entre/Data/Main studies/Study 2/Data/R data/study_2.rds")
study_3 <- readRDS("~/Library/CloudStorage/OneDrive-McGillUniversity/Work/Projects/BS in entre/Data/Main studies/Study 3/Data/R data/study_3.rds")Study 1
Regression analyses
To explore how evaluator benevolent sexism impacts perceptions of startup viability differently based on the entrepreneur’s gender, let’s run a hierarchical moderated regression analysis, which unfolds in four key steps:
- Step 1 - control variables: includes evaluator hostile sexism and gender as controls.
- Step 2 - main effects: adds main effects of evaluator benevolent sexism and entrepreneur gender.
- Step 3 - two-way interaction: introduces the interaction between evaluator benevolent sexism and entrepreneur gender.
- Step 4 - three-way interaction: adds a three-way interaction between evaluator benevolent sexism, evaluator gender, and entrepreneur gender to explore if this interaction varies between men and women evaluators.
Before diving in, we standardize our key variables (benevolent sexism, hostile sexism, viability) to have a mean of 0 and a standard deviation of 1. This makes it easier to interpret the regression coefficients, as changes are expressed in standard deviation units.
# Standardizing variables for easy comparison
study_1 <- study_1 %>% mutate(across(c(BS, HS, viable), ~scale(.), .names = "{.col}_s")) Let’s quickly check to make sure our standardization worked.
# Checking the standardized variables
study_1 %>% select(BS, HS, viable, BS_s, HS_s, viable_s) %>% psych::describe() vars n mean sd median trimmed mad min max range skew kurtosis
BS 1 388 3.22 0.82 3.27 3.24 0.81 1.00 5.18 4.18 -0.23 -0.14
HS 2 388 2.84 0.96 2.91 2.81 1.08 1.00 5.64 4.64 0.19 -0.41
viable 3 388 4.67 1.37 5.00 4.74 1.48 1.00 7.00 6.00 -0.45 -0.30
BS_s 4 388 0.00 1.00 0.06 0.03 0.99 -2.72 2.40 5.12 -0.23 -0.14
HS_s 5 388 0.00 1.00 0.08 -0.02 1.12 -1.91 2.92 4.83 0.19 -0.41
viable_s 6 388 0.00 1.00 0.24 0.05 1.08 -2.68 1.71 4.39 -0.45 -0.30
se
BS 0.04
HS 0.05
viable 0.07
BS_s 0.05
HS_s 0.05
viable_s 0.05Great, everything looks in order! Now, let’s dive into our regression models.
# Running the regression models
# In the first model (m1), we include our control variables - evaluator hostile sexism and evaluator gender
m1 <- lm(viable_s ~ HS_s + sex, data = study_1)
# In the second model (m2), we add main effects of evaluator benevolent sexism and entrepreneur gender.
m2 <- lm(viable_s ~ HS_s + sex + Condition + BS_s, data = study_1)
# The third model (m3) introduces the interaction between benevolent sexism and entrepreneur gender.
m3 <- lm(viable_s ~ HS_s + sex + Condition*BS_s, data = study_1)
# In the fourth model (m4), we explore the three-way interaction involving evaluator benevolent sexism, evaluator gender, and entrepreneur gender.
m4 <- lm(viable_s ~ HS_s + sex*Condition*BS_s, data = study_1)Now, let’s use stargazer to create a side-by-side comparison of the four regression models. This makes it easier to see how each addition of variables and interactions changes our story about startup viability.
# Stargazer to compare regression models
stargazer::stargazer(m1, m2, m3, m4, # Chooses the models to display
type = "text", # Outputs the table in text format
intercept.bottom = FALSE, # Positions the intercept term at the top of the table for easier reference
digits = 2, # Rounds the numerical values in the table to two decimal places for clarity.
star.cutoffs = c(0.05, 0.01, 0.001)) # Sets the significance levels for the stars in the table (0.05, 0.01, 0.001).
======================================================================================================
Dependent variable:
----------------------------------------------------------------------------------
viable_s
(1) (2) (3) (4)
------------------------------------------------------------------------------------------------------
Constant -0.12 -0.15 -0.14 -0.12
(0.07) (0.08) (0.08) (0.10)
HS_s -0.04 -0.10 -0.12* -0.11
(0.05) (0.06) (0.06) (0.06)
sex 0.26* 0.29** 0.29** 0.20
(0.11) (0.11) (0.11) (0.15)
Condition 0.04 0.04 -0.03
(0.10) (0.10) (0.13)
BS_s 0.15** 0.25** 0.32**
(0.06) (0.08) (0.10)
sex:Condition 0.16
(0.21)
sex:BS_s -0.17
(0.15)
Condition:BS_s -0.20* -0.22
(0.10) (0.14)
sex:Condition:BS_s 0.07
(0.21)
------------------------------------------------------------------------------------------------------
Observations 385 385 385 385
R2 0.02 0.04 0.05 0.06
Adjusted R2 0.02 0.03 0.04 0.04
Residual Std. Error 0.99 (df = 382) 0.98 (df = 380) 0.98 (df = 379) 0.98 (df = 376)
F Statistic 4.36* (df = 2; 382) 4.00** (df = 4; 380) 4.03** (df = 5; 379) 2.81** (df = 8; 376)
======================================================================================================
Note: *p<0.05; **p<0.01; ***p<0.001In m3 (our main model), the coefficient for BS_s is positive and statistically significant, indicating a positive effect of benevolent sexism on the perceived viability of men-led startups (the reference group in Condition). More specifically, a one standard deviation increase in benevolent sexism is associated with a 0.25 standard deviation increase in the perceived viability of male-led startups.
The coefficient for the interaction term Condition:BS_s is negative and statistically significant, suggesting that the positive impact of benevolent sexism on perceived startup viability is reduced for women-led startups compared to male-led startups. More specifically, a one standard deviation increase in benevolent sexism is only associated with a 0.05 (0.25 + (-0.20) = 0.05) standard deviation increase in the perceived viability of women-led startup.
Our next step is to run a simple slope analysis. To do this, we use the sim_slopes() function from the interactions package. This analysis helps us see not just if there’s a relationship, but how strong and significant it is.
sim_slopes(m3, # performs a simple slopes analysis for the interaction in model m3.
pred = BS_s, # Specifies benevolent sexism as the predictor variable.
modx = Condition, # Specifies entrepreneur gender as the moderating variable.
johnson_neyman = FALSE, # Disables the Johnson-Neyman technique, which is used for finding regions of significance.
digits = 3) # Rounds the output to 3 decimal places.SIMPLE SLOPES ANALYSIS
Slope of BS_s when Condition = 0.000 (0):
Est. S.E. t val. p
------- ------- -------- -------
0.254 0.077 3.286 0.001
Slope of BS_s when Condition = 1.000 (1):
Est. S.E. t val. p
------- ------- -------- -------
0.051 0.073 0.698 0.485The results suggests that the positive relationship between evaluators’ benevolent sexism and their perceptions of viability for men-led startups is statistically significant (p = 0.001). However, no significant relationship was found between benevolent sexism and viability perceptions for women-led startups (p = 0.485).
It is also worth noting that when we added a three-way interaction in Model 4, this interaction was not statistically significant, indicating that these biases are similarly present among both men and women evaluators.
Visualizing the interaction effect
Beyond numerical analysis, let’s also graph these interactions to see how the effect of benevolent sexism on perceived startup viability changes with the entrepreneur’s gender. To do this, we use the interact_plot() function from the interactions package.
# Setting graph features
# Define labels for the categories in the interaction plot.
labels_cond <- c("Men-led startup", "Women-led startup") # Labels for the entrepreneur gender condition
labels_sex <- c("Men participants", "Women participants") # Labels for the evaluator gender
# The theme_pubr function from ggpubr package is used to set a consistent theme for plots.
theme_pubr <- ggpubr::theme_pubr(base_size = 12, # Sets the base font size to 12.
base_family = "Times New Roman", # Uses 'Times New Roman' as the font family.
border = FALSE, # Adjusts border and margin settings.
margin = TRUE,
legend = c("top", "bottom", "left", "right", "none"), # Specifies legend placement options.
x.text.angle = 0)
Here we see how the slope of benevolent sexism’s effect on viability perception is steeper for men-led startups. For women-led startups, it’s much flatter, confirming our earlier findings.
And even though the three-way interaction wasn’t significant, let’s take a look at what it looks like:
Although the three-way interaction was not statistically significant, we can see that the biased decisions are a bit more pronounced among men evaluators than among women evaluators. However, both men and women evaluators tend to give unfair advantages to men-led startups the more they endorse benevolent sexism.
Moderated Mediation Analysis
Finally, we explore the indirect effect of evaluator benevolent Sexism and entrepreneur gender on funding decisions through perceived startup viability. To do this, we use Andrew Hayes’ PROCESS macro to conduct a moderated mediation analysis (Model 7). Hayes has created a specific function to run these models in R, which can be downloaded from his website. After running the file process.r, we can use the process() function to execute our moderated mediation model. Here’s how we set it up:
- evaluator benevolent sexism (
BS_s) as the independent variable (X) - funding allocations (
Invest) as the dependent variable (Y) - perceived startup viability (
viable_s) as the mediator - entrepreneur gender (
Condition) as the moderator (W) - evaluator hostile sexism (
HS_s) and gender (sex) as controls (COV)
# Bringing in the process.r functions
source("process.r")
********************* PROCESS for R Version 4.3.1 *********************
Written by Andrew F. Hayes, Ph.D. www.afhayes.com
Documentation available in Hayes (2022). www.guilford.com/p/hayes3
***********************************************************************
PROCESS is now ready for use.
Copyright 2020-2023 by Andrew F. Hayes ALL RIGHTS RESERVED
Workshop schedule at http://haskayne.ucalgary.ca/CCRAM
# run moderated mediation model
process (data = study_1,
y = "Invest", # Dependent variable: funding allocations.
x = "BS_s", # Independent variable: benevolent sexism.
m = "viable_s", # Mediator: perceived startup viability.
w = "Condition", # Moderator: entrepreneur gender.
model = 7, # Specifies the PROCESS model number (Model 7 for moderated mediation).
cov = c("HS_s", "sex"), # Control variables: hostile sexism and evaluator gender.
center = 2, # Centers the predictor variables.
moments = 1, # Computes moments (means and variances) for the bootstrap distribution.
modelbt = 1, # Specifies bootstrapping for the model.
boot = 10000, # Number of bootstrap samples for computing confidence intervals.
seed = 911996) # Seed for random number generation in bootstrapping.
********************* PROCESS for R Version 4.3.1 *********************
Written by Andrew F. Hayes, Ph.D. www.afhayes.com
Documentation available in Hayes (2022). www.guilford.com/p/hayes3
***********************************************************************
Model : 7
Y : Invest
X : BS_s
M : viable_s
W : Condition
Covariates:
HS_s sex
Sample size: 384
Custom seed: 911996
***********************************************************************
Outcome Variable: viable_s
Model Summary:
R R-sq MSE F df1 df2 p
0.2249 0.0506 0.9441 4.0291 5.0000 378.0000 0.0014
Model:
coeff se t p LLCI ULCI
constant -0.1238 0.0840 -1.4737 0.1414 -0.2890 0.0414
BS_s 0.2589 0.0767 3.3746 0.0008 0.1080 0.4097
Condition 0.0216 0.0996 0.2169 0.8284 -0.1743 0.2175
Int_1 -0.2085 0.1000 -2.0855 0.0377 -0.4051 -0.0119
HS_s -0.1185 0.0577 -2.0549 0.0406 -0.2318 -0.0051
sex 0.2735 0.1067 2.5635 0.0107 0.0637 0.4832
Product terms key:
Int_1 : BS_s x Condition
Test(s) of highest order unconditional interaction(s):
R2-chng F df1 df2 p
X*W 0.0109 4.3493 1.0000 378.0000 0.0377
----------
Focal predictor: BS_s (X)
Moderator: Condition (W)
Conditional effects of the focal predictor at values of the moderator(s):
Condition effect se t p LLCI ULCI
0.0000 0.2589 0.0767 3.3746 0.0008 0.1080 0.4097
1.0000 0.0503 0.0723 0.6962 0.4867 -0.0918 0.1925
***********************************************************************
Outcome Variable: Invest
Model Summary:
R R-sq MSE F df1 df2 p
0.4877 0.2378 437362120.7462 29.5653 4.0000 379.0000 0.0000
Model:
coeff se t p LLCI ULCI
constant 34694.9194 1453.4867 23.8701 0.0000 31837.0109 37552.8279
BS_s 957.1742 1195.7892 0.8005 0.4239 -1394.0382 3308.3866
viable_s 10861.0161 1100.6624 9.8677 0.0000 8696.8461 13025.1862
HS_s 435.4616 1232.1664 0.3534 0.7240 -1987.2773 2858.2006
sex 6376.7227 2315.0448 2.7545 0.0062 1824.7814 10928.6639
***********************************************************************
Bootstrapping progress:
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**************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
Direct effect of X on Y:
effect se t p LLCI ULCI
957.1742 1195.7892 0.8005 0.4239 -1394.0382 3308.3866
Conditional indirect effects of X on Y:
INDIRECT EFFECT:
BS_s -> viable_s -> Invest
Condition Effect BootSE BootLLCI BootULCI
0.0000 2811.6493 780.7516 1330.3427 4395.6253
1.0000 546.7402 789.4335 -1040.9960 2103.7351
Index of moderated mediation
(differences beween conditional indirect effects):
Index BootSE BootLLCI BootULCI
Condition -2264.9091 1032.6958 -4355.7949 -267.2072
********** BOOTSTRAP RESULTS FOR REGRESSION MODEL PARAMETERS **********
Outcome variable: viable_s
Coeff BootMean BootSE BootLLCI BootULCI
constant -0.1238 -0.1231 0.0863 -0.2973 0.0469
BS_s 0.2589 0.2585 0.0693 0.1231 0.3934
Condition 0.0216 0.0204 0.0988 -0.1736 0.2139
Int_1 -0.2085 -0.2099 0.0942 -0.3946 -0.0239
HS_s -0.1185 -0.1169 0.0591 -0.2318 0.0003
sex 0.2735 0.2739 0.1050 0.0678 0.4809
----------
Outcome variable: Invest
Coeff BootMean BootSE BootLLCI BootULCI
constant 34694.9194 34714.0621 1482.4518 31799.7225 37663.2718
BS_s 957.1742 951.3042 1247.0191 -1487.3240 3403.3735
viable_s 10861.0161 10862.1793 1051.4864 8775.3489 12892.9706
HS_s 435.4616 424.3688 1168.6134 -1876.9497 2705.7225
sex 6376.7227 6331.3097 2403.1579 1555.1854 10906.5685
******************** ANALYSIS NOTES AND ERRORS ************************
Level of confidence for all confidence intervals in output: 95
Number of bootstraps for percentile bootstrap confidence intervals: 10000
NOTE: The following variables were mean centered prior to analysis:
BS_s
NOTE: Some cases with missing data were deleted. The number of deleted cases was: 4Conditional Indirect Effects (Moderated Mediation) For men-led startups (Condition = 0), a one standard deviation increase in evaluator benevolent sexism is indirectly linked to an increase in funding by about 2811 dollars. This effect is statistically significant, as the confidence interval does not include 0. However, for women-led startups (Condition = 1), the increase in funding is only 547 dollars, and the confidence interval includes zero. This suggests that benevolent sexism does not translate into significant funding boosts for women-led startups like it does for men-led startups.
Index of Moderated Mediation The confidence interval for this index does not include 0, suggesting that the indirect effect of benevolent sexism on funding decisions through perceived viability is significantly different for men-led and women-led startups. The negative value ndicates that this indiret effect is weaker for women-led startups than men-led startups.
Automation for Studies 2 and 3
To maintain consistency and enhance efficiency across our studies, let’s create a function to automate the analysis for Studies 2 and 3. This function, called automate_regression_analysis, takes a dataset and standardizes key variables, performs regression modeling, and visualizes interactions. If the interaction term is statistically significant, it dives deeper with simple slope and moderated mediation analyses. All results are compiled into a list.
# Defining the function
automate_regression_analysis <- function(data) {
# Standardizing specified variables
data <- data %>% mutate(across(c(BS, HS, viable), ~scale(.), .names = "{.col}_s"))
# Running regression models
m1 <- lm(viable_s ~ HS_s + sex, data = data)
m2 <- lm(viable_s ~ HS_s + sex + Condition + BS_s, data = data)
m3 <- lm(viable_s ~ HS_s + sex + Condition*BS_s, data = data)
m4 <- lm(viable_s ~ HS_s + sex*Condition*BS_s, data = data)
# Stargazer to compare regression models
regression_result <- stargazer::stargazer(m1, m2, m3, m4, type = "text", intercept.bottom = FALSE, digits = 2, star.cutoffs = c(0.05, 0.01, 0.001))
# Interaction plot for m3 (two-way interaction)
interaction_plot_m3 <- interact_plot(m3,
pred = "BS_s",
modx = "Condition",
modx.labels = labels_cond,
legend.main = "",
line.thickness = 2,
vary.lty = F,
colors = c("black", "#bdbdbd")) +
labs(x = "Benevolent sexism (standardized)", y = "Perceived startup viability (standardized)") +
theme(legend.title = element_blank()) +
scale_x_continuous(limits = c(-3, 3), breaks = c(-3, -2, -1, 0, 1, 2, 3)) +
scale_y_continuous(limits = c(-3, 3), breaks = c(-3, -2, -1, 0, 1, 2, 3)) + #
ggpubr::theme_pubr(base_size = 16) +
theme(legend.text = element_text(size = 16),
axis.title = element_text(size = 16),
text = element_text(family = "Times New Roman"))
# Interaction plot for m4 (three-way interaction)
interaction_plot_m4 <- interact_plot(m4,
pred = "BS_s",
modx = "Condition",
mod2 = "sex",
modx.labels = labels_cond,
mod2.labels = labels_sex,
legend.main = "",
line.thickness = 2,
vary.lty = F,
colors = c("black", "#bdbdbd")) +
labs(x = "Benevolent sexism (standardized)", y = "Perceived startup viability (standardized)") +
theme(legend.title = element_blank()) +
scale_x_continuous(limits = c(-3, 3), breaks = c(-3, -2, -1, 0, 1, 2, 3)) +
scale_y_continuous(limits = c(-3, 3), breaks = c(-3, -2, -1, 0, 1, 2, 3)) +
ggpubr::theme_pubr(base_size = 20) +
theme(legend.title = element_blank(),
legend.position = "top",
legend.text = element_text(size=20),
axis.text = element_text(size=20),
axis.title = element_text(size=20),
text = element_text(family = "Times New Roman"))
# Check if interaction in m3 is significant
m3_summary <- summary(m3)
interaction_effect_significant <- "Condition:BS_s" %in% rownames(m3_summary$coefficients) && m3_summary$coefficients["Condition:BS_s", "Pr(>|t|)"] < 0.05
# Initialize results
simple_slopes_result <- NULL
moderated_mediation_model <- NULL
# Conditional execution based on the significance of the interaction in m3
if (interaction_effect_significant) {
simple_slopes_result <- sim_slopes(m3, pred = "BS_s", modx = "Condition", johnson_neyman = FALSE, digits = 3)
moderated_mediation_model <- capture.output(process(data = data, y = "Invest", x = "BS_s", m = "viable_s", w = "Condition", model = 7, cov = c("HS_s", "sex"), center = 2, moments = 1, modelbt = 1, boot = 10000, seed = 911996))
}
# Return the results as a list
list(regression_result = regression_result,
simple_slopes_result = simple_slopes_result,
moderated_mediation_model = moderated_mediation_model,
interaction_plot_two_way = interaction_plot_m3,
interaction_plot_three_way = interaction_plot_m4)
}Study 2
We now apply our automated function to the Study 2 dataset.
# Applying the function to Study 2 data
study_2_results <- automate_regression_analysis(study_2)
========================================================================================================
Dependent variable:
------------------------------------------------------------------------------------
viable_s
(1) (2) (3) (4)
--------------------------------------------------------------------------------------------------------
Constant -0.09 -0.07 -0.07 -0.14
(0.06) (0.07) (0.07) (0.08)
HS_s 0.04 -0.06 -0.07 -0.08
(0.04) (0.05) (0.05) (0.05)
sex 0.19* 0.26** 0.27** 0.34**
(0.09) (0.09) (0.09) (0.12)
Condition -0.12 -0.12 -0.004
(0.08) (0.08) (0.12)
BS_s 0.24*** 0.29*** 0.41***
(0.05) (0.07) (0.10)
sex:Condition -0.14
(0.17)
sex:BS_s -0.19
(0.13)
Condition:BS_s -0.09 -0.29*
(0.08) (0.12)
sex:Condition:BS_s 0.35*
(0.17)
--------------------------------------------------------------------------------------------------------
Observations 567 567 567 567
R2 0.01 0.06 0.06 0.07
Adjusted R2 0.005 0.05 0.05 0.05
Residual Std. Error 1.00 (df = 564) 0.98 (df = 562) 0.98 (df = 561) 0.98 (df = 558)
F Statistic 2.36 (df = 2; 564) 8.25*** (df = 4; 562) 6.84*** (df = 5; 561) 4.89*** (df = 8; 558)
========================================================================================================
Note: *p<0.05; **p<0.01; ***p<0.001Regression analyses
First, we examine the regression outcomes to see how variables interact.
# Displaying regression results from Study 2
study_2_results$regression_result [1] ""
[2] "========================================================================================================"
[3] " Dependent variable: "
[4] " ------------------------------------------------------------------------------------"
[5] " viable_s "
[6] " (1) (2) (3) (4) "
[7] "--------------------------------------------------------------------------------------------------------"
[8] "Constant -0.09 -0.07 -0.07 -0.14 "
[9] " (0.06) (0.07) (0.07) (0.08) "
[10] " "
[11] "HS_s 0.04 -0.06 -0.07 -0.08 "
[12] " (0.04) (0.05) (0.05) (0.05) "
[13] " "
[14] "sex 0.19* 0.26** 0.27** 0.34** "
[15] " (0.09) (0.09) (0.09) (0.12) "
[16] " "
[17] "Condition -0.12 -0.12 -0.004 "
[18] " (0.08) (0.08) (0.12) "
[19] " "
[20] "BS_s 0.24*** 0.29*** 0.41*** "
[21] " (0.05) (0.07) (0.10) "
[22] " "
[23] "sex:Condition -0.14 "
[24] " (0.17) "
[25] " "
[26] "sex:BS_s -0.19 "
[27] " (0.13) "
[28] " "
[29] "Condition:BS_s -0.09 -0.29* "
[30] " (0.08) (0.12) "
[31] " "
[32] "sex:Condition:BS_s 0.35* "
[33] " (0.17) "
[34] " "
[35] "--------------------------------------------------------------------------------------------------------"
[36] "Observations 567 567 567 567 "
[37] "R2 0.01 0.06 0.06 0.07 "
[38] "Adjusted R2 0.005 0.05 0.05 0.05 "
[39] "Residual Std. Error 1.00 (df = 564) 0.98 (df = 562) 0.98 (df = 561) 0.98 (df = 558) "
[40] "F Statistic 2.36 (df = 2; 564) 8.25*** (df = 4; 562) 6.84*** (df = 5; 561) 4.89*** (df = 8; 558)"
[41] "========================================================================================================"
[42] "Note: *p<0.05; **p<0.01; ***p<0.001"In Study 2, the two-way interaction between benevolent sexism and entrepreneur gender isn’t statistically significant. However, when we add evaluator gender to the mix, something interesting happens. That is, the interaction between benevolent sexism, entrepreneur gender, and evaluator gender is significant. To unpack these, we analyze benevolent sexism’s interaction with entrepreneur gender for men and women evaluators separately.
# standardized continuous variable
study_2 <- study_2 %>% mutate(across(c(BS, HS, viable), ~scale(.), .names = "{.col}_s"))
# test the interaction between benevolent sexism and entrepreneur gender among men evaluators
m3_men_evaluator <- lm(viable_s ~ HS_s + BS_s*Condition, data = study_2 %>% filter(sex == 0))
# test the interaction between benevolent sexism and entrepreneur gender among women evaluators
m3_women_evaluator <- lm(viable_s ~ HS_s + BS_s*Condition, data = study_2 %>% filter(sex == 1))
stargazer::stargazer(m3_men_evaluator, m3_women_evaluator, type = "text", intercept.bottom = FALSE, digits = 2, star.cutoffs = c(0.05, 0.01, 0.001))
==============================================================
Dependent variable:
------------------------------------------
viable_s
(1) (2)
--------------------------------------------------------------
Constant -0.13 0.21*
(0.09) (0.09)
HS_s -0.09 -0.05
(0.07) (0.07)
BS_s 0.42*** 0.21*
(0.10) (0.09)
Condition -0.005 -0.15
(0.12) (0.12)
BS_s:Condition -0.29* 0.06
(0.13) (0.12)
--------------------------------------------------------------
Observations 295 272
R2 0.06 0.06
Adjusted R2 0.05 0.04
Residual Std. Error 1.01 (df = 290) 0.93 (df = 267)
F Statistic 4.77*** (df = 4; 290) 3.98** (df = 4; 267)
==============================================================
Note: *p<0.05; **p<0.01; ***p<0.001For male evaluators, we observe a pattern similar our findings from Study 1: benevolent sexism skews their perception of viability in favor of men-led startups. Specifically, a one standard deviation increase in benevolent sexism among male evaluators correlates with a 0.42 standard deviation rise in perceived viability for men-led startups. However, this effect diminishes for women-led startups, with only a 0.13 standard deviation increase.
To quantify the significance of these relationships, let’s turn to a simple slope analysis:
# Simple slope analysis for men evaluators
sim_slopes(m3_men_evaluator, pred = BS_s, modx = Condition, johnson_neyman = FALSE, digits = 3)SIMPLE SLOPES ANALYSIS
Slope of BS_s when Condition = 0.000 (0):
Est. S.E. t val. p
------- ------- -------- -------
0.416 0.101 4.112 0.000
Slope of BS_s when Condition = 1.000 (1):
Est. S.E. t val. p
------- ------- -------- -------
0.122 0.085 1.429 0.154The analysis confirms a significant positive relationship between men evaluators’ benevolent sexism and their perceptions of viability for men-led startups (p < 0.001), but not for women-led startups (p = 0.154).
Among women evaluators, the interaction term BS_s:Condition is not significant. This suggests that in contrast to the men evaluators, the women evaluators in Study 2 evaluated men- and women-led startups similarly regardless of their endorsement of benevolent sexism.
Visualizing the interaction effect
Let’s take a look at the graph for these interactions.
Moderated Mediation Analysis
Given the significant interaction observed among men evaluators, let’s also run a moderated mediation model to test the indirect effect of their benevolent sexism on funding allocations via perceived startup viability.
process (data = study_2 %>% filter(sex == 0), # select men evaluators as the dataset
y = "Invest", # Dependent variable: funding allocations.
x = "BS_s", # Independent variable: benevolent sexism.
m = "viable_s", # Mediator: perceived startup viability.
w = "Condition", # Moderator: entrepreneur gender.
model = 7, # Specifies the PROCESS model number (Model 7 for moderated mediation).
cov = c("HS_s"), # Control variables: hostile sexism.
center = 2, # Centers the predictor variables.
moments = 1, # Computes moments (means and variances) for the bootstrap distribution.
modelbt = 1, # Specifies bootstrapping for the model.
boot = 10000, # Number of bootstrap samples for computing confidence intervals.
seed = 911996) # Sets seed for reproducibility
********************* PROCESS for R Version 4.3.1 *********************
Written by Andrew F. Hayes, Ph.D. www.afhayes.com
Documentation available in Hayes (2022). www.guilford.com/p/hayes3
***********************************************************************
Model : 7
Y : Invest
X : BS_s
M : viable_s
W : Condition
Covariates:
HS_s
Sample size: 293
Custom seed: 911996
***********************************************************************
Outcome Variable: viable_s
Model Summary:
R R-sq MSE F df1 df2 p
0.2410 0.0581 1.0246 4.4383 4.0000 288.0000 0.0017
Model:
coeff se t p LLCI ULCI
constant -0.0117 0.0853 -0.1378 0.8905 -0.1795 0.1561
BS_s 0.3996 0.1021 3.9124 0.0001 0.1985 0.6006
Condition -0.0953 0.1189 -0.8019 0.4233 -0.3294 0.1387
Int_1 -0.2789 0.1296 -2.1519 0.0322 -0.5340 -0.0238
HS_s -0.0853 0.0652 -1.3081 0.1919 -0.2137 0.0431
Product terms key:
Int_1 : BS_s x Condition
Test(s) of highest order unconditional interaction(s):
R2-chng F df1 df2 p
X*W 0.0151 4.6309 1.0000 288.0000 0.0322
----------
Focal predictor: BS_s (X)
Moderator: Condition (W)
Conditional effects of the focal predictor at values of the moderator(s):
Condition effect se t p LLCI ULCI
0.0000 0.3996 0.1021 3.9124 0.0001 0.1985 0.6006
1.0000 0.1207 0.0851 1.4174 0.1575 -0.0469 0.2882
***********************************************************************
Outcome Variable: Invest
Model Summary:
R R-sq MSE F df1 df2 p
0.5892 0.3472 423537149.8319 51.2283 3.0000 289.0000 0.0000
Model:
coeff se t p LLCI ULCI
constant 35762.4303 1256.0754 28.4716 0.0000 33290.2140 38234.6467
BS_s -3098.5559 1389.3337 -2.2302 0.0265 -5833.0521 -364.0597
viable_s 14568.5008 1187.2339 12.2710 0.0000 12231.7788 16905.2227
HS_s -1348.3140 1314.3412 -1.0258 0.3058 -3935.2093 1238.5813
***********************************************************************
Bootstrapping progress:
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**************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
Direct effect of X on Y:
effect se t p LLCI ULCI
-3098.5559 1389.3337 -2.2302 0.0265 -5833.0521 -364.0597
Conditional indirect effects of X on Y:
INDIRECT EFFECT:
BS_s -> viable_s -> Invest
Condition Effect BootSE BootLLCI BootULCI
0.0000 5820.9305 1587.0345 2682.2090 8834.6366
1.0000 1757.9357 1154.8047 -547.8088 3987.6076
Index of moderated mediation
(differences beween conditional indirect effects):
Index BootSE BootLLCI BootULCI
Condition -4062.9948 1946.3462 -7880.5141 -254.1127
********** BOOTSTRAP RESULTS FOR REGRESSION MODEL PARAMETERS **********
Outcome variable: viable_s
Coeff BootMean BootSE BootLLCI BootULCI
constant -0.0117 -0.0096 0.0832 -0.1765 0.1478
BS_s 0.3996 0.3952 0.1050 0.1848 0.5970
Condition -0.0953 -0.1009 0.1180 -0.3342 0.1252
Int_1 -0.2789 -0.2753 0.1306 -0.5322 -0.0178
HS_s -0.0853 -0.0848 0.0674 -0.2194 0.0441
----------
Outcome variable: Invest
Coeff BootMean BootSE BootLLCI BootULCI
constant 35762.4303 35746.2977 1235.5302 33300.5156 38150.8747
BS_s -3098.5559 -3099.7382 1432.4954 -5942.6847 -362.9248
viable_s 14568.5008 14562.7401 1057.3033 12503.9497 16630.9346
HS_s -1348.3140 -1315.1212 1347.9920 -3918.9054 1405.1346
******************** ANALYSIS NOTES AND ERRORS ************************
Level of confidence for all confidence intervals in output: 95
Number of bootstraps for percentile bootstrap confidence intervals: 10000
NOTE: The following variables were mean centered prior to analysis:
BS_s
NOTE: Some cases with missing data were deleted. The number of deleted cases was: 4Conditional Indirect Effects (Moderated Mediation) For men-led startups, a one standard deviation increase in men evaluators’ benevolent sexism is indirectly linked to an increase in funding by about 5820 dollars. This effect is statistically significant, as the confidence interval does not include 0. However, for women-led startups, the increase in funding is only 1757 dollars, and the confidence interval includes zero. This suggests this indirect relationship is not significant for women-led startups.
Index of Moderated Mediation The confidence interval for this index does not include 0, suggesting that the indirect effect of benevolent sexism is significantly different for men-led and women-led startups. The negative value points to a weaker indirect effect for women-led startups than men-led startups.
Study 3
As we proceed to Study 3, we apply the function to Study 3 dataset.
# Applying the automated function to Study 3 data
study_3_results <- automate_regression_analysis(study_3)
=====================================================================================================
Dependent variable:
---------------------------------------------------------------------------------
viable_s
(1) (2) (3) (4)
-----------------------------------------------------------------------------------------------------
Constant -0.08 -0.22* -0.23* -0.23*
(0.08) (0.09) (0.09) (0.11)
HS_s -0.05 -0.11 -0.11 -0.12
(0.06) (0.06) (0.06) (0.06)
sex 0.19 0.25* 0.27* 0.36*
(0.12) (0.12) (0.12) (0.18)
Condition 0.22 0.22 0.27
(0.11) (0.11) (0.15)
BS_s 0.17** 0.29** 0.25*
(0.06) (0.09) (0.11)
sex:Condition -0.14
(0.24)
sex:BS_s 0.15
(0.18)
Condition:BS_s -0.23* -0.27
(0.11) (0.16)
sex:Condition:BS_s 0.01
(0.24)
-----------------------------------------------------------------------------------------------------
Observations 310 310 310 310
R2 0.01 0.05 0.06 0.07
Adjusted R2 0.01 0.03 0.04 0.04
Residual Std. Error 1.00 (df = 307) 0.99 (df = 305) 0.98 (df = 304) 0.98 (df = 301)
F Statistic 1.99 (df = 2; 307) 3.77** (df = 4; 305) 3.86** (df = 5; 304) 2.64** (df = 8; 301)
=====================================================================================================
Note: *p<0.05; **p<0.01; ***p<0.001Regression analyses
First, we examine the regression outcomes.
# Displaying regression results from Study 3
study_3_results$regression_result [1] ""
[2] "====================================================================================================="
[3] " Dependent variable: "
[4] " ---------------------------------------------------------------------------------"
[5] " viable_s "
[6] " (1) (2) (3) (4) "
[7] "-----------------------------------------------------------------------------------------------------"
[8] "Constant -0.08 -0.22* -0.23* -0.23* "
[9] " (0.08) (0.09) (0.09) (0.11) "
[10] " "
[11] "HS_s -0.05 -0.11 -0.11 -0.12 "
[12] " (0.06) (0.06) (0.06) (0.06) "
[13] " "
[14] "sex 0.19 0.25* 0.27* 0.36* "
[15] " (0.12) (0.12) (0.12) (0.18) "
[16] " "
[17] "Condition 0.22 0.22 0.27 "
[18] " (0.11) (0.11) (0.15) "
[19] " "
[20] "BS_s 0.17** 0.29** 0.25* "
[21] " (0.06) (0.09) (0.11) "
[22] " "
[23] "sex:Condition -0.14 "
[24] " (0.24) "
[25] " "
[26] "sex:BS_s 0.15 "
[27] " (0.18) "
[28] " "
[29] "Condition:BS_s -0.23* -0.27 "
[30] " (0.11) (0.16) "
[31] " "
[32] "sex:Condition:BS_s 0.01 "
[33] " (0.24) "
[34] " "
[35] "-----------------------------------------------------------------------------------------------------"
[36] "Observations 310 310 310 310 "
[37] "R2 0.01 0.05 0.06 0.07 "
[38] "Adjusted R2 0.01 0.03 0.04 0.04 "
[39] "Residual Std. Error 1.00 (df = 307) 0.99 (df = 305) 0.98 (df = 304) 0.98 (df = 301) "
[40] "F Statistic 1.99 (df = 2; 307) 3.77** (df = 4; 305) 3.86** (df = 5; 304) 2.64** (df = 8; 301)"
[41] "====================================================================================================="
[42] "Note: *p<0.05; **p<0.01; ***p<0.001"In study 3, we observe similar patterns as study 1: the interaction between benevolent sexism and entrepreneur gender is significant, with a one standard deviation increase in benevolent sexism correlating with a 0.29 standard deviation rise in perceived viability for men-led startups. This effect is much less pronounced for women-led startups, with a mere 0.06 standard deviation increase.
Unlike Study 2, the three-way interaction involving evaluator gender is not significant, mirroring the trends seen in Study 1.
Next, we assess the strength of benevolent sexism’s effects across entrepreneur genders through simple slope analysis:
study_3_results$simple_slopes_resultSIMPLE SLOPES ANALYSIS
Slope of BS_s when Condition = 0.000 (0):
Est. S.E. t val. p
------- ------- -------- -------
0.288 0.088 3.287 0.001
Slope of BS_s when Condition = 1.000 (1):
Est. S.E. t val. p
------- ------- -------- -------
0.063 0.082 0.771 0.441The results shows a statistically significant positive effect of benevolent sexism on perceived viability for men-led startups (p = 0.001), while this effect is not significant for women-led startups (p = 0.441).
Visualizing the interaction effect
Let’s take a look at the graph for the two-way interaction.
Warning: Removed 8 row(s) containing missing values (geom_path).
Though not statistically significant, let’s also take a look at the three-way interaction graph.
Warning: Removed 8 row(s) containing missing values (geom_path).
Moderated Mediation Analysis
Lastly, we assess the indirect influence of benevolent sexism on funding decisions via perceived startup viability.
study_3_results$moderated_mediation_model [1] ""
[2] "********************* PROCESS for R Version 4.3.1 ********************* "
[3] " "
[4] " Written by Andrew F. Hayes, Ph.D. www.afhayes.com "
[5] " Documentation available in Hayes (2022). www.guilford.com/p/hayes3 "
[6] " "
[7] "*********************************************************************** "
[8] " "
[9] "Model : 7 "
[10] " Y : Invest "
[11] " X : BS_s "
[12] " M : viable_s "
[13] " W : Condition"
[14] ""
[15] "Covariates: "
[16] " HS_s sex"
[17] ""
[18] "Sample size: 310"
[19] ""
[20] "Custom seed: 911996"
[21] ""
[22] ""
[23] "*********************************************************************** "
[24] "Outcome Variable: viable_s"
[25] ""
[26] "Model Summary: "
[27] " R R-sq MSE F df1 df2 p"
[28] " 0.2443 0.0597 0.9616 3.8581 5.0000 304.0000 0.0021"
[29] ""
[30] "Model: "
[31] " coeff se t p LLCI ULCI"
[32] "constant -0.2242 0.0929 -2.4127 0.0164 -0.4070 -0.0413"
[33] "BS_s 0.2885 0.0878 3.2871 0.0011 0.1158 0.4612"
[34] "Condition 0.2179 0.1117 1.9508 0.0520 -0.0019 0.4378"
[35] "Int_1 -0.2255 0.1120 -2.0128 0.0450 -0.4459 -0.0050"
[36] "HS_s -0.1105 0.0620 -1.7822 0.0757 -0.2324 0.0115"
[37] "sex 0.2692 0.1194 2.2547 0.0249 0.0342 0.5041"
[38] ""
[39] "Product terms key:"
[40] "Int_1 : BS_s x Condition "
[41] ""
[42] "Test(s) of highest order unconditional interaction(s):"
[43] " R2-chng F df1 df2 p"
[44] "X*W 0.0125 4.0513 1.0000 304.0000 0.0450"
[45] "----------"
[46] "Focal predictor: BS_s (X)"
[47] " Moderator: Condition (W)"
[48] ""
[49] "Conditional effects of the focal predictor at values of the moderator(s):"
[50] " Condition effect se t p LLCI ULCI"
[51] " 0.0000 0.2885 0.0878 3.2871 0.0011 0.1158 0.4612"
[52] " 1.0000 0.0630 0.0817 0.7713 0.4411 -0.0977 0.2237"
[53] ""
[54] "*********************************************************************** "
[55] "Outcome Variable: Invest"
[56] ""
[57] "Model Summary: "
[58] " R R-sq MSE F df1 df2 p"
[59] " 0.5998 0.3598 348685244.3962 42.8571 4.0000 305.0000 0.0000"
[60] ""
[61] "Model: "
[62] " coeff se t p LLCI ULCI"
[63] "constant 28877.9953 1443.3269 20.0079 0.0000 26037.8560 31718.1346"
[64] "BS_s 679.6391 1221.5984 0.5564 0.5784 -1724.1889 3083.4672"
[65] "viable_s 13408.5409 1078.2180 12.4358 0.0000 11286.8529 15530.2288"
[66] "HS_s -516.6339 1185.7557 -0.4357 0.6634 -2849.9317 1816.6638"
[67] "sex 4184.1369 2280.4189 1.8348 0.0675 -303.2093 8671.4830"
[68] ""
[69] "*********************************************************************** "
[70] "Bootstrapping progress:"
[71] "\r | \r | | 0%\r | \r | | 1%\r | \r |> | 1%\r | \r |> | 2%\r | \r |>> | 2%\r | \r |>> | 3%\r | \r |>> | 4%\r | \r |>>> | 4%\r | \r |>>> | 5%\r | \r |>>> | 6%\r | \r |>>>> | 6%\r | \r |>>>> | 7%\r | \r |>>>>> | 7%\r | \r |>>>>> | 8%\r | \r |>>>>> | 9%\r | \r |>>>>>> | 9%\r | \r |>>>>>> | 10%\r | \r |>>>>>>> | 10%\r | \r |>>>>>>> | 11%\r | \r |>>>>>>> | 12%\r | \r |>>>>>>>> | 12%\r | \r |>>>>>>>> | 13%\r | \r |>>>>>>>> | 14%\r | \r |>>>>>>>>> | 14%\r | \r |>>>>>>>>> | 15%\r | \r |>>>>>>>>>> | 15%\r | \r |>>>>>>>>>> | 16%\r | \r |>>>>>>>>>> | 17%\r | \r |>>>>>>>>>>> | 17%\r | \r |>>>>>>>>>>> | 18%\r | \r |>>>>>>>>>>> | 19%\r | \r |>>>>>>>>>>>> | 19%\r | \r |>>>>>>>>>>>> | 20%\r | \r |>>>>>>>>>>>>> | 20%\r | \r |>>>>>>>>>>>>> | 21%\r | \r |>>>>>>>>>>>>> | 22%\r | \r |>>>>>>>>>>>>>> | 22%\r | \r |>>>>>>>>>>>>>> | 23%\r | \r |>>>>>>>>>>>>>>> | 23%\r | \r |>>>>>>>>>>>>>>> | 24%\r | \r |>>>>>>>>>>>>>>> | 25%\r | \r |>>>>>>>>>>>>>>>> | 25%\r | \r |>>>>>>>>>>>>>>>> | 26%\r | \r 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[72] ""
[73] "**************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************"
[74] ""
[75] "Direct effect of X on Y:"
[76] " effect se t p LLCI ULCI"
[77] " 679.6391 1221.5984 0.5564 0.5784 -1724.1889 3083.4672"
[78] ""
[79] "Conditional indirect effects of X on Y:"
[80] ""
[81] "INDIRECT EFFECT:"
[82] ""
[83] "BS_s -> viable_s -> Invest"
[84] ""
[85] " Condition Effect BootSE BootLLCI BootULCI"
[86] " 0.0000 3867.9787 1245.2924 1490.8572 6375.0136"
[87] " 1.0000 844.5533 1245.0180 -1498.9699 3404.5096"
[88] ""
[89] " Index of moderated mediation"
[90] " (differences beween conditional indirect effects):"
[91] " Index BootSE BootLLCI BootULCI"
[92] "Condition -3023.4254 1646.2255 -6263.3260 290.2788"
[93] ""
[94] "********** BOOTSTRAP RESULTS FOR REGRESSION MODEL PARAMETERS **********"
[95] ""
[96] "Outcome variable: viable_s"
[97] ""
[98] " Coeff BootMean BootSE BootLLCI BootULCI"
[99] "constant -0.2242 -0.2253 0.0907 -0.4036 -0.0484"
[100] "BS_s 0.2885 0.2889 0.0911 0.1130 0.4684"
[101] "Condition 0.2179 0.2187 0.1121 -0.0017 0.4358"
[102] "Int_1 -0.2255 -0.2241 0.1228 -0.4662 0.0214"
[103] "HS_s -0.1105 -0.1099 0.0638 -0.2334 0.0167"
[104] "sex 0.2692 0.2701 0.1172 0.0439 0.5035"
[105] "----------"
[106] "Outcome variable: Invest"
[107] ""
[108] " Coeff BootMean BootSE BootLLCI BootULCI"
[109] "constant 28877.9953 28844.0474 1409.2481 26094.9637 31642.1353"
[110] "BS_s 679.6391 697.2015 1136.6141 -1523.6896 3001.1986"
[111] "viable_s 13408.5409 13393.5617 990.2418 11435.3904 15335.0133"
[112] "HS_s -516.6339 -535.6635 1036.8839 -2621.0807 1486.0520"
[113] "sex 4184.1369 4241.9120 2300.1924 -301.3974 8705.8003"
[114] ""
[115] "******************** ANALYSIS NOTES AND ERRORS ************************ "
[116] ""
[117] "Level of confidence for all confidence intervals in output: 95"
[118] ""
[119] "Number of bootstraps for percentile bootstrap confidence intervals: 10000"
[120] " "
[121] "NOTE: The following variables were mean centered prior to analysis: "
[122] " BS_s"
[123] " "
[124] "NOTE: Some cases with missing data were deleted. The number of deleted cases was: 2" Once again, the indirect effect of benevolent sexism through perceived startup viability is significant for men-led startups (with the confidence interval excluding 0). Specifically, a one standard deviation increase in benevolent sexism is indirectly related to an increase by 3867 dollars in funding amount for men-led startups. For women-led startups, however, the boost in funding is only 844 dollars, and is not statistically significant (with the confidence interval including 0).
However, the index of moderated mediation is not significantly, as the confidence interval includes 0. This suggests that the indirect effects of benevolent sexism on funding allocation do not differ significantly between men- and women-led startups.
Conclusion
In the analyses above, we explore how evaluator benevolent sexism differentially impacts their perceptions of startup viability depending on the gender of the startup founder. To do this, we perform regression modeling, simple slope analysis, moderated mediation modeling, and visualization of the two- and three-way interactions. The results reveal a clear pattern: higher benevolent sexism correlates with higher evaluations of men-led startups, while it is unrelated to evaluations of women-led startups. These findings underscore the subtle yet powerful role of benevolent sexism in perpetuating gender disparities in entrepreneurship, not through directly undermining women, but by conferring unfair advantages to men while leaving women’s outcomes unchanged.