Study 1 Analyses
Patricia Andrews Fearon
2024-05-11
Hypothesis 1
A zero-sum mindset (generalized zero-sum belief) is psychologically distinct from economic-domain zero-sum beliefs.
Analysis Strategy
Across the datasets, we adopted a two-fold approach to test our prediction that general zero-sum beliefs are psychologically distinct from economic zero-sum beliefs (Hypothesis 1): First, we ran confirmatory factor analyses comparing a unidimensional solution to a two-factor solution where generalized belief items are assigned to one factor and the economic items to a second factor. Second, we conducted paired samples t-tests to compare mean levels of agreement with the different types of beliefs.
Loading Libraries
library(here)
library(tidyverse)
library(readr)
library(lavaan)
library(psych)
library(ggplot2)
here()## [1] "/Users/patricia/Desktop/JPJP R&R 2 /The_Zero-Sum_Mindset"Factor Analysis (US) - Sample 1a (pre-registered)
Loading Dataset
s1 <- read_csv(here("data", "s1a.csv"))Creating dataframe with items
zs_df <- select(s1, zsm_1, zsm_2, zsm_3, zsm_4, zsm_5, zs_econ_1 , zs_econ_2 , zs_econ_3) Examining Data Fitness for Factor Analysis
Kaiser-Meyer Test – “The test measures sampling adequacy for each variable in the model and the complete model. The statistic is a measure of the proportion of variance among variables that might be common variance. The higher the proportion, the higher the KMO-value, the more suited the data is to factor analysis”
Values above .60 considered adequate, above .9 considered “marvelous” :)
psych::KMO(zs_df) ## Kaiser-Meyer-Olkin factor adequacy
## Call: psych::KMO(r = zs_df)
## Overall MSA = 0.87
## MSA for each item =
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.90 0.87 0.94 0.91 0.87 0.88 0.78 0.80Scree Plot
A scree plot is a visualization of the analysis performed to evaluate how many factors or dimensions best account for the data – the rule of thumb here is to look for the “elbow” – essentially where you are no longer gaining much in explanatory strength with an additional dimension or where eigenvalues fall below a certain threshold
ncol(zs_df)## [1] 8fafitfree <- fa(zs_df,nfactors = ncol(zs_df), rotate = "none")
n_factors <- length(fafitfree$e.values)
scree <- data.frame(
Factor_n = as.factor(1:n_factors),
Eigenvalue = fafitfree$e.values)
ggplot(scree, aes(x = Factor_n, y = Eigenvalue, group = 1)) +
geom_point() + geom_line() +
xlab("Number of factors") +
ylab("Initial eigenvalue") +
labs( title = "Scree Plot",
subtitle = "(Based on the unreduced correlation matrix)")
Parellel Analysis
parallel <- fa.parallel(zs_df)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2Parallel analysis suggests 2 factors and two components
Descriptive Statistics
zs_df_clean <- filter(zs_df, complete.cases(zs_df))
# Calculate means and standard deviations
means <- colMeans(zs_df_clean)
std_deviations <- apply(zs_df_clean, 2, sd)
# Create a data frame with the results
summary_table <- data.frame(Column = colnames(zs_df_clean),
Mean = means,
StandardDeviation = std_deviations)
# Print the summary table
print(summary_table)## Column Mean StandardDeviation
## zsm_1 zsm_1 3.074300 1.629180
## zsm_2 zsm_2 3.153471 1.655244
## zsm_3 zsm_3 3.467722 1.503003
## zsm_4 zsm_4 2.724726 1.600224
## zsm_5 zsm_5 2.840438 1.607186
## zs_econ_1 zs_econ_1 4.909866 1.601573
## zs_econ_2 zs_econ_2 4.043849 1.626916
## zs_econ_3 zs_econ_3 4.009744 1.669644Factor Analysis
Now we examine the item loadings
# Fitting data to 2 factors
factanal.2 <- factanal(zs_df_clean, factors=2, scores = c("regression"), rotation = "promax")
print(factanal.2, cutoff=0.2)##
## Call:
## factanal(x = zs_df_clean, factors = 2, scores = c("regression"), rotation = "promax")
##
## Uniquenesses:
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.274 0.207 0.595 0.457 0.195 0.566 0.129 0.302
##
## Loadings:
## Factor1 Factor2
## zsm_1 0.819
## zsm_2 0.874
## zsm_3 0.646
## zsm_4 0.732
## zsm_5 0.923
## zs_econ_1 0.667
## zs_econ_2 0.934
## zs_econ_3 0.816
##
## Factor1 Factor2
## SS loadings 3.241 1.990
## Proportion Var 0.405 0.249
## Cumulative Var 0.405 0.654
##
## Factor Correlations:
## Factor1 Factor2
## Factor1 1.000 0.525
## Factor2 0.525 1.000
##
## Test of the hypothesis that 2 factors are sufficient.
## The chi square statistic is 71.12 on 13 degrees of freedom.
## The p-value is 4.99e-10factanal.2b <- factanal(zs_df_clean, factors=2, scores = c("regression"), rotation = "promax")
print(factanal.2b, cutoff=0)##
## Call:
## factanal(x = zs_df_clean, factors = 2, scores = c("regression"), rotation = "promax")
##
## Uniquenesses:
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.274 0.207 0.595 0.457 0.195 0.566 0.129 0.302
##
## Loadings:
## Factor1 Factor2
## zsm_1 0.819 0.059
## zsm_2 0.874 0.031
## zsm_3 0.646 -0.019
## zsm_4 0.732 0.011
## zsm_5 0.923 -0.051
## zs_econ_1 -0.016 0.667
## zs_econ_2 -0.001 0.934
## zs_econ_3 0.037 0.816
##
## Factor1 Factor2
## SS loadings 3.241 1.990
## Proportion Var 0.405 0.249
## Cumulative Var 0.405 0.654
##
## Factor Correlations:
## Factor1 Factor2
## Factor1 1.000 0.525
## Factor2 0.525 1.000
##
## Test of the hypothesis that 2 factors are sufficient.
## The chi square statistic is 71.12 on 13 degrees of freedom.
## The p-value is 4.99e-10factanal.1 <- factanal(zs_df_clean, factors=1, scores = c("regression"), rotation = "promax")
print(factanal.1, cutoff=0.2)##
## Call:
## factanal(x = zs_df_clean, factors = 1, scores = c("regression"), rotation = "promax")
##
## Uniquenesses:
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.267 0.204 0.602 0.466 0.231 0.849 0.703 0.730
##
## Loadings:
## Factor1
## zsm_1 0.856
## zsm_2 0.892
## zsm_3 0.631
## zsm_4 0.731
## zsm_5 0.877
## zs_econ_1 0.389
## zs_econ_2 0.545
## zs_econ_3 0.520
##
## Factor1
## SS loadings 3.948
## Proportion Var 0.494
##
## Test of the hypothesis that 1 factor is sufficient.
## The chi square statistic is 932.16 on 20 degrees of freedom.
## The p-value is 1.12e-184CFA for Zero-Sum Mindset and Economic Zero-Sum Beliefs
Unidimensional CFA
zero.sum.cfa.model.1<-' zero.sum.mindset.latent.variable =~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5 + zs_econ_1 + zs_econ_2 + zs_econ_3 '
fit.1<-cfa(zero.sum.cfa.model.1, data = zs_df_clean)
summary(fit.1, fit.measures=TRUE)## lavaan 0.6.17 ended normally after 28 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 16
##
## Number of observations 821
##
## Model Test User Model:
##
## Test statistic 938.067
## Degrees of freedom 20
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 4103.815
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.775
## Tucker-Lewis Index (TLI) 0.685
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -10864.336
## Loglikelihood unrestricted model (H1) -10395.302
##
## Akaike (AIC) 21760.671
## Bayesian (BIC) 21836.040
## Sample-size adjusted Bayesian (SABIC) 21785.230
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.236
## 90 Percent confidence interval - lower 0.224
## 90 Percent confidence interval - upper 0.249
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.126
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable =~
## zsm_1 1.000
## zsm_2 1.059 0.031 33.754 0.000
## zsm_3 0.680 0.034 19.963 0.000
## zsm_4 0.838 0.034 24.487 0.000
## zsm_5 1.010 0.031 32.773 0.000
## zs_econ_1 0.447 0.040 11.268 0.000
## zs_econ_2 0.635 0.038 16.593 0.000
## zs_econ_3 0.622 0.040 15.673 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .zsm_1 0.708 0.045 15.726 0.000
## .zsm_2 0.558 0.040 13.786 0.000
## .zsm_3 1.359 0.071 19.202 0.000
## .zsm_4 1.191 0.065 18.410 0.000
## .zsm_5 0.597 0.040 14.746 0.000
## .zs_econ_1 2.174 0.109 19.977 0.000
## .zs_econ_2 1.859 0.095 19.587 0.000
## .zs_econ_3 2.033 0.103 19.670 0.000
## zr.sm.mndst.l. 1.943 0.129 15.036 0.000Two Dimension CFA
zero.sum.cfa.model.2 <-' zero.sum.mindset.latent.variable =~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5
econ.latent.variable =~ zs_econ_1 + zs_econ_2 + zs_econ_3 '
fit.2 <-cfa(zero.sum.cfa.model.2, data = zs_df_clean)
zero.sum.cfa.model.2 <-' zero.sum.mindset.latent.variable =~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5
econ.latent.variable =~ zs_econ_1 + zs_econ_2 + zs_econ_3 '
summary(fit.2, fit.measures=TRUE)## lavaan 0.6.17 ended normally after 34 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 17
##
## Number of observations 821
##
## Model Test User Model:
##
## Test statistic 87.630
## Degrees of freedom 19
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 4103.815
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.983
## Tucker-Lewis Index (TLI) 0.975
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -10439.117
## Loglikelihood unrestricted model (H1) -10395.302
##
## Akaike (AIC) 20912.234
## Bayesian (BIC) 20992.313
## Sample-size adjusted Bayesian (SABIC) 20938.327
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.066
## 90 Percent confidence interval - lower 0.053
## 90 Percent confidence interval - upper 0.081
## P-value H_0: RMSEA <= 0.050 0.026
## P-value H_0: RMSEA >= 0.080 0.059
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.024
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable =~
## zsm_1 1.000
## zsm_2 1.063 0.031 33.849 0.000
## zsm_3 0.684 0.034 20.102 0.000
## zsm_4 0.843 0.034 24.620 0.000
## zsm_5 1.024 0.031 33.420 0.000
## econ.latent.variable =~
## zs_econ_1 1.000
## zs_econ_2 1.428 0.069 20.708 0.000
## zs_econ_3 1.332 0.065 20.406 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable ~~
## econ.ltnt.vrbl 0.792 0.073 10.919 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .zsm_1 0.710 0.045 15.698 0.000
## .zsm_2 0.544 0.040 13.474 0.000
## .zsm_3 1.348 0.070 19.174 0.000
## .zsm_4 1.179 0.064 18.360 0.000
## .zsm_5 0.545 0.039 13.963 0.000
## .zs_econ_1 1.450 0.079 18.400 0.000
## .zs_econ_2 0.374 0.062 6.048 0.000
## .zs_econ_3 0.811 0.066 12.364 0.000
## zr.sm.mndst.l. 1.941 0.129 15.013 0.000
## econ.ltnt.vrbl 1.112 0.109 10.171 0.000Comparing Model Fit
anova_model <- anova(fit.1, fit.2) ## significantly better fit with two factors
print(anova_model)##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit.2 19 20912 20992 87.63
## fit.1 20 21761 21836 938.07 850.44 1.0172 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comparing Means
zsm_df <- select(zs_df_clean, zsm_1,zsm_2, zsm_3, zsm_4, zsm_5)
psych::alpha(zsm_df)##
## Reliability analysis
## Call: psych::alpha(x = zsm_df)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.9 0.9 0.89 0.64 9 0.0055 3.1 1.4 0.61
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.89 0.9 0.91
## Duhachek 0.89 0.9 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## zsm_1 0.87 0.87 0.85 0.63 6.8 0.0072 0.0092 0.59
## zsm_2 0.86 0.86 0.84 0.61 6.3 0.0078 0.0084 0.58
## zsm_3 0.91 0.91 0.89 0.71 9.6 0.0054 0.0073 0.72
## zsm_4 0.89 0.89 0.87 0.66 7.8 0.0064 0.0166 0.66
## zsm_5 0.86 0.86 0.84 0.60 6.1 0.0080 0.0098 0.58
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## zsm_1 821 0.87 0.86 0.83 0.78 3.1 1.6
## zsm_2 821 0.89 0.89 0.87 0.82 3.2 1.7
## zsm_3 821 0.75 0.75 0.65 0.62 3.5 1.5
## zsm_4 821 0.82 0.82 0.75 0.71 2.7 1.6
## zsm_5 821 0.90 0.90 0.89 0.84 2.8 1.6
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## zsm_1 0.15 0.32 0.20 0.08 0.15 0.07 0.03 0
## zsm_2 0.15 0.29 0.21 0.08 0.16 0.07 0.03 0
## zsm_3 0.07 0.25 0.22 0.18 0.17 0.09 0.02 0
## zsm_4 0.23 0.34 0.19 0.06 0.11 0.05 0.03 0
## zsm_5 0.19 0.36 0.18 0.07 0.12 0.06 0.03 0zs_df_clean$zsm_mean <- rowMeans(zsm_df)
zs_econ_df <- select(zs_df_clean, contains("ec"))
psych::alpha(zs_econ_df)##
## Reliability analysis
## Call: psych::alpha(x = zs_econ_df)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.85 0.85 0.81 0.65 5.5 0.0094 4.3 1.4 0.61
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.83 0.85 0.86
## Duhachek 0.83 0.85 0.87
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## zs_econ_1 0.88 0.88 0.78 0.78 7.1 0.0087 NA 0.78
## zs_econ_2 0.71 0.71 0.55 0.55 2.4 0.0203 NA 0.55
## zs_econ_3 0.76 0.76 0.61 0.61 3.2 0.0167 NA 0.61
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## zs_econ_1 821 0.82 0.82 0.66 0.62 4.9 1.6
## zs_econ_2 821 0.91 0.91 0.87 0.79 4.0 1.6
## zs_econ_3 821 0.89 0.89 0.82 0.74 4.0 1.7
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## zs_econ_1 0.03 0.09 0.09 0.10 0.31 0.24 0.16 0
## zs_econ_2 0.06 0.15 0.20 0.12 0.29 0.12 0.06 0
## zs_econ_3 0.06 0.18 0.17 0.13 0.26 0.14 0.06 0zs_df_clean$zs_econ_mean <- rowMeans(zs_econ_df)
t.test(zs_df_clean$zsm_mean, zs_df_clean$zs_econ_mean, paired = T)##
## Paired t-test
##
## data: zs_df_clean$zsm_mean and zs_df_clean$zs_econ_mean
## t = -25.437, df = 820, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -1.366945 -1.171099
## sample estimates:
## mean difference
## -1.269022Factor Analysis Replication (Italy) - Sample 7
s7 <- read_csv(here( "data","s7.csv"))Creating dataframe with items
zs_it_df <- select(s7, zsm_1, zsm_2, zsm_3, zsm_4, zsm_5, zs_econ_1 , zs_econ_2 , zs_econ_3) Examining Data Fitness for Factor Analysis
Kaiser-Meyer Test – “The test measures sampling adequacy for each variable in the model and the complete model. The statistic is a measure of the proportion of variance among variables that might be common variance. The higher the proportion, the higher the KMO-value, the more suited the data is to factor analysis”
Values above .60 considered adequate, above .9 considered “marvelous” :)
psych::KMO(zs_it_df) ## Kaiser-Meyer-Olkin factor adequacy
## Call: psych::KMO(r = zs_it_df)
## Overall MSA = 0.79
## MSA for each item =
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.78 0.77 0.83 0.88 0.86 0.74 0.77 0.74Scree Plot
A scree plot is a visualization of the analysis performed to evaluate how many factors or dimensions best account for the data – the rule of thumb here is to look for the “elbow” – essentially where you are no longer gaining much in explanatory strength with an additional dimension or where eigenvalues fall below a certain threshold
ncol(zs_it_df)## [1] 8fafitfree <- fa(zs_it_df,nfactors = ncol(zs_it_df), rotate = "none")
n_factors <- length(fafitfree$e.values)
scree <- data.frame(
Factor_n = as.factor(1:n_factors),
Eigenvalue = fafitfree$e.values)
ggplot(scree, aes(x = Factor_n, y = Eigenvalue, group = 1)) +
geom_point() + geom_line() +
xlab("Number of factors") +
ylab("Initial eigenvalue") +
labs( title = "Scree Plot",
subtitle = "(Based on the unreduced correlation matrix)")
Parellel Analysis
parallel <- fa.parallel(zs_it_df)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2Parallel analysis suggests 2 factors and two components
Factor Analysis
Now we examine the item loadings
zs_it_df_clean <- filter(zs_it_df, complete.cases(zs_it_df))
# Fitting data to 2 factors
factanal.2 <- factanal(zs_it_df_clean, factors=2, scores = c("regression"), rotation = "promax")
print(factanal.2, cutoff=0.2)##
## Call:
## factanal(x = zs_it_df_clean, factors = 2, scores = c("regression"), rotation = "promax")
##
## Uniquenesses:
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.426 0.264 0.685 0.679 0.442 0.250 0.532 0.344
##
## Loadings:
## Factor1 Factor2
## zsm_1 0.775
## zsm_2 0.863
## zsm_3 0.522
## zsm_4 0.534
## zsm_5 0.742
## zs_econ_1 0.841
## zs_econ_2 0.719
## zs_econ_3 0.814
##
## Factor1 Factor2
## SS loadings 2.475 1.906
## Proportion Var 0.309 0.238
## Cumulative Var 0.309 0.548
##
## Factor Correlations:
## Factor1 Factor2
## Factor1 1.00 0.35
## Factor2 0.35 1.00
##
## Test of the hypothesis that 2 factors are sufficient.
## The chi square statistic is 35.8 on 13 degrees of freedom.
## The p-value is 0.000637factanal.2b <- factanal(zs_it_df_clean, factors=2, scores = c("regression"), rotation = "promax")
print(factanal.2b, cutoff=0)##
## Call:
## factanal(x = zs_it_df_clean, factors = 2, scores = c("regression"), rotation = "promax")
##
## Uniquenesses:
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.426 0.264 0.685 0.679 0.442 0.250 0.532 0.344
##
## Loadings:
## Factor1 Factor2
## zsm_1 0.775 -0.057
## zsm_2 0.863 -0.014
## zsm_3 0.522 0.093
## zsm_4 0.534 0.079
## zsm_5 0.742 0.016
## zs_econ_1 0.065 0.841
## zs_econ_2 -0.134 0.719
## zs_econ_3 -0.012 0.814
##
## Factor1 Factor2
## SS loadings 2.475 1.906
## Proportion Var 0.309 0.238
## Cumulative Var 0.309 0.548
##
## Factor Correlations:
## Factor1 Factor2
## Factor1 1.00 0.35
## Factor2 0.35 1.00
##
## Test of the hypothesis that 2 factors are sufficient.
## The chi square statistic is 35.8 on 13 degrees of freedom.
## The p-value is 0.000637factanal.1 <- factanal(zs_it_df_clean, factors=1, scores = c("regression"), rotation = "promax")
print(factanal.1, cutoff=0.2)##
## Call:
## factanal(x = zs_it_df_clean, factors = 1, scores = c("regression"), rotation = "promax")
##
## Uniquenesses:
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.462 0.296 0.676 0.671 0.439 0.821 0.962 0.878
##
## Loadings:
## Factor1
## zsm_1 0.734
## zsm_2 0.839
## zsm_3 0.569
## zsm_4 0.573
## zsm_5 0.749
## zs_econ_1 0.423
## zs_econ_2
## zs_econ_3 0.349
##
## Factor1
## SS loadings 2.794
## Proportion Var 0.349
##
## Test of the hypothesis that 1 factor is sufficient.
## The chi square statistic is 318.56 on 20 degrees of freedom.
## The p-value is 1.29e-55library(knitr)
# Perform factor analysis
factanal.2b <- factanal(zs_it_df_clean, factors = 2, scores = "regression", rotation = "promax")
# Calculate means and standard deviations rounded to two decimal places
var_means <- round(colMeans(zs_it_df_clean), 2)
var_sds <- round(apply(zs_it_df_clean, 2, sd), 2)
# Create a combined table
combined_table <- data.frame(
Variable_Means = var_means,
Variable_Standard_Deviations = var_sds
)
# Assign factor analysis results to the table
loadings <- factanal.2b$loadings[1:8,]
combined_table <- bind_cols(combined_table,loadings)
combined_table <- round(combined_table, 2)
# Print the combined table using kable
kableExtra::kable(combined_table, format = "markdown")| Variable_Means | Variable_Standard_Deviations | Factor1 | Factor2 | |
|---|---|---|---|---|
| zsm_1 | 1.86 | 1.42 | 0.78 | -0.06 |
| zsm_2 | 2.12 | 1.49 | 0.86 | -0.01 |
| zsm_3 | 2.70 | 1.67 | 0.52 | 0.09 |
| zsm_4 | 2.42 | 1.79 | 0.53 | 0.08 |
| zsm_5 | 1.77 | 1.43 | 0.74 | 0.02 |
| zs_econ_1 | 3.77 | 1.95 | 0.06 | 0.84 |
| zs_econ_2 | 5.07 | 1.75 | -0.13 | 0.72 |
| zs_econ_3 | 4.05 | 1.82 | -0.01 | 0.81 |
# Calculate means and standard deviations
means <- colMeans(zs_it_df_clean)
std_deviations <- apply(zs_it_df_clean, 2, sd)
# Create a data frame with the results
summary_table <- data.frame(Column = colnames(zs_it_df_clean),
Mean = means,
StandardDeviation = std_deviations)
# Print the summary table
print(summary_table)## Column Mean StandardDeviation
## zsm_1 zsm_1 1.862319 1.420330
## zsm_2 zsm_2 2.119565 1.488201
## zsm_3 zsm_3 2.699275 1.669012
## zsm_4 zsm_4 2.423913 1.790279
## zsm_5 zsm_5 1.768116 1.431032
## zs_econ_1 zs_econ_1 3.768116 1.949508
## zs_econ_2 zs_econ_2 5.068841 1.753637
## zs_econ_3 zs_econ_3 4.054348 1.819275nrow(zs_it_df_clean)## [1] 276CFA for Zero-Sum Mindset and Economic Zero-Sum Beliefs
zero.sum.cfa.model.1<-' zero.sum.mindset.latent.variable =~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5 + zs_econ_1 + zs_econ_2 + zs_econ_3 '
zero.sum.cfa.model.2 <-' zero.sum.mindset.latent.variable =~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5
econ.latent.variable =~ zs_econ_1 + zs_econ_2 + zs_econ_3 '
fit.1<-cfa(zero.sum.cfa.model.1, data = zs_it_df_clean)
summary(fit.1, fit.measures=TRUE)## lavaan 0.6.17 ended normally after 29 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 16
##
## Number of observations 276
##
## Model Test User Model:
##
## Test statistic 324.642
## Degrees of freedom 20
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 875.606
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.641
## Tucker-Lewis Index (TLI) 0.497
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3965.576
## Loglikelihood unrestricted model (H1) -3803.255
##
## Akaike (AIC) 7963.153
## Bayesian (BIC) 8021.079
## Sample-size adjusted Bayesian (SABIC) 7970.346
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.235
## 90 Percent confidence interval - lower 0.213
## 90 Percent confidence interval - upper 0.258
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.154
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable =~
## zsm_1 1.000
## zsm_2 1.198 0.095 12.592 0.000
## zsm_3 0.911 0.104 8.795 0.000
## zsm_4 0.985 0.111 8.865 0.000
## zsm_5 1.028 0.089 11.522 0.000
## zs_econ_1 0.791 0.121 6.535 0.000
## zs_econ_2 0.330 0.109 3.026 0.002
## zs_econ_3 0.608 0.113 5.381 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .zsm_1 0.928 0.098 9.421 0.000
## .zsm_2 0.654 0.093 7.053 0.000
## .zsm_3 1.877 0.173 10.821 0.000
## .zsm_4 2.143 0.198 10.799 0.000
## .zsm_5 0.896 0.098 9.191 0.000
## .zs_econ_1 3.109 0.274 11.330 0.000
## .zs_econ_2 2.946 0.252 11.671 0.000
## .zs_econ_3 2.897 0.252 11.483 0.000
## zr.sm.mndst.l. 1.082 0.163 6.649 0.000fit.2 <-cfa(zero.sum.cfa.model.2, data = zs_it_df_clean)
summary(fit.2, fit.measures=TRUE)## lavaan 0.6.17 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 17
##
## Number of observations 276
##
## Model Test User Model:
##
## Test statistic 51.924
## Degrees of freedom 19
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 875.606
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.961
## Tucker-Lewis Index (TLI) 0.943
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3829.217
## Loglikelihood unrestricted model (H1) -3803.255
##
## Akaike (AIC) 7692.434
## Bayesian (BIC) 7753.981
## Sample-size adjusted Bayesian (SABIC) 7700.077
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent confidence interval - lower 0.054
## 90 Percent confidence interval - upper 0.105
## P-value H_0: RMSEA <= 0.050 0.031
## P-value H_0: RMSEA >= 0.080 0.509
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.052
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable =~
## zsm_1 1.000
## zsm_2 1.202 0.092 13.074 0.000
## zsm_3 0.883 0.100 8.813 0.000
## zsm_4 0.950 0.107 8.839 0.000
## zsm_5 1.007 0.085 11.789 0.000
## econ.latent.variable =~
## zs_econ_1 1.000
## zs_econ_2 0.667 0.063 10.651 0.000
## zs_econ_3 0.840 0.068 12.293 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable ~~
## econ.ltnt.vrbl 0.663 0.140 4.735 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .zsm_1 0.886 0.096 9.230 0.000
## .zsm_2 0.582 0.092 6.356 0.000
## .zsm_3 1.899 0.175 10.877 0.000
## .zsm_4 2.179 0.200 10.869 0.000
## .zsm_5 0.900 0.097 9.234 0.000
## .zs_econ_1 0.829 0.201 4.125 0.000
## .zs_econ_2 1.749 0.173 10.112 0.000
## .zs_econ_3 1.210 0.169 7.160 0.000
## zr.sm.mndst.l. 1.124 0.165 6.829 0.000
## econ.ltnt.vrbl 2.958 0.367 8.069 0.000anova_model <- anova(fit.1, fit.2) ## significantly better fit with two factors
print(anova_model)##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit.2 19 7692.4 7754.0 51.924
## fit.1 20 7963.2 8021.1 324.642 272.72 0.99221 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comparing Means
zsm_df <- select(zs_it_df_clean, zsm_1,zsm_2, zsm_3, zsm_4, zsm_5)
psych::alpha(zsm_df)##
## Reliability analysis
## Call: psych::alpha(x = zsm_df)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.82 0.81 0.48 4.7 0.018 2.2 1.2 0.46
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.78 0.82 0.85
## Duhachek 0.78 0.82 0.85
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## zsm_1 0.78 0.78 0.74 0.48 3.6 0.022 0.0073 0.46
## zsm_2 0.74 0.75 0.70 0.43 3.0 0.025 0.0073 0.42
## zsm_3 0.81 0.82 0.79 0.53 4.5 0.019 0.0111 0.52
## zsm_4 0.81 0.81 0.79 0.52 4.3 0.020 0.0178 0.54
## zsm_5 0.76 0.77 0.75 0.45 3.3 0.024 0.0160 0.42
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## zsm_1 276 0.76 0.77 0.72 0.62 1.9 1.4
## zsm_2 276 0.84 0.85 0.83 0.73 2.1 1.5
## zsm_3 276 0.70 0.69 0.57 0.51 2.7 1.7
## zsm_4 276 0.73 0.71 0.58 0.54 2.4 1.8
## zsm_5 276 0.80 0.81 0.75 0.68 1.8 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## zsm_1 0.62 0.18 0.05 0.08 0.03 0.03 0.01 0
## zsm_2 0.49 0.22 0.11 0.07 0.07 0.02 0.02 0
## zsm_3 0.31 0.24 0.17 0.10 0.09 0.06 0.02 0
## zsm_4 0.47 0.18 0.08 0.07 0.11 0.05 0.03 0
## zsm_5 0.66 0.17 0.05 0.04 0.03 0.02 0.03 0zs_it_df_clean$zsm_mean <- rowMeans(zsm_df)
zs_econ_df <- select(zs_it_df_clean, contains("ec"))
psych::alpha(zs_econ_df)##
## Reliability analysis
## Call: psych::alpha(x = zs_econ_df)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.82 0.76 0.61 4.6 0.018 4.3 1.6 0.58
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.78 0.82 0.86
## Duhachek 0.79 0.82 0.86
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## zs_econ_1 0.71 0.71 0.54 0.54 2.4 0.035 NA 0.54
## zs_econ_2 0.82 0.82 0.70 0.70 4.6 0.021 NA 0.70
## zs_econ_3 0.73 0.73 0.58 0.58 2.7 0.032 NA 0.58
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## zs_econ_1 276 0.89 0.88 0.81 0.73 3.8 1.9
## zs_econ_2 276 0.81 0.82 0.66 0.61 5.1 1.8
## zs_econ_3 276 0.87 0.87 0.78 0.70 4.1 1.8
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## zs_econ_1 0.17 0.16 0.15 0.10 0.20 0.14 0.09 0
## zs_econ_2 0.05 0.07 0.10 0.07 0.21 0.26 0.24 0
## zs_econ_3 0.10 0.15 0.14 0.14 0.21 0.18 0.08 0zs_it_df_clean$zs_econ_mean <- rowMeans(zs_econ_df)
t.test(zs_it_df_clean$zsm_mean, zs_it_df_clean$zs_econ_mean, paired = T)##
## Paired t-test
##
## data: zs_it_df_clean$zsm_mean and zs_it_df_clean$zs_econ_mean
## t = -20.994, df = 275, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -2.321494 -1.923434
## sample estimates:
## mean difference
## -2.122464Multi-national Dataset
bzsg <- read_csv(here("data", "bzsg.csv"))Subset
bz_df <- select(bzsg, zsm_1, zsm_2, zsm_3, zsm_4, zsm_5, zs_econ_1 , zs_econ_2 , zs_econ_3) Examining Data Fitness for Factor Analysis
Kaiser-Meyer Test – “The test measures sampling adequacy for each variable in the model and the complete model. The statistic is a measure of the proportion of variance among variables that might be common variance. The higher the proportion, the higher the KMO-value, the more suited the data is to factor analysis”
Values above .60 considered adequate, above .9 considered “marvelous” :)
psych::KMO(bz_df) ## Kaiser-Meyer-Olkin factor adequacy
## Call: psych::KMO(r = bz_df)
## Overall MSA = 0.89
## MSA for each item =
## zsm_1 zsm_2 zsm_3 zsm_4 zsm_5 zs_econ_1 zs_econ_2 zs_econ_3
## 0.92 0.88 0.93 0.89 0.91 0.86 0.87 0.92Multilevel CFA – Grouped by Country
bz_df_clean <- filter(bz_df, complete.cases(bz_df))
bz_df_clean$Country <- bzsg$Country
bzsg_zsm_cfa_model_1 <-
' bzsg_latent = ~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5 + zs_econ_1 + zs_econ_2 + zs_econ_3'
fit_1 <-cfa(bzsg_zsm_cfa_model_1, data = bz_df_clean, group = "Country")
fit_1_summary <- summary(fit_1, fit.measures=TRUE)
bzsg_zsm_cfa_model_2 <-
' zsm_variable = ~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5
zs_econ_variable =~ zs_econ_1 + zs_econ_2 + zs_econ_3'
fit_2 <-cfa(bzsg_zsm_cfa_model_2, data = bz_df_clean, group = "Country")
fit_2_summary <- summary(fit_2, fit.measures=TRUE)
fit_1_summary$fit## npar fmin chisq
## 1032.000 0.153 3478.208
## df pvalue baseline.chisq
## 860.000 0.000 36653.619
## baseline.df baseline.pvalue cfi
## 1204.000 0.000 0.926
## tli logl unrestricted.logl
## 0.897 -154124.974 -152385.870
## aic bic ntotal
## 310313.947 317887.339 11368.000
## bic2 rmsea rmsea.ci.lower
## 314607.769 0.107 0.104
## rmsea.ci.upper rmsea.ci.level rmsea.pvalue
## 0.111 0.900 0.000
## rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
## 0.050 1.000 0.080
## srmr
## 0.046fit_2_summary$fit## npar fmin chisq
## 1075.000 0.111 2525.322
## df pvalue baseline.chisq
## 817.000 0.000 36653.619
## baseline.df baseline.pvalue cfi
## 1204.000 0.000 0.952
## tli logl unrestricted.logl
## 0.929 -153648.531 -152385.870
## aic bic ntotal
## 309447.062 317336.011 11368.000
## bic2 rmsea rmsea.ci.lower
## 313919.792 0.089 0.085
## rmsea.ci.upper rmsea.ci.level rmsea.pvalue
## 0.093 0.900 0.000
## rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
## 0.050 1.000 0.080
## srmr
## 0.040anova(fit_1, fit_2) ## significantly better fit with two factors##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit_2 817 309447 317336 2525.3
## fit_1 860 310314 317887 3478.2 952.89 0.28291 43 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comparing Country-Level Means
bzsg_country_means <- read_csv(here("data", "bzsg_country_level.csv" ))CFA for Zero-Sum Mindset and Economic Zero-Sum Beliefs (no country-level grouping)
zero.sum.cfa.model.1<-' zero.sum.mindset.latent.variable =~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5 + zs_econ_1 + zs_econ_2 + zs_econ_3 '
zero.sum.cfa.model.2 <-' zero.sum.mindset.latent.variable =~ zsm_1 + zsm_2 + zsm_3 + zsm_4 + zsm_5
econ.latent.variable =~ zs_econ_1 + zs_econ_2 + zs_econ_3 '
fit.1<-cfa(zero.sum.cfa.model.1, data = bz_df_clean)
summary(fit.1, fit.measures=TRUE)## lavaan 0.6.17 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 16
##
## Number of observations 11368
##
## Model Test User Model:
##
## Test statistic 1660.973
## Degrees of freedom 20
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 32826.969
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.950
## Tucker-Lewis Index (TLI) 0.930
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -160345.201
## Loglikelihood unrestricted model (H1) -159514.714
##
## Akaike (AIC) 320722.401
## Bayesian (BIC) 320839.818
## Sample-size adjusted Bayesian (SABIC) 320788.972
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.085
## 90 Percent confidence interval - lower 0.082
## 90 Percent confidence interval - upper 0.088
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.991
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.034
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable =~
## zsm_1 1.000
## zsm_2 1.339 0.021 62.517 0.000
## zsm_3 0.572 0.016 36.521 0.000
## zsm_4 1.227 0.021 59.142 0.000
## zsm_5 0.737 0.017 42.189 0.000
## zs_econ_1 1.325 0.021 61.683 0.000
## zs_econ_2 1.275 0.021 61.791 0.000
## zs_econ_3 1.001 0.019 51.643 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .zsm_1 1.958 0.028 69.940 0.000
## .zsm_2 1.093 0.019 57.626 0.000
## .zsm_3 1.888 0.026 73.556 0.000
## .zsm_4 1.407 0.022 63.862 0.000
## .zsm_5 2.073 0.029 72.610 0.000
## .zs_econ_1 1.205 0.020 59.624 0.000
## .zs_econ_2 1.100 0.019 59.388 0.000
## .zs_econ_3 1.875 0.027 69.683 0.000
## zr.sm.mndst.l. 1.040 0.032 32.631 0.000fit.2 <-cfa(zero.sum.cfa.model.2, data = bz_df_clean)
summary(fit.2, fit.measures=TRUE)## lavaan 0.6.17 ended normally after 38 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 17
##
## Number of observations 11368
##
## Model Test User Model:
##
## Test statistic 995.189
## Degrees of freedom 19
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 32826.969
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.970
## Tucker-Lewis Index (TLI) 0.956
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -160012.309
## Loglikelihood unrestricted model (H1) -159514.714
##
## Akaike (AIC) 320058.617
## Bayesian (BIC) 320183.373
## Sample-size adjusted Bayesian (SABIC) 320129.349
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.067
## 90 Percent confidence interval - lower 0.064
## 90 Percent confidence interval - upper 0.071
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.027
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable =~
## zsm_1 1.000
## zsm_2 1.342 0.021 63.732 0.000
## zsm_3 0.577 0.015 37.446 0.000
## zsm_4 1.242 0.020 60.892 0.000
## zsm_5 0.733 0.017 42.824 0.000
## econ.latent.variable =~
## zs_econ_1 1.000
## zs_econ_2 0.969 0.011 87.704 0.000
## zs_econ_3 0.740 0.012 63.966 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## zero.sum.mindset.latent.variable ~~
## econ.ltnt.vrbl 1.312 0.028 46.952 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .zsm_1 1.906 0.028 68.321 0.000
## .zsm_2 0.991 0.020 49.980 0.000
## .zsm_3 1.865 0.026 73.019 0.000
## .zsm_4 1.290 0.022 58.841 0.000
## .zsm_5 2.050 0.029 71.890 0.000
## .zs_econ_1 1.062 0.021 51.522 0.000
## .zs_econ_2 0.943 0.019 50.135 0.000
## .zs_econ_3 1.838 0.027 68.182 0.000
## zr.sm.mndst.l. 1.092 0.033 33.204 0.000
## econ.ltnt.vrbl 1.968 0.041 48.552 0.000anova_model <- anova(fit.1, fit.2) ## significantly better fit with two factors
print(anova_model)##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit.2 19 320059 320183 995.19
## fit.1 20 320722 320840 1660.97 665.78 0.24182 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comparing Means
zsm_df <- select(bz_df_clean, zsm_1,zsm_2, zsm_3, zsm_4, zsm_5)
psych::alpha(zsm_df)##
## Reliability analysis
## Call: psych::alpha(x = zsm_df)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.75 0.75 0.72 0.37 3 0.0036 3.6 1.2 0.33
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.74 0.75 0.76
## Duhachek 0.74 0.75 0.76
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## zsm_1 0.70 0.70 0.66 0.37 2.3 0.0044 0.0192 0.33
## zsm_2 0.66 0.66 0.60 0.33 1.9 0.0051 0.0091 0.30
## zsm_3 0.75 0.75 0.71 0.43 3.0 0.0037 0.0130 0.44
## zsm_4 0.66 0.65 0.60 0.32 1.9 0.0052 0.0094 0.30
## zsm_5 0.74 0.74 0.70 0.41 2.8 0.0039 0.0159 0.39
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## zsm_1 11368 0.72 0.71 0.60 0.53 3.7 1.7
## zsm_2 11368 0.79 0.78 0.74 0.63 3.6 1.7
## zsm_3 11368 0.58 0.60 0.42 0.37 4.4 1.5
## zsm_4 11368 0.80 0.79 0.75 0.65 3.4 1.7
## zsm_5 11368 0.63 0.63 0.48 0.42 2.9 1.6bz_df_clean$zsm_mean <- rowMeans(zsm_df)
zs_econ_df <- select(bz_df_clean, contains("ec"))
psych::alpha(zs_econ_df)##
## Reliability analysis
## Call: psych::alpha(x = zs_econ_df)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.78 0.78 0.72 0.54 3.6 0.0036 3.7 1.4 0.5
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.77 0.78 0.79
## Duhachek 0.77 0.78 0.79
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## zs_econ_1 0.67 0.67 0.50 0.50 2.0 0.0062 NA 0.50
## zs_econ_2 0.64 0.64 0.47 0.47 1.8 0.0067 NA 0.47
## zs_econ_3 0.80 0.80 0.66 0.66 3.9 0.0038 NA 0.66
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## zs_econ_1 11368 0.85 0.85 0.75 0.65 3.6 1.7
## zs_econ_2 11368 0.86 0.86 0.78 0.68 3.6 1.7
## zs_econ_3 11368 0.79 0.79 0.59 0.53 4.0 1.7bz_df_clean$zs_econ_mean <- rowMeans(zs_econ_df)
t.test(bz_df_clean$zsm_mean, bz_df_clean$zs_econ_mean, paired = T)##
## Paired t-test
##
## data: bz_df_clean$zsm_mean and bz_df_clean$zs_econ_mean
## t = -11.05, df = 11367, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.12697425 -0.08871188
## sample estimates:
## mean difference
## -0.1078431Summarizing Mean Differences
library(dplyr)
# Create a list of dataset names and corresponding datasets
datasets <- list("US - Sample 1a" = zs_df_clean, "Italy - Sample 7" = zs_it_df_clean, "43 Nations - Country Level" = bzsg_country_means, "43 Nations - Individual Level" = bz_df_clean)
# Create an empty data frame to store the results
results_table <- data.frame(
Dataset = character(),
Rows = numeric(),
Mean_zsm_mean = numeric(),
SD_zsm_mean = numeric(),
Mean_zs_econ_mean = numeric(),
SD_zs_econ_mean = numeric(),
t_value = numeric(),
p_value = numeric(),
Cohens_d = numeric(),
stringsAsFactors = FALSE
)
# Iterate over each dataset
for (dataset_name in names(datasets)) {
# Extract the dataset
dataset <- datasets[[dataset_name]]
# Run the paired t-test
t_result <- t.test(dataset$zsm_mean, dataset$zs_econ_mean, paired = TRUE)
# Calculate mean difference
mean_difference <- mean(dataset$zsm_mean - dataset$zs_econ_mean)
# Calculate pooled standard deviation
pooled_sd <- sqrt(sum((dataset$zsm_mean - dataset$zs_econ_mean - mean_difference)^2) / (length(dataset$zsm_mean) - 1))
# Calculate Cohen's d
cohens_d <- mean_difference / pooled_sd
# Add the results to the data frame
results_table <- results_table %>%
add_row(
Dataset = dataset_name,
Rows = nrow(dataset),
Mean_zsm_mean = mean(dataset$zsm_mean),
SD_zsm_mean = sd(dataset$zsm_mean),
Mean_zs_econ_mean = mean(dataset$zs_econ_mean),
SD_zs_econ_mean = sd(dataset$zs_econ_mean),
t_value = t_result$statistic,
p_value = t_result$p.value,
Cohens_d = cohens_d
)
}
# Print the results table
print(results_table)## Dataset Rows Mean_zsm_mean SD_zsm_mean
## 1 US - Sample 1a 821 3.052132 1.3537702
## 2 Italy - Sample 7 276 2.174638 1.1879738
## 3 43 Nations - Country Level 43 3.665806 0.4327221
## 4 43 Nations - Individual Level 11368 3.619849 1.1762078
## Mean_zs_econ_mean SD_zs_econ_mean t_value p_value Cohens_d
## 1 4.321153 1.4287459 -25.437466 1.100186e-105 -0.8877737
## 2 4.297101 1.5830847 -20.993530 4.640507e-59 -1.2636620
## 3 3.760588 0.3491216 -2.660038 1.101510e-02 -0.4056519
## 4 3.727692 1.4238091 -11.049552 3.067044e-28 -0.1036341| Dataset | Rows | Mean_zsm_mean | SD_zsm_mean |
|---|---|---|---|
| US - Sample 1a | 821 | 3.052 | 1.354 |
| Italy - Sample 7 | 276 | 2.175 | 1.188 |
| 43 Nations - Country Level | 43 | 3.666 | 0.4327 |
| 43 Nations - Individual Level | 11368 | 3.62 | 1.176 |
| Mean_zs_econ_mean | SD_zs_econ_mean | t_value | p_value | Cohens_d |
|---|---|---|---|---|
| 4.321 | 1.429 | -25.44 | 1.1e-105 | -0.8878 |
| 4.297 | 1.583 | -20.99 | 4.641e-59 | -1.264 |
| 3.761 | 0.3491 | -2.66 | 0.01102 | -0.4057 |
| 3.728 | 1.424 | -11.05 | 3.067e-28 | -0.1036 |
Examining Correlations Between Economic and General ZSM
# BZSG
bzsg <- read_csv(here("data", "bzsg.csv"))
nrow(bzsg)## [1] 11368zs_econ_df <- select(bzsg, contains("ec"))
bzsg$zs_econ_mean <- rowMeans(zs_econ_df)
zsm_df <- select(bzsg, starts_with("zsm_"))
bzsg$zsm_mean <- rowMeans(zsm_df)
bzsg_country_means <- read_csv(here("data", "bzsg_country_level.csv" ))
# US 1
s1 <- read_csv(here( "data","s1a.csv"))
# Italy
s7 <- read_csv(here("data", "s7.csv"))
cor.test(bzsg$zs_econ_mean, bzsg$zsm_mean)##
## Pearson's product-moment correlation
##
## data: bzsg$zs_econ_mean and bzsg$zsm_mean
## t = 103.05, df = 11366, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.6853715 0.7043817
## sample estimates:
## cor
## 0.694998cor.test(s1$zs_econ_mean, s1$zsm_mean)##
## Pearson's product-moment correlation
##
## data: s1$zs_econ_mean and s1$zsm_mean
## t = 15.374, df = 819, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4183725 0.5246792
## sample estimates:
## cor
## 0.4732469cor.test(s7$zs_econ_mean, s7$zsm_mean)##
## Pearson's product-moment correlation
##
## data: s7$zs_econ_mean and s7$zsm_mean
## t = 5.0438, df = 274, p-value = 8.316e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1795875 0.3959201
## sample estimates:
## cor
## 0.2914763