PURPOSE

The Parsimony composite showed unacceptably low reliability (alpha = .48). This analysis examines the two items separately to understand:

Whether they correlate differently with punitiveness and correlates
Why they don’t hang together as a scale
Whether one item is more useful than the other

The two items (after reverse coding, higher = more punitive):

parsimony_1_R: “Criminal punishments should be as light as possible” (reversed)
- Rejecting this = wanting harsher punishment
- This is an EXTREME position (absolute minimization)
parsimony_2_R: “The state should not punish more than necessary” (reversed)
- Rejecting this = accepting excessive punishment
- This is more MODERATE (proportionality principle)

SETUP

library(tidyverse)
library(psych)
library(cocor)
library(knitr)

options(scipen = 999)
options(digits = 4)

# Load the cleaned data
df_clean <- read.csv("punishment_212_cleaned_data.csv", stringsAsFactors = FALSE)
cat("Loaded N =", nrow(df_clean), "\n\n")

## Loaded N = 496

SECTION 1: BASIC DESCRIPTIVES

1.1 Item Distributions

cat("=== PARSIMONY ITEM DESCRIPTIVES ===\n\n")

## === PARSIMONY ITEM DESCRIPTIVES ===

# Note: These are the REVERSED items (higher = more punitive)
cat("parsimony_1_R: 'Punishments should be as light as possible' (reversed)\n")

## parsimony_1_R: 'Punishments should be as light as possible' (reversed)

cat("  Interpreting high scores: Rejecting absolute minimization of punishment\n\n")

##   Interpreting high scores: Rejecting absolute minimization of punishment

cat("parsimony_2_R: 'State should not punish more than necessary' (reversed)\n")

## parsimony_2_R: 'State should not punish more than necessary' (reversed)

cat("  Interpreting high scores: Accepting excessive/disproportionate punishment\n\n")

##   Interpreting high scores: Accepting excessive/disproportionate punishment

# Descriptives
desc_table <- df_clean %>%
  summarise(
    across(c(parsimony_1_R, parsimony_2_R, parsimony_comp), 
           list(
             Mean = ~mean(., na.rm = TRUE),
             SD = ~sd(., na.rm = TRUE),
             Median = ~median(., na.rm = TRUE)
           ))
  ) %>%
  pivot_longer(everything()) %>%
  separate(name, into = c("Variable", "Stat"), sep = "_(?=[^_]+$)") %>%
  pivot_wider(names_from = Stat, values_from = value)

print(as.data.frame(desc_table), row.names = FALSE)

##        Variable  Mean    SD Median
##   parsimony_1_R 5.417 1.553      6
##   parsimony_2_R 2.996 1.667      3
##  parsimony_comp 4.207 1.306      4

cat("\n")

# Distribution comparison
cat("Distribution of Responses (1-7 scale):\n\n")

## Distribution of Responses (1-7 scale):

cat("parsimony_1_R:\n")

## parsimony_1_R:

print(table(df_clean$parsimony_1_R))

## 
##   1   2   3   4   5   6   7 
##  12  21  28  60  88 140 147

cat("\nparsimony_2_R:\n")

## 
## parsimony_2_R:

print(table(df_clean$parsimony_2_R))

## 
##   1   2   3   4   5   6   7 
## 108 107 116  84  33  21  27

1.2 Cross-tabulation

cat("\n=== CROSS-TABULATION OF ITEMS ===\n\n")

## 
## === CROSS-TABULATION OF ITEMS ===

# How do people respond to both items?
crosstab <- table(df_clean$parsimony_1_R, df_clean$parsimony_2_R)
cat("Rows = parsimony_1_R (light as possible), Columns = parsimony_2_R (not more than necessary)\n\n")

## Rows = parsimony_1_R (light as possible), Columns = parsimony_2_R (not more than necessary)

print(crosstab)

##    
##      1  2  3  4  5  6  7
##   1 10  0  1  0  0  0  1
##   2  9  6  1  5  0  0  0
##   3  9  7  5  4  2  1  0
##   4 15 15 15 11  4  0  0
##   5 21 22 30  9  5  1  0
##   6 18 36 40 27 10  8  1
##   7 26 21 24 28 12 11 25

# Correlation between items
item_cor <- cor(df_clean$parsimony_1_R, df_clean$parsimony_2_R, use = "pairwise.complete.obs")
cat(sprintf("\nCorrelation between items: r = %.2f\n", item_cor))

## 
## Correlation between items: r = 0.31

cat("(This explains the low alpha - items only moderately correlated)\n")

## (This explains the low alpha - items only moderately correlated)

1.3 Mean Comparison

cat("\n=== MEAN COMPARISON ===\n\n")

## 
## === MEAN COMPARISON ===

# Paired t-test
t_result <- t.test(df_clean$parsimony_1_R, df_clean$parsimony_2_R, paired = TRUE)

cat(sprintf("parsimony_1_R Mean: %.2f (SD = %.2f)\n", 
            mean(df_clean$parsimony_1_R, na.rm = TRUE),
            sd(df_clean$parsimony_1_R, na.rm = TRUE)))

## parsimony_1_R Mean: 5.42 (SD = 1.55)

cat(sprintf("parsimony_2_R Mean: %.2f (SD = %.2f)\n", 
            mean(df_clean$parsimony_2_R, na.rm = TRUE),
            sd(df_clean$parsimony_2_R, na.rm = TRUE)))

## parsimony_2_R Mean: 3.00 (SD = 1.67)

cat(sprintf("\nPaired t-test: t(%d) = %.2f, p = %.4f\n", 
            t_result$parameter, t_result$statistic, t_result$p.value))

## 
## Paired t-test: t(495) = 28.56, p = 0.0000

# Effect size
mean_diff <- mean(df_clean$parsimony_1_R - df_clean$parsimony_2_R, na.rm = TRUE)
sd_diff <- sd(df_clean$parsimony_1_R - df_clean$parsimony_2_R, na.rm = TRUE)
d <- mean_diff / sd_diff
cat(sprintf("Cohen's d = %.2f\n", d))

## Cohen's d = 1.28

cat("\nInterpretation:\n")

## 
## Interpretation:

if(mean(df_clean$parsimony_1_R, na.rm = TRUE) > mean(df_clean$parsimony_2_R, na.rm = TRUE)) {
  cat("People are MORE willing to reject 'light as possible' than 'not more than necessary'\n")
  cat("This makes sense: rejecting proportionality is more extreme than rejecting minimization\n")
} else {
  cat("People are LESS willing to reject 'light as possible' than 'not more than necessary'\n")
}

## People are MORE willing to reject 'light as possible' than 'not more than necessary'
## This makes sense: rejecting proportionality is more extreme than rejecting minimization

SECTION 2: CORRELATIONS WITH PUNITIVENESS

2.1 Correlations with Punitiveness Aggregate

cat("=== CORRELATIONS WITH PUNITIVENESS ===\n\n")

## === CORRELATIONS WITH PUNITIVENESS ===

# Correlation of each item with the OTHER punitiveness measures
# (excluding parsimony from the aggregate for this)

# Create punitiveness without parsimony
df_clean$punitiveness_no_parsimony <- rowMeans(
  df_clean[, c("punishmore_comp", "threestrikes_comp", "LWOP", "deathpenalty")],
  na.rm = TRUE
)
df_clean$punitiveness_no_parsimony_z <- scale(df_clean$punitiveness_no_parsimony)[,1]

# Also include Sentence_z
df_clean$punitiveness_no_pars_full <- rowMeans(
  cbind(df_clean$punitiveness_no_parsimony_z, df_clean$Sentence_z),
  na.rm = TRUE
)

cat("Correlations with Punitiveness (excluding parsimony from DV):\n\n")

## Correlations with Punitiveness (excluding parsimony from DV):

cor1 <- cor.test(df_clean$parsimony_1_R, df_clean$punitiveness_no_pars_full)
cor2 <- cor.test(df_clean$parsimony_2_R, df_clean$punitiveness_no_pars_full)

cat(sprintf("parsimony_1_R ('light as possible' R): r = %.3f, p < .001\n", cor1$estimate))

## parsimony_1_R ('light as possible' R): r = 0.424, p < .001

cat(sprintf("parsimony_2_R ('not more than necessary' R): r = %.3f, p < .001\n", cor2$estimate))

## parsimony_2_R ('not more than necessary' R): r = 0.417, p < .001

# Steiger test comparing the two
r12 <- cor(df_clean$parsimony_1_R, df_clean$parsimony_2_R, use = "pairwise.complete.obs")
n <- sum(complete.cases(df_clean[, c("parsimony_1_R", "parsimony_2_R", "punitiveness_no_pars_full")]))

steiger <- cocor.dep.groups.overlap(
  r.jk = cor1$estimate,
  r.jh = cor2$estimate,
  r.kh = r12,
  n = n,
  test = "steiger1980"
)

cat(sprintf("\nSteiger's Z comparing item correlations: Z = %.2f, p = %.4f\n",
            steiger@steiger1980$statistic, steiger@steiger1980$p.value))

## 
## Steiger's Z comparing item correlations: Z = 0.16, p = 0.8739

cat("Interpretation: ", 
    ifelse(steiger@steiger1980$p.value < .05, 
           "Items correlate DIFFERENTLY with punitiveness",
           "Items correlate SIMILARLY with punitiveness"), "\n")

## Interpretation:  Items correlate SIMILARLY with punitiveness

2.2 Correlations with Other Punitiveness Components

cat("\n=== CORRELATIONS WITH PUNITIVENESS COMPONENTS ===\n\n")

## 
## === CORRELATIONS WITH PUNITIVENESS COMPONENTS ===

punitiveness_components <- c("punishmore_comp", "threestrikes_comp", "LWOP", 
                              "deathpenalty", "Sentence_z")
component_labels <- c("Punish More", "Three Strikes", "LWOP", "Death Penalty", "Sentence")

# Create correlation table
cor_table <- data.frame(Component = component_labels)

cor_table$parsimony_1_R <- sapply(punitiveness_components, function(var) {
  round(cor(df_clean$parsimony_1_R, df_clean[[var]], use = "pairwise.complete.obs"), 2)
})

cor_table$parsimony_2_R <- sapply(punitiveness_components, function(var) {
  round(cor(df_clean$parsimony_2_R, df_clean[[var]], use = "pairwise.complete.obs"), 2)
})

cor_table$Difference <- cor_table$parsimony_1_R - cor_table$parsimony_2_R

print(as.data.frame(cor_table), row.names = FALSE)

##      Component parsimony_1_R parsimony_2_R Difference
##    Punish More          0.48          0.53      -0.05
##  Three Strikes          0.21          0.42      -0.21
##           LWOP          0.32          0.28       0.04
##  Death Penalty          0.36          0.36       0.00
##       Sentence          0.26          0.18       0.08

cat("\nPositive Difference = parsimony_1_R correlates more strongly\n")

## 
## Positive Difference = parsimony_1_R correlates more strongly

cat("Negative Difference = parsimony_2_R correlates more strongly\n")

## Negative Difference = parsimony_2_R correlates more strongly

SECTION 3: CORRELATIONS WITH CORRELATE CLUSTERS

3.1 Cluster-Level Correlations

cat("=== CORRELATIONS WITH CORRELATE CLUSTERS ===\n\n")

## === CORRELATIONS WITH CORRELATE CLUSTERS ===

cluster_vars <- c("crime_concerns_agg", "emotions_agg", "hostile_agg", "personality_agg")
cluster_labels <- c("Crime Concerns", "Emotions", "Hostile Aggression", "Personality")

cluster_cor_table <- data.frame(Cluster = cluster_labels)

cluster_cor_table$parsimony_1_R <- sapply(cluster_vars, function(var) {
  round(cor(df_clean$parsimony_1_R, df_clean[[var]], use = "pairwise.complete.obs"), 2)
})

cluster_cor_table$parsimony_2_R <- sapply(cluster_vars, function(var) {
  round(cor(df_clean$parsimony_2_R, df_clean[[var]], use = "pairwise.complete.obs"), 2)
})

cluster_cor_table$parsimony_comp <- sapply(cluster_vars, function(var) {
  round(cor(df_clean$parsimony_comp, df_clean[[var]], use = "pairwise.complete.obs"), 2)
})

cluster_cor_table$Difference <- cluster_cor_table$parsimony_1_R - cluster_cor_table$parsimony_2_R

print(as.data.frame(cluster_cor_table), row.names = FALSE)

##             Cluster parsimony_1_R parsimony_2_R parsimony_comp Difference
##      Crime Concerns          0.11          0.19           0.18      -0.08
##            Emotions          0.33          0.34           0.41      -0.01
##  Hostile Aggression          0.35          0.45           0.49      -0.10
##         Personality          0.20          0.43           0.39      -0.23

3.2 Construct-Level Correlations

cat("\n=== CORRELATIONS WITH INDIVIDUAL CONSTRUCTS ===\n\n")

## 
## === CORRELATIONS WITH INDIVIDUAL CONSTRUCTS ===

construct_vars <- c(
  "crime_rates_comp", "fear_comp",
  "hatred_comp", "anger_comp",
  "exclusion_comp", "degradation_comp", "suffering_comp",
  "prisonvi_comp", "harsh_comp", "revenge_comp",
  "rwa_comp", "sdo_comp", "venge_comp", "vprone_comp",
  "raceresent_comp", "bloodsports_comp"
)

construct_labels <- c(
  "Crime Rates", "Fear",
  "Hatred", "Anger",
  "Exclusion", "Degradation", "Suffering",
  "Prison Violence", "Harsh Conditions", "Revenge",
  "RWA", "SDO", "Vengefulness", "Violence Prone",
  "Racial Resentment", "Blood Sports"
)

construct_cor_table <- data.frame(Construct = construct_labels)

construct_cor_table$parsimony_1_R <- sapply(construct_vars, function(var) {
  round(cor(df_clean$parsimony_1_R, df_clean[[var]], use = "pairwise.complete.obs"), 2)
})

construct_cor_table$parsimony_2_R <- sapply(construct_vars, function(var) {
  round(cor(df_clean$parsimony_2_R, df_clean[[var]], use = "pairwise.complete.obs"), 2)
})

construct_cor_table$Difference <- construct_cor_table$parsimony_1_R - construct_cor_table$parsimony_2_R

# Sort by difference
construct_cor_table <- construct_cor_table %>% arrange(desc(Difference))

print(as.data.frame(construct_cor_table), row.names = FALSE)

##          Construct parsimony_1_R parsimony_2_R Difference
##        Crime Rates          0.24          0.21       0.03
##            Revenge          0.25          0.24       0.01
##              Anger          0.25          0.25       0.00
##          Exclusion          0.34          0.35      -0.01
##             Hatred          0.35          0.36      -0.01
##          Suffering          0.25          0.33      -0.08
##                RWA          0.28          0.37      -0.09
##       Vengefulness          0.00          0.10      -0.10
##  Racial Resentment          0.29          0.40      -0.11
##    Prison Violence          0.28          0.41      -0.13
##   Harsh Conditions          0.34          0.48      -0.14
##               Fear         -0.02          0.12      -0.14
##        Degradation          0.24          0.38      -0.14
##     Violence Prone          0.20          0.35      -0.15
##                SDO          0.15          0.37      -0.22
##       Blood Sports         -0.12          0.10      -0.22

cat("\nConstructs where items diverge most (|Diff| > .05):\n")

## 
## Constructs where items diverge most (|Diff| > .05):

print(construct_cor_table %>% filter(abs(Difference) > 0.05), row.names = FALSE)

##          Construct parsimony_1_R parsimony_2_R Difference
##          Suffering          0.25          0.33      -0.08
##                RWA          0.28          0.37      -0.09
##       Vengefulness          0.00          0.10      -0.10
##  Racial Resentment          0.29          0.40      -0.11
##    Prison Violence          0.28          0.41      -0.13
##   Harsh Conditions          0.34          0.48      -0.14
##               Fear         -0.02          0.12      -0.14
##        Degradation          0.24          0.38      -0.14
##     Violence Prone          0.20          0.35      -0.15
##                SDO          0.15          0.37      -0.22
##       Blood Sports         -0.12          0.10      -0.22

SECTION 4: H2 TEST FOR EACH ITEM

cat("=== H2 (HOSTILE > CRIME) FOR EACH PARSIMONY ITEM ===\n\n")

## === H2 (HOSTILE > CRIME) FOR EACH PARSIMONY ITEM ===

# parsimony_1_R
r1_hostile <- cor(df_clean$parsimony_1_R, df_clean$hostile_agg, use = "pairwise.complete.obs")
r1_crime <- cor(df_clean$parsimony_1_R, df_clean$crime_concerns_agg, use = "pairwise.complete.obs")
r_hc <- cor(df_clean$hostile_agg, df_clean$crime_concerns_agg, use = "pairwise.complete.obs")
n <- nrow(df_clean)

steiger1 <- cocor.dep.groups.overlap(r1_hostile, r1_crime, r_hc, n, test = "steiger1980")

cat("parsimony_1_R ('light as possible' reversed):\n")

## parsimony_1_R ('light as possible' reversed):

cat(sprintf("  r(Hostile) = %.3f, r(Crime) = %.3f\n", r1_hostile, r1_crime))

##   r(Hostile) = 0.346, r(Crime) = 0.107

cat(sprintf("  Difference = %.3f, Z = %.2f, p = %.4f\n", 
            r1_hostile - r1_crime, steiger1@steiger1980$statistic, steiger1@steiger1980$p.value))

##   Difference = 0.240, Z = 4.98, p = 0.0000

cat(sprintf("  H2 Supported: %s\n\n", 
            ifelse(r1_hostile > r1_crime & steiger1@steiger1980$p.value < .05, "YES", "NO")))

##   H2 Supported: YES

# parsimony_2_R
r2_hostile <- cor(df_clean$parsimony_2_R, df_clean$hostile_agg, use = "pairwise.complete.obs")
r2_crime <- cor(df_clean$parsimony_2_R, df_clean$crime_concerns_agg, use = "pairwise.complete.obs")

steiger2 <- cocor.dep.groups.overlap(r2_hostile, r2_crime, r_hc, n, test = "steiger1980")

cat("parsimony_2_R ('not more than necessary' reversed):\n")

## parsimony_2_R ('not more than necessary' reversed):

cat(sprintf("  r(Hostile) = %.3f, r(Crime) = %.3f\n", r2_hostile, r2_crime))

##   r(Hostile) = 0.445, r(Crime) = 0.189

cat(sprintf("  Difference = %.3f, Z = %.2f, p = %.4f\n", 
            r2_hostile - r2_crime, steiger2@steiger1980$statistic, steiger2@steiger1980$p.value))

##   Difference = 0.256, Z = 5.53, p = 0.0000

cat(sprintf("  H2 Supported: %s\n\n", 
            ifelse(r2_hostile > r2_crime & steiger2@steiger1980$p.value < .05, "YES", "NO")))

##   H2 Supported: YES

# Composite for comparison
rc_hostile <- cor(df_clean$parsimony_comp, df_clean$hostile_agg, use = "pairwise.complete.obs")
rc_crime <- cor(df_clean$parsimony_comp, df_clean$crime_concerns_agg, use = "pairwise.complete.obs")

steigerc <- cocor.dep.groups.overlap(rc_hostile, rc_crime, r_hc, n, test = "steiger1980")

cat("parsimony_comp (composite - for comparison):\n")

## parsimony_comp (composite - for comparison):

cat(sprintf("  r(Hostile) = %.3f, r(Crime) = %.3f\n", rc_hostile, rc_crime))

##   r(Hostile) = 0.490, r(Crime) = 0.184

cat(sprintf("  Difference = %.3f, Z = %.2f, p = %.4f\n", 
            rc_hostile - rc_crime, steigerc@steiger1980$statistic, steigerc@steiger1980$p.value))

##   Difference = 0.306, Z = 6.70, p = 0.0000

cat(sprintf("  H2 Supported: %s\n", 
            ifelse(rc_hostile > rc_crime & steigerc@steiger1980$p.value < .05, "YES", "NO")))

##   H2 Supported: YES

SECTION 5: INTERPRETATION

cat("\n")

cat(paste(rep("=", 70), collapse = ""), "\n")

## ======================================================================

cat("INTERPRETATION AND RECOMMENDATIONS\n")

## INTERPRETATION AND RECOMMENDATIONS

cat(paste(rep("=", 70), collapse = ""), "\n\n")

## ======================================================================

cat("WHY THE LOW RELIABILITY?\n\n")

## WHY THE LOW RELIABILITY?

cat("The two items measure related but distinct constructs:\n\n")

## The two items measure related but distinct constructs:

cat("parsimony_1_R: 'Punishments should be as light as possible'\n")

## parsimony_1_R: 'Punishments should be as light as possible'

cat("  - This is an ABSOLUTIST position\n")

##   - This is an ABSOLUTIST position

cat("  - Rejecting it means wanting SOME level of punishment (most people)\n")

##   - Rejecting it means wanting SOME level of punishment (most people)

cat("  - Higher variance, more central tendency\n\n")

##   - Higher variance, more central tendency

cat("parsimony_2_R: 'State should not punish more than necessary'\n")

## parsimony_2_R: 'State should not punish more than necessary'

cat("  - This is a PROPORTIONALITY principle\n")

##   - This is a PROPORTIONALITY principle

cat("  - Rejecting it means accepting EXCESSIVE punishment\n")

##   - Rejecting it means accepting EXCESSIVE punishment

cat("  - This is a more EXTREME position to reject\n\n")

##   - This is a more EXTREME position to reject

cat("The items ask fundamentally different questions:\n")

## The items ask fundamentally different questions:

cat("  - Item 1: Do you want ANY punishment? (Most say yes)\n")

##   - Item 1: Do you want ANY punishment? (Most say yes)

cat("  - Item 2: Do you want EXCESSIVE punishment? (More variation)\n\n")

##   - Item 2: Do you want EXCESSIVE punishment? (More variation)

cat("RECOMMENDATION:\n\n")

## RECOMMENDATION:

# Compare correlations
mean_r1 <- mean(abs(c(r1_hostile, r1_crime)))
mean_r2 <- mean(abs(c(r2_hostile, r2_crime)))

if(mean_r1 > mean_r2) {
  cat("parsimony_1_R shows STRONGER correlations with psychological factors.\n")
  cat("Consider using parsimony_1_R alone or reporting items separately.\n")
} else {
  cat("parsimony_2_R shows STRONGER correlations with psychological factors.\n")
  cat("Consider using parsimony_2_R alone or reporting items separately.\n")
}

## parsimony_2_R shows STRONGER correlations with psychological factors.
## Consider using parsimony_2_R alone or reporting items separately.

cat("\nAlternatively, given low reliability, consider:\n")

## 
## Alternatively, given low reliability, consider:

cat("  1. Dropping parsimony from the punitiveness aggregate\n")

##   1. Dropping parsimony from the punitiveness aggregate

cat("  2. Reporting results with and without parsimony\n")

##   2. Reporting results with and without parsimony

cat("  3. Discussing this as a measurement limitation\n")

##   3. Discussing this as a measurement limitation

SECTION 6: SAVE OUTPUTS

cat("\n=== SAVING OUTPUTS ===\n\n")

## 
## === SAVING OUTPUTS ===

# Save correlation tables
write.csv(construct_cor_table, "parsimony_items_construct_correlations.csv", row.names = FALSE)
cat("Saved: parsimony_items_construct_correlations.csv\n")

## Saved: parsimony_items_construct_correlations.csv

write.csv(cluster_cor_table, "parsimony_items_cluster_correlations.csv", row.names = FALSE)
cat("Saved: parsimony_items_cluster_correlations.csv\n")

## Saved: parsimony_items_cluster_correlations.csv

cat("\n")

cat(paste(rep("=", 70), collapse = ""), "\n")

## ======================================================================

cat("PARSIMONY ANALYSIS COMPLETE\n")

## PARSIMONY ANALYSIS COMPLETE

cat(paste(rep("=", 70), collapse = ""), "\n")

## ======================================================================

Punishment Study 2.1.2 - Parsimony Items Analysis

DGK

January 2026