Created
November 10, 2025 22:40
-
-
Save LukasWallrich/01eae59cb003c143d1014f7a9a26e882 to your computer and use it in GitHub Desktop.
ML loss framing effect size calculation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| ``` r | |
| # ============================================ | |
| # ORIGINAL STUDY (Tversky & Kahneman, 1981) | |
| # ============================================ | |
| # Create contingency table | |
| original <- matrix(c( | |
| 109, 43, # Gain frame: 72% chose A, 28% chose B | |
| 34, 121 # Loss frame: 22% chose C, 78% chose D | |
| ), nrow = 2, byrow = TRUE) | |
| rownames(original) <- c("Gain frame", "Loss frame") | |
| colnames(original) <- c("Sure thing", "Gamble") | |
| print("Original Study Contingency Table:") | |
| #> [1] "Original Study Contingency Table:" | |
| print(original) | |
| #> Sure thing Gamble | |
| #> Gain frame 109 43 | |
| #> Loss frame 34 121 | |
| print(addmargins(original)) | |
| #> Sure thing Gamble Sum | |
| #> Gain frame 109 43 152 | |
| #> Loss frame 34 121 155 | |
| #> Sum 143 164 307 | |
| # Chi-square test | |
| original_chisq <- chisq.test(original, correct = FALSE) | |
| print(original_chisq) | |
| #> | |
| #> Pearson's Chi-squared test | |
| #> | |
| #> data: original | |
| #> X-squared = 76.411, df = 1, p-value < 2.2e-16 | |
| # Manual calculation to verify | |
| observed <- c(109, 43, 34, 121) | |
| expected <- original_chisq$expected | |
| manual_chisq <- sum((observed - as.vector(expected))^2 / as.vector(expected)) | |
| cat("\nManual χ² calculation:", round(manual_chisq, 2), "\n") | |
| #> | |
| #> Manual χ² calculation: 77.48 | |
| # ============================================ | |
| # REPLICATION STUDY | |
| # ============================================ | |
| # Total valid responses: 6344 - 73 = 6271 | |
| # Assume even split: 3135.5 per condition, round to 3136 and 3135 | |
| # Create contingency table | |
| replication <- matrix(c( | |
| round(3136 * 0.622), round(3136 * 0.378), # Gain: 62.2% A, 37.8% B | |
| round(3135 * 0.335), round(3135 * 0.665) # Loss: 33.5% C, 66.5% D | |
| ), nrow = 2, byrow = TRUE) | |
| rownames(replication) <- c("Gain frame", "Loss frame") | |
| colnames(replication) <- c("Sure thing", "Gamble") | |
| print("\n\nReplication Study Contingency Table:") | |
| #> [1] "\n\nReplication Study Contingency Table:" | |
| print(replication) | |
| #> Sure thing Gamble | |
| #> Gain frame 1951 1185 | |
| #> Loss frame 1050 2085 | |
| print(addmargins(replication)) | |
| #> Sure thing Gamble Sum | |
| #> Gain frame 1951 1185 3136 | |
| #> Loss frame 1050 2085 3135 | |
| #> Sum 3001 3270 6271 | |
| # Chi-square test | |
| replication_chisq <- chisq.test(replication, correct = FALSE) | |
| print(replication_chisq) | |
| #> | |
| #> Pearson's Chi-squared test | |
| #> | |
| #> data: replication | |
| #> X-squared = 518.22, df = 1, p-value < 2.2e-16 | |
| # Manual calculation to verify | |
| observed_rep <- c(1951, 1185, 1050, 2085) | |
| expected_rep <- replication_chisq$expected | |
| manual_chisq_rep <- sum((observed_rep - as.vector(expected_rep))^2 / as.vector(expected_rep)) | |
| cat("\nManual χ² calculation:", round(manual_chisq_rep, 2), "\n") | |
| #> | |
| #> Manual χ² calculation: 534.82 | |
| # ============================================ | |
| # COMPARISON | |
| # ============================================ | |
| cat("\n\n=== COMPARISON ===\n") | |
| #> | |
| #> | |
| #> === COMPARISON === | |
| cat( | |
| "Original Study: χ²(1) =", round(original_chisq$statistic, 2), | |
| ", p =", format.pval(original_chisq$p.value, digits = 4), "\n" | |
| ) | |
| #> Original Study: χ²(1) = 76.41 , p = < 2.2e-16 | |
| cat( | |
| "Replication Study: χ²(1) =", round(replication_chisq$statistic, 2), | |
| ", p =", format.pval(replication_chisq$p.value, digits = 4), "\n" | |
| ) | |
| #> Replication Study: χ²(1) = 518.22 , p = < 2.2e-16 | |
| cat("Reported in paper: χ²(1) = 516.41, p < .0001\n") | |
| #> Reported in paper: χ²(1) = 516.41, p < .0001 |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment