This paper presents a comprehensive statistical analysis comparing the NIST-standardized SHA-3 hash function against the original Keccak algorithm that won the SHA-3 competition. Through extensive empirical testing including avalanche effect analysis, statistical randomness tests (NIST SP 800-22), performance benchmarking, and bit-level correlation studies, we identify significant anomalies in SHA-3's design. Our findings reveal: (1) a 10-43× performance degradation in SHA-3 compared to Keccak without corresponding security improvements, (2) statistical deviations in runs tests and serial correlation patterns, (3) anomalous avalanche effect distributions in SHA-512, and (4) non-random Hamming distance patterns between SHA-3 and Keccak outputs. We demonstrate that the sole algorithmic difference—the padding scheme modification—introduces unexplained computational overhead and measurable statistical weaknesses. These findings raise critical questions about the standardization process and potential backdoor mechanisms in cryptographic standards.