Extra-Sensory Perception: Part I. General Introduction: Appendix to Chapter 2. Mathematics of Probability Used in Evaluation

This is a methodological chapter from J. B. Rhine's 1934 foundational parapsychology text, explaining the statistical framework he uses to evaluate ESP card-guessing experiments. Rhine describes how he applies standard probability math to his five-symbol card trials (1/5 chance per guess), computing a "critical ratio" he calls X (deviation divided by probable error) as an index of how strongly results depart from chance — a value of 4 or above, representing 142-to-1 odds against chance, being his threshold for significance. The most distinctive contribution is Rhine's proposed formula for combining X-values across separate experimental groups: rather than pooling all results together (which he argues would dilute high-scoring subjects among low scorers), he takes the square root of the sum of squares of individual X-values to produce a composite anti-chance index. He acknowledges this formula is not found in existing statistical literature and is offered tentatively, defending it primarily on the grounds that it errs conservatively and that he verified it empirically by subdividing large datasets and confirming the formula reproduces the directly computed X-value. The chapter is essentially a transparent accounting of Rhine's statistical toolkit, written accessibly for non-mathematicians while engaging seriously with the problem of aggregating evidence across heterogeneous experimental conditions — a problem still live in meta-analysis today.

Extra-Sensory Perception: Part I. General Introduction: Appendix to Chapter 2. Mathematics of Probability Used in Evaluation

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