Under ideal conditions where recall outcomes are binary (remembered or forgotten), the distribution follows a binomial model. Utilizing frequency to estimate probability yields an unbiased estimate, with the primary source of error stemming from the variance of the binomial distribution.
- X represents the number of successes
- N denotes the total number of trials
- p denotes the true probability of success
- The average variance per experiment is
- The standard deviation can be used to estimate the magnitude of error:
- In the worst-case scenario, where p equals 0.5, the error is
To achieve an error margin of 0.01 when p = 0.5, at least 2,500 trials are needed.