The relationship between true ability (operationally defined as the number of items for which the examinee actually knew the correct answer) and the effects of guessing upon observed test variance was investigated. Three basic hypotheses were treated mathematically: there is no functional relationship between true ability and guessing success; there is a moderate functional relationship between true ability and guessing success; and there is a strong functional relationship between true ability and guessing success. Under the hypothesis of no functional relationship, true ability variance was found to be higher than the observed variance, suggesting that correction for guessing is advisable. Under the hypothesis of a moderate functional relationship, the observed and true test variances were about the same, implying no need for correction for guessing. Under the assumption of a strong functional relationship, observed test variance was much higher than the true variance (approximately twice as much), suggesting that approximately half of the observed test variance was due to guessing. The paper considered the appropriateness of correction for guessing dependent upon the assumed functional relationship between true ability and successful guessing. (Author)