The Cross-Battery Assessment (XBA) approach to identifying a specific learning disorder (SLD) is based on the postulate that deficits in cognitive abilities in the presence of otherwise average general intelligence are causally related to academic achievement weaknesses. To examine this postulate, we conducted a classification agreement analysis using the Woodcock-Johnson III Tests of Cognitive Abilities and Achievement. We examined the broad cognitive abilities of the Cattell-Horn-Carroll theory held to be meaningfully related to basic reading, reading comprehension, mathematics calculation, and mathematics reasoning across age groups. Results of analyses of 300 participants in three age groups (6-8, 9-13, and 14-19 years) indicated that the XBA method is very reliable and accurate in detecting true negatives. Mean specificity and negative predictive value were 92% and 89% across all broad cognitive abilities and academic domains. Mean sensitivity and positive predictive values, however, were generally quite low, indicating that this method is very poor at detecting true positives. Mean sensitivity and positive predictive value were 21% and 34% across all broad cognitive abilities and academic domains. In sum, results of this study do not support the use of the XBA method for identifying SLD. Implications of our findings for research and practice are discussed.