Final answer:
Connor Corporation has likely violated the quality of consistency by changing accounting methods for depreciation, which affects the comparability of financial statements over time.
Step-by-step explanation:
Connor Corporation's decision to allow their new accountant to use four different accounting methods for depreciation over four years likely violates the quality of consistency. Consistency in accounting refers to the use of the same accounting principles and methods from period to period by the same business entity. Consistent application provides comparability and enables users of financial statements to make meaningful comparisons between periods. If Connor Corporation is using different methods of depreciation, then it hinders the ability of stakeholders to track performance accurately and make informed decisions, thus diminishing the quality of comparability as well.