The item response theory (IRT) is widely used in many fields recently because it provides us the abilities of examinees and the difficulties of items simultaneously. Online IRT test systems are often equipped with the adaptive testing. Such a testing method selects the most appropriate items to examinees automatically. However, the item difficulty values remain the same even if the features of the examinees and the size of the items change. Calibration of the difficulty values is required in such cases, and the dually adaptive online IRT testing system works, where "dually adaptive" means that one is targeted to the adequate item selection and the other is targeted to the adjustment of the item difficulty values. Using this, the database in the system will automatically be growing and be updated. In this paper, we introduce such a novel system with applications.

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