Tatsuoka (1984) suggested several extended caution indices and their standardized versions that have been used as person-fit statistics by researchers such as Drasgow, Levine, and McLaughlin (1987), Glas and Meijer (2003), and Molenaar and Hoijtink (1990). However, these indices are only defined for tests with dichotomous items. This paper extends two of the popular standardized extended caution indices (Tatsuoka, 1984) for use with polytomous items and mixed-format tests. Two additional new person-fit statistics are obtained by applying the asymptotic standardization of person-fit statistics for mixed-format tests (Sinharay, 2016c). Detailed simulations are then performed to compute the Type I error rate and power of the four new person-fit statistics. Two real data illustrations follow. The new person-fit statistics appear to be satisfactory tools for assessing person fit for polytomous items and mixed-format tests. [This paper will be published in the "British Journal of Mathematical and Statistical Psychology."]