Mokken models have recently started to become the preferred method of researchers from different fields in studies of nonparametric item response theory (NIRT). Despite increasing application of these models, some features of this type of modelling need further study and explanation. Invariant item ordering (IIO) is one of these areas, which the present study aims to exemplify using a real dataset and comparing the findings of different methods. The main purpose of this study is to check the IIO assumption for a large scale test by using different methods. Data relating to the high school placement test (applied in 2016) was investigated. The sample size was determined as being 250, which complies with NIRT. Two different methods have been used for dichotomous items in the IIO testing: rest-scores and P-matrix methods. The H[superscript T] coefficients were also calculated in order to define the placement of item response functions. Findings show that the test battery is not suitable for Mokken scaling. IIO property was not met for any of the tests, and findings from the different methods were not consistent with each other. As for the results, the rest-score method defined more items violating IIO properties than the P-matrix method for all the tests. The H[superscript T] coefficients were also estimated from the critical value, which shows that the tests do not have IIO properties. The conflicting results indicate that there is a need for new studies to investigate IIO empirically.