The purpose of this study was to evaluate the population invariance of equating functions across country subgroups in TIMSS 2015 mathematics tests in relation to the raw-score distribution, DIF, and DTF. We used equipercentile and IRT observed-score equating methods. The results of the study indicate that there is a relationship between the population invariance and raw-score and skewness differences for both equating methods. The association between the population invariance and the number of DIF items is explicit in the equipercentile equating but not clear in the IRT equating. Furthermore, we have observed that when the number of DIF items is high, if the DTF value is relatively low, the equating errors tend to be moderate to low.