Test-time adaptation (TTA) has demonstrated effectiveness in addressing distribution shifts between training and testing data by adjusting a given model on test samples. However, when faced with testing data that exhibit dynamic patterns, wherein a single test sample batch is drawn from various distribution, the traditional TTA methods, which typically follow a fixed pattern of estimating batch normalization (BN) statistics and then performing back-propagation, tend to experience performance degradation. The key reasons we observed are as follows: (i) different scenarios require different normalization approaches (such as instance normalization (IN) is optimal in mixture domains, but not for static domains) and (ii) back-propagation could potentially degrade the model and waste time. Based on these observations, in this paper, we introduce a novel one-size-fits-all approach, named distribution adaptive test-time adaptation (DA). DA is designed to adaptively select the appropriate batch normalization method and back-propagation approach. It utilizes an IN–based projection method to differentiate between various scenarios. Our method allows the model to achieve a more robust representation, enabling it to adapt effectively to both static and dynamic data patterns. Furthermore, our method avoids unnecessary or potentially harmful backward passes, paving the way for further enhancements. The results show that our method demonstrates robustness while maintaining good performance of the model. It can effectively respond to data stream patterns, and the selective back-propagation approach is more lightweight.