The article presents new tests for checking if a time series has a unit root, which is a key concept in analyzing data trends. These tests are designed to be very effective, especially when the series has an unknown mean or trend. The researchers found that their modified test, based on the Dickey-Fuller t test, performs much better in such cases, even in small samples. This means that the new test can help researchers accurately analyze data trends, even when some key information is missing.