Final answer:
The statement is false; the independent t-test requires the data points to be independent. Degrees of freedom for a test of independence are calculated differently than stated, and a test of independence usually involves right-tailed tests based on a contingency table.
Step-by-step explanation:
The statement that the independent t-test is robust to violation of the independence assumption is false. The independent t-test requires that the data points are independent of one another. If this assumption is violated, the conclusions drawn from the test can be questionable. It is not to be confused with tests that assess the independence of categorical variables, which use chi-square distribution.
Regarding the subject of the question, the number of degrees of freedom in a test of independence is not simply the sample size minus one. Instead, it is calculated as the product of the number of categories minus one in each dimension, that is (number of rows - 1)(number of columns - 1), in a contingency table. This misinterpretation of degrees of freedom is common and thus important to clarify.
When a test of independence is conducted, it often uses right-tailed tests because we are typically interested in determining whether the observed frequencies are significantly greater than the expected frequencies under the hypothesis of independence. This is common in tests such as a goodness-of-fit test.