Multiple measurements from the same set of subjects cannot be treated as separate, unrelated data sets
This point is well taken, and it is easy to make a mistake. Treating repeated measurements as if they were separate artificially inflates the sample size and may result in misleading p-values. It reminds me of the importance of study design: often, statistical mistakes reflect structural problems in how evidence was collected and analyzed.
The means of two independent samples may be compared for a statistically significant difference by the unpaired or independent samples t-test
A significant advantage of the unpaired t-test is that, for moderate sample sizes, it has high statistical power to compare two groups. That is efficient for clinical trials or public health studies where you’re comparing outcomes of treatment versus control groups. It creates familiarity in hypothesis testing, which simplifies the interpretation of results in different disciplines
Numerical data that are normally distributed can be analyzed with parametric tests, that is, tests which are based on the parameters that define a normal distribution curve.
This clarifies why normality is such a basic assumption. It’s not simply a default rule; parametric tests, such as the t-test, for instance, depend on the parameters of the distribution (mean and SD) to resemble the population. When the distribution is off, those numbers do not accurately reflect the data, which can be misleading for the results.