The answer briefed below. t-test when your independent variable has more than 2 groups.
What is t-test?
ANOVA determines whether three or more populations are statistically distinct from one another, while the t-test determines whether two populations are statistically different from one another. Both of them examine the variations in means and the variance between groups, but their methods for determining statistical significance differ.
These tests are run when the samples are independent of one another, the distributions are (about) normal, or there are a lot of samples (e.g., more than 50 in each group). Although more samples are preferable, the tests can be run with as little as 2 samples per condition.
When comparing healthy and ill individuals, we want to see if there are any appreciable differences in the serum levels of Proteins 1 through 4.
Proteins 1 & 2 have different group variances, although their protein concentration means differ by the same amount. In contrast, Proteins 3 & 4 show comparable variances, while Protein 4 has a bigger variation in protein concentration means between the patient groups.
Hence the briefing.
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