One sample t-test, unpaired and paired two sample t-test, one tailed test and two tailed test.
Could you please provide some additional information? Are you seeking a theoretical example for teaching or examples from published research? Many thanks!
ok... theoretical examples:
we are talking about some variable that under same(similar) conditions gives values that are expected to scatter unimodally and symmetrically with finite variance around an (unknown) common center (µ) that can be estimated as the sample mean.
a) You measure the variable under a given condition. The individual measurements are independent. You want to test µ=µ0
b) You measure the variable under two different conditions (groups or samples) A and B (e.g. two species, two treatments, two habitats, ...). All measurements within and between the groups are indendent. You want to test µA=µB.
c) You measure the variable under two different conditions (groups or samples) A and B, but every one measurement of A is related to a "partner-measurement" in B, so there are pairs of measurments that are not independent (they share a common source of variance). For instance these pairs of measurements are taken from the same individual (e.g. before and after a treatment), or were obtained within the same assay. You want to test µA=µB. The common source of variance between paired values can be removed by considering the pair-wise differences Di=Ai-Bi (i=1...n), so the test is much more powerful when µD=0 is tested.
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