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A one-tailed $$t$$-test evaluates differences in only one specific, pre-determined direction. It places the entire extreme $$5\%$$ of the probability distribution into a single tail. This test is only appropriate when researchers have a strong theoretical justification to expect the difference to occur in that particular direction prior to data collection.

One-Tailed $$t$$-Test

A one-tailed test has a less extreme critical value than a two-tailed test, providing a better chance of rejecting the null hypothesis if the observed difference aligns with the predicted direction. However, if the sample mean differs in the unexpected direction, a one-tailed test offers zero chance of rejecting the null hypothesis, unlike a two-tailed test which can detect effects in either direction.

Comparing One-Tailed and Two-Tailed $$t$$-Tests

When is it considered appropriate for researchers to utilize a one-tailed $$t$$-test?

A researcher can appropriately decide to use a one-tailed $$t$$-test after initially reviewing their collected data, provided they notice that the difference between the groups occurs in only one direction.

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