In hypothesis testing, a one-tailed test (or what is also called, a directional test) is either a right-tailed or a left-tailed test, while a 2-tailed test (called, non-directional) is both right and left-tailed at the same time. A right-tailed test is applied when the research or alternative hypothesis indicates that the population parameter is greater than the hypothesized value. For example, to test if a population mean is greater than 20, we would use a right-tailed test. A right-tailed test is also called an upper -tailed test. Other keywords for right-tailed tests include more, higher, larger, increased, exceed, above, over, beyond, and so on. The critical value for a right-tailed test will always be positive and the critical or rejection region under the curve will be to the extreme right. Hence, right-tail. Note that the direction of the test is indicated in the alternative hypothesis, and not in the null hypothesis. In contrast to a right-tailed test, a left-tailed or lower-tailed test is used when the alternative hypothesis specifies that the population parameter is less than the hypothesized value. For example, testing if the mean of a population is less than 40. Other keywords for left-tailed tests include lower, smaller, decreased, below, under, reduced, and so on. In the distribution curve for left-tailed tests, the critical or rejection region will be at the extreme left. And for z tests & t tests, the critical values for left-tailed tests will be negative Note that the direction is not always immediately clear based on the wording of the problem. In some cases, you need to carefully consider the context to determine the direction of the test. For example, suppose we want to test if car A is better than car B. It could be that car A covers more distance than car B, given the same amount of time. In which case we write A > B for distance covered. It could also be that A is more battery efficient than B. That is, A consumes less battery power covering the same distance as B. In that case we write A < B for the alternative hypothesis. In essence, the word “better” should be interpreted in the context of the problem to determine the appropriate direction of the test. Other keywords like improved or worsened, stronger or weaker, outperform or underperform, and so on, should also be critically examined in context. Now, on the other hand, a two-tailed test is non-directional. That is, it does not commit to only one direction. It is used when the research hypothesis specifies that the population parameter is different from the hypothesized value. In essence, the parameter is either greater than or less than the hypothesized value. For example, testing if the mean of a population is not equal to 50. “Not equal to 50” could mean “greater than 50” or “less than 50”. Hence, it’s two-tailed. Other keywords or phrases for the alternative hypothesis in two-tailed tests include different from, changed, deviate from, inconsistent with, and so on. 2-tailed tests usually have two critical values -one on the left and another on the right. If the test statistic falls beyond any of them in a 2-tailed test, we will reject the null hypothesis and state that the result is significant. And that’s a quick overview of one-tailed and two-tailed tests. Thanks for watching.