Which test requires a larger sample size for efficacy in a two-tailed test scenario?

In statistical hypothesis testing, a two-tailed test requires a larger sample size compared to a one-tailed test to achieve the same level of statistical power. This is because a two-tailed test examines the possibility of an effect in both directions (i.e., it looks for differences that are either greater than or less than a particular value), which divides the significance level (alpha) between both tails of the distribution.

For instance, if the alpha level is set at 0.05 for a two-tailed test, this means that 0.025 is allocated to each tail. In comparison, a one-tailed test would allocate the entire alpha level of 0.05 to just one tail. Consequently, to maintain the same level of confidence and power when testing for differences, a two-tailed test necessitates a larger sample size to detect an effect of the same magnitude.

Regarding the other options, while the chi-square test and t-test can be either one-tailed or two-tailed based on the study design, they also fall under the broader scenarios that include two-tailed tests, which inherently require larger sample sizes for establishing statistical significance. The one-tailed test is particularly more efficient in terms of sample size needed to detect an