One- and two-tailed tests

<p>In statistical <a href="/facts/Significance_testing/yv9RPF6U">significance testing</a>, a one-tailed test and a two-tailed test are alternative ways of computing the <a href="/facts/Statistical_significance/PMxjdlAu">statistical significance</a> of a <a href="/facts/Parameter/zFvVFMv9">parameter</a> inferred from a data set, in terms of a <a href="/facts/Test_statistic/IBwfN5Kx">test statistic</a>. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for <a href="/facts/Null_hypothesis/C8NwSE9J">null hypothesis</a> testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis.  
A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, left or right, but not both. An example can be whether a machine produces more than one-percent defective products. In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest (greater than or less than), the alternative hypothesis is accepted over the null hypothesis. Alternative names are one-sided and two-sided tests; the terminology "tail" is used because the extreme portions of distributions, where observations lead to rejection of the null hypothesis, are small and often "tail off" toward zero as in the <a href="/facts/Normal_distribution/UapjjPyQ">normal distribution</a>, colored in yellow, or "bell curve", pictured on the right and colored in green.
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One- and two-tailed tests open-in-new

One- and two-tailed tests