Onetailed test is also known as a directional hypothesis or test
That is a onetailedhypothesis because it specifies that the correlation must bepositive.
When should we use onetailed hypothesis testing?  …
It is Richard Shahinian's belief that a loudspeaker should radiate soundinto a room in much the same way that acoustic instruments do which means thatthe speaker should approach being omnidirectional.
While testing a hypothesis, we often talk of twotailed tests and onetailed tests. In the previous tests the critical region lay along both the tails of the distributions. That is, we did not want sample statistic ( say mean ) to be away from the population parameter (say mean) in either direction. The test for such a hypothesis is nondirectional or twosided or twotailed. A twotailed test of hypothesis will reject the null hypothesis H_{o}, if the sample statistic is significantly higher than or lower than the hypothesized population parameter. Thus in twotailed test the rejection (critical) region is located in both the tails.
Directional Tests  Emory University
Now our predetermined probability level is 95% i.e. 5% level of significance for this test. Both tests have the rejection (or critical) region of 5% i.e. 0.05. Now this rejection region is divided between both the tails of the distribution ( see figure 1 ) i.e. 2.5% or 0.25 in the upper tail and 2.5% or 0.25 in the upper tail and 2.5% or 0.25 in the lower tail since your hypothesis gives only a difference and not a direction. You will reject the null hypothesis on the basis that the sample mean falls into the area beyond 1.96 S.E. Otherwise if it falls into area 0.475 corresponds to 1.96 S.E. you can accept the null hypothesis.
As distinguished from the twotailed test, we can apply a directional  one sided i.e. onetailed test also because in some cases it is necessary to guard against only small values of (i.e. sample mean). Onetailed test is so called because the rejection region will be located in only onetail, which may either be on the upper or the lower side of the distribution depending upon the alternative ( H_{a} ) hypothesis formula. For example, we want to test a hypothesis that the average income per household is greater than $ 5000 against the alternative hypothesis that the income is $ 1000 or more. We will place all risk on the upperside of the theoretical sampling distribution and the test will be onetailed. On the other hand, if we are testing that the average income per household is $ 5000 against H_{a} that the income is less than $ 5000 or less, the risk is on the lower side of the distribution and the test will be one sided.
Relationship between direction and one or two tail
Hypotheses can have a direction. In particular, a directional hypothesis not only states that an effect exists, but also states the direction of the effect. In the terminology of hypothesis testing, this is known as the number of tails of the hypothesis:
 Avian genomes are small and streamlined compared with those of other amniotes, with fewer repetitive elements and less noncoding DNA (a typical bird genome consists of about 1.45 billion base pairs; h genomes are another billion base pairs longer). This condition has been suggested to represent a key adaptation for flight in birds, by reducing the metabolic costs associated with having large genome and cell sizes. However, the evolution of genome architecture in birds, or any other lineage, is difficult to study because genomic information is often absent for longextinct relatives. Organ et al. (2007) found that bonecell size correlates well with genome size in extant vertebrates, and used that relationship to estimate the genome sizes of 31 species of extinct dinosaur, including several species of extinct birds. Their results indicate that the small genomes typically associated with avian flight evolved in the saurischian dinosaur lineage between 230 and 250 million years ago, long before this lineage gave rise to the first birds. By comparison, ornithischian dinosaurs were inferred to have had much larger genomes, probably typical of ancestral Dinosauria. Using comparative genomic data, Organ et al. (2007) estimated that genomewide interspersed mobile elements, a class of repetitive DNA, comprised 5–12% of the total genome size in the saurischian dinosaur lineage, but was 7–19% of total genome size in ornithischian dinosaurs, suggesting that repetitive elements became less active in the saurischian lineage. These genomic characteristics should be added to the list of attributes previously considered avian, but now thought to have arisen in nonavian dinosaurs, such as feathers, pulmonary innovations, and parental care and nesting.
Test of hypothesis (onetail)  UNI Department of …

Is twotailed testing for directional research hypotheses …
The practical significance of this distinction is that you canuse a smaller sample to test a onetailed hypothesis.

hypothesis testing  SPSS from two  to one tailed test  …
Thus,strong selection of this kind (directional) leads to reduced variability in thepopulation.

the OTT is the one to call when testing a directional hypothesis
Thus,strong selection of this kind (directional) leads to reduced variability in thepopulation.
A one tailed hypothesis, or directional hypothesis, ..
Remember the example of testing the effect of antibiotics on mice in Lesson 7. The point of the study was to find out if the mice who were treated with the antibiotic would outlive those who were not treated (i.e., the control group). Are you surprised that the researcher did not hypothesize that the control group might outlive the treatment group? Would it make any difference in how the hypothesis testing were carried out? These questions raise the issue of directional testing, or onetailed vs twotailed tests.
this is known as the number of tails of the hypothesis: One tail
Now don't get confused  we're not testing to see if our mice have two tails! We're testing to see if the mean of the sample group is either less than or greater than the mean of the control group, which  in statistical terms  is considered to be a twodirection or twotailed test. Remember that the hypotheses were Ho:XbarA = XbarB and Ha: XbarA is not equal to XbarB. In this alternate hypothesis, all that has been said is that the two means are not the same, which would be true (a) if the mean of the sample group is higher than that of the control group or (b) if the mean of the sample group is lower than that of the control group. There is nothing in the phrasing of the hypothesis that stipulates the group A animals (treated) must actually have longer life spans as compared to the group B animals.
A onetailed test is sometimes called a directional test and a two ..
If the conclusion were to support the claim that the antibiotic prolonged group A life spans, then the researchers should use a directional alternate hypothesis, such as Ha: XbarA > XbarB. Here group A's life span is hypothesized to be greater (longer) than group B's (the control group). In this case, an alpha level of 0.05 implies that all 0.05 would have to appear in the right or high tail of the curve, which then is a onetailed or directional test, as shown in Figure 83. This figure shows that the critical tvalue will actually be smaller for the onetail test, that is, +1.65 instead of 1.96 or 2.00 from the twotail test. This happens because 95% of the area under the curve begins to accumulate from the leftmost side of the curve (including that tail) and includes less of the right side of the curve. The result is that t_{calc} can be smaller (1.65 instead of 1.96) and still cause Ho to be rejected.
See also: One Tailed Hypothesis.
To reiterate, if you are standing right at the gate (1.96) for a twotail test, then you have just barely met the p=0.05 requirement. However, if you are standing at the 1.96 point when running a onetail test, then you have already exceeded the 1.65 gate and the probability must be even more significant, say p=0.025. It's important to find the critical tvalue that is correct for the intended directional nature of the test.