The statistical alternative is merely a logical complement to the null hypothesis. As the null hypothesis states that there is no difference between two (or more) alternatives, the statistical alternative simply states that there is a difference. It does not offer any conceptual or scientific explanation as to why the null was rejected. When the null is rejected, the statistical alternative is inferred to be true.
In turn, statistical alternatives may either be directional or not. When the alternative merely states that there is a difference, it is non-directional (it makes no guesses about which way the difference would lean). On the other hand, when the alternative specifies which way the results will lean, it is a directional alternative hypothesis.
An investigator is comparing two antihypertensive drugs: A, and B. The null hypothesis (H0) states that there is no difference between A and B. In other words, both A and B will cause blood pressure to fall by the same/ similar magnitude.
H0: A = B
The alternative hypothesis (Ha) could be stated in two ways:
- Ha: A ≠ B [A is not equal to B- there is a difference between A and B]
- Ha: A > B (or A < B) [A is superior to B (or vice-versa)]
The first alternative merely states that there is a difference between A and B but does not specify if either A or B is superior. Therefore, the first alternative is non-directional (two-tailed). This type of alternative is best used when the investigator cannot guess if one alternative will be superior to the other beforehand.
However, the second alternative specifies that either A or B is superior to the other. Therefore, the second alternative is directional (one-tailed). This is appropriate for situations where the investigator anticipates either A or B will be superior to the other. However, the investigator may not know the magnitude of the difference, and will both test the assumption (that A is superior to B (say), and obtain the magnitude of difference between A and B (if any).