One Tailed and Two Tailed Tests
Consider a process control study in which we are interested in ensuring that photo-masks in a production process have mean line-widths of 500 micrometers. The null hypothesis, in this case, is that the mean line-width is 500 micrometers. Implicit in this statement is the need to flag photo-masks which have mean line-widths that are either greater or less than 500 micrometers. This translates into the alternative hypothesis that the mean line-widths are not equal to 500 micrometers.
This is a two-tailed alternative because it guards against alternatives in opposite directions; namely, that the line-widths are too small or too large.
Consider a study to ensure that a lot of light bulbs have a mean lifetime of at least 500 hours. The null hypothesis, in this case, is that the mean lifetime is greater than or equal to 500 hours. The complement or alternative hypothesis that is being guarded against is that the mean lifetime is less than 500 hours. This is an example of null and alternative hypotheses that is one-tailed. [1]
Two-tailed tests always use = and ≠ in the statistical hypotheses and are directionless in that the alternative hypothesis allows for either the greater than (>) or less than (<) possibility.
One-tailed tests are always directional and the alternative hypothesis uses either the greater than (>) or the less than (<) sign. A one-tailed test should only be used when the researcher knows for certain that the outcome of an experiment is going to occur only in one direction or the researcher is only interested in one direction of the experiment.
There are three basic ways to set up a null and alternate hypothesis.[2]
1.
Equal hypothesis verses not equal
hypothesis (two-tailed test)
H0: µ = some value
Ha: µ ≠ some value
2.
Equal hypothesis verses less than
hypothesis (left-tailed test)
H0: µ = some value
Ha: µ < some value
3.
Equal hypothesis verses greater than
hypothesis (right-tailed test)
H0: µ = some value
Ha: µ > some value
In one-tailed problems, the researcher is trying to prove that something is older, younger, higher, lower, more, less, greater, and so on. These words are considered directional words in that they indicate the direction of the focus of the research.
Note: Never use an equal sign (=) in the alternative hypothesis, Ha. You can have =, ≠,≤ and ≥ in the null hypothesis, H0.
Without these directional words, the alternative hypothesis of a one-tailed test cannot be established.
