Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Statistical Tests Fundamendals OneSided vs. TwoSided Tests  
See also: types of error, hypothesis testing  
OneSided vs. TwoSided TestsSince making a decision is  statistically speaking  the selection of a threshold value on a onedimensional scale (i.e. on the argument axis of the probability density plot), we have to distinguish between two cases: first, one may ask whether a property lies above or below a predefined threshold (left figure, below). In this case we have to apply a onesided test. Secondly, one may be interested to determine whether a property is within certain boundaries. This question involves setting two boundaries and asks for the probability of an event lying either between or outside these boundaries (right figure). In this case we have to apply a twosided test.
Generally speaking, we base the decision on the value of a test
statistic, e.g. the average concentration of iron or the degree of "doneness"
of the pizza. This test statistic can be an average of a property, its
variance etc. The set of all possible values of this test statistic is
called the sample space. Our decision divides the sample space into two
mutually exclusive regions: the acceptance region and the rejection region.
When you look at the figure above, it immediately becomes clear why some
tests are called onesided and others are called twosided. Onesided tests
have one rejection region, i.e. you check whether the parameter of interest
is larger (or smaller) than a given value. Twosided tests are used when
we test a parameter for equivalence to a certain value. Deviations from
that value in both directions are rejected.


Home Statistical Tests Fundamendals OneSided vs. TwoSided Tests 