Example:
H0:
The mean value of the difference is zero.
Assumptions:
The difference is Normal distributed. If there is any reason to doubt this
assumption, use another, distribution-free, test (e.g.,
>
Wilcoxon Matched-Pairs Signed-Ranks Test).
Scale:
Interval
Procedure:
Calculate the Mean value and standard deviation (SD) of the differences,
determine the number of sample pairs, N, and Degrees of Freedom
(= N-1, in this case).
The test parameter is t = ( Mean / SD ) * sqrt( N ).
If necessary, Mean can be replaced by (Mean - expected value).
Level of Significance:
The significance levels of t for different Degrees of Freedom
are tabulated.
Approximation:
If the Degrees of Freedom > 30, the distribution of t can
be approximated by a
>
Standard Normal Distribution.
Remarks:
Because of its popularity, this test is very often applied indiscriminately,
when the underlying assumptions are invalid, i.e., when the observations are
not Normal distributed. This can lead to illusory high sensitivities.
Although it is the most powerfull test when the experimental data are
indeed Normal distributed, do not hesitate to use a distribution-free
test instead whenever there is some doubt about Normality (the
>
Wilcoxon Matched-Pairs Signed-Ranks Test is almost as sensitive).
The name Student-t test is derived from the pen-name of the man who
developed the test. It has nothing to do with the popularity of this test in
introductory courses.
WARNING: the level of significance given here is only an approximation,
take care when using it! (use a table if necessary)