Example:
Prob( |t|>=2.665 | Degrees of Freedom=7 ) <=
0.03633
Characteristics:
This is not a test, but a distribution. The Student-t distribution, is
derived from the
Normal distribution. It is the distribution of the (mean/SD) of a
sample of Normal distributed values with unknown variance. This means that
this distribution should be used when the test parameter has a
Normal distribution and the variance is estimated from the same sample as
the mean value is.
The Student-t distribution varies with the number of items in the sample,
more specific, with the number of independent values from which the
variance is calculated. This number is called the Degrees of
Freedom of the distribution.
H0:
The distribution of t has mean 0.
Assumptions:
The values from which the mean and variance are calculated are themselves Normal
distributed.
Scale:
Interval
Procedure:
Calculate
t = ( Mean/(Estimated Standard Deviation) ) *
sqrt(Sample Size).
Degrees of Freedom = Number of independent values from which the variance
is calculated.
Other stochastic parameters have distributions that are related to the Student-t
distribution, e.g., the
Correlation coefficient
Level of significance:
Use a table to look up the level of significance associated with t and
the Degrees of Freedom.
Approximation:
If the Degrees of Freedom > 30, the distribution of t can
be approximated by a
Standard Normal Distribution.
Remarks:
Because of their popularity, tests based on this distribution are 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.
The name Student-t distribution is derived from the pen-name of the
man who first published it's properties. It has nothing to do with the
popularity of the tests based on it in introductory courses.
WARNING: the level of significance given here is only an approximation,
take care when using it! (use a table if necessary)