t test for outlier detection

t test for detecting outliers.

Hi, it is possible to use a test for outlier detection in the
following way?

Consider the case we want to detect an outlier in
a set of n data points:
(p1,...,pN).

Consider x as outlier if

x- mean(x)
------------ > critical value
sqrt(var(x))

x- mean(x)
------------ < critical value
sqrt(var(x))

critical_value=t(1-alpha/2,N-1)

Most standard outlier test cannot be used to remove more than a single point or cannot be used for small data sets. However a t-test is usually unproblematic. Since if the degrees of freedom are small, a higher
value is needed to become an outlier which is quite what is expected.

Thanks for any remarks,

Tim.
.