  We consider all radiative corrections to the total electron-positron cross
section showing how the renormalization group equation can be used to sum the
logarithmic contributions in two ways. First of all, one can sum leading-log
etc. contributions. A second summation shows how all logarithmic corrections
can be expressed in terms of log-independent contributions. Next, using
Stevenson's characterization of renormalization scheme, we examine scheme
dependence when using the second way of summing logarithms. The renormalization
scheme invariants that arise are then related to those of Stevenson. We
consider two choices of renormalization scheme, one resulting in two powers of
a running coupling, the second in an infinite series in the two loop running
constant. We then establish how the coupling constant arising in one
renormalization scheme can be expressed as a power series of the coupling in
any other scheme. Next we establish how by using different mass scale at each
order of perturbation theory, all renormalization scheme dependence can be
absorbed into these mass scales when one uses the second way of summing
logarithmic corrections. We then employ this approach to renormalization scheme
dependency to the effective potential in a scalar model, showing the result
that it is independent of the background field is scheme independent. The way
in which the "principle of minimal sensitivity" can be applied after summation
is then discussed.
