function may be assessed by noting that the observed values are to be considered as the
minimum value of two (independent) realisations of X and thus distributed according to the
distribution (minimum):
min() 1 (1 ())^2
FxX FxX (A.1)A fourth step is the experiment design in the sense of determining an appropriate number of
experiments to be performed for each set of free (controlled) variables. This process is
optimally to be seen a two phase process where in the first phase sufficient experiments are
performed for all sets of the free variables (say in the order of 10) such that the statistical
uncertainty will not be dominating the experiment results, i.e. the dependent variables. In the
second phase due consideration is given to the importance of the uncertainty associated with
the dependent variables and this may give rise to a modified experiment plan in the sense that
additional experiments are performed for some combinations of the free variables in order to
reduce the uncertainty of selected dependent variables. This issue is to be considered within
the context of decision analysis and requires an appropriate modelling of benefits and
consequences. If the second step is not actually included in the experiment planning it is
important that the subject is discussed in the light of the results obtained on the basis of the
phase one experiment plan. This will enable successive experimental works to benefit from
the achieved results.
The fifth step is to conduct the experiments according to the experiment plans. Emphasis
shall be given to ensure that the experiments are performed independently of each other.
Experiment results shall be documented and reported such that all value sets of free and
dependent variables may be identified. Notes shall furthermore be made in regard to any
observation made during the experiments, which could give rise to suspicion in regard to the
validity of the experiment results.
All notes made during the conduction of the experiments shall be discussed in regard to their
relevance for the interpretation of the experiment results as a part of the final assessment of
the experimental investigations.
The sixth step concerns the testing of the hypothesis; see also Lecture Notes on Basic
Probability and Statistics in Civil Engineering. The ingredients of this step will highly depend
on the postulated hypothesis and the characteristics of the dependent variables. However, as a
general guideline the following statistical tools are required
Plotting of test results in probability paper giving indications in regard to the family of
distribution functions, which may be adequate to describe the dependent variables. Testing in
regard to distribution hypothesis may also be conducted according to e.g. the U^2 test or the
Kolmogorov-Smirnov test. Correlation analyses shall finally be performed in order to test
whether or not dependent variables are correlated.
Variance analyses may be performed in order to verify hypothesis in regard to e.g. variations
in distribution parameters as a function of the free parameters. This may be considered as a
special application of groups testing. Group testing may be performed using the F-test
whereby it may be tested if groups of data with a common (but not necessarily known)
Annex B.4