What has been described is only prerequisite of the analysis. The analysis proper of three steps:
a) identifying environments;
b) arranging distribution;
c) comparing distributions o units.
Before proceeding to exemplification the analysis it is necessary to define the main terms used here - environment and distribution..
Environment is listing the units of the same type appearing before and after the selected unit in a certain utterance. A limit of a large unit (the beginning or the end of a word if we analyse morphs) is considered to be a "unit of the same type". For example the environment of the morph [s] in the utterance we segmented is: | ba:k|_ | #, where # marks the end of the word. The environment of[ ba:k] in the same utterance is #|_|s. |_| mar the position of the respective unit. This is the first step of the analyses.
Distribution is the sum of all environments the selected unit can appear. Making up distributions of units is the second step of the analysis. The distribution of the morph [ba:k] is:
#|_|#
#|_|s#
#|_|t#
#|_|ing#
#|_|er#
The distribution of the morph [s] is composed of # to the right and any morph or a group of morph which call "verbs" and which are ended with [p], [f], [t] or [k], e.g. jump, cut, cough, look.
The nix and the final step of the procedure is comparing distributions of units. If we take the distribution of |s| as it was described above look what other units of the same type can appear in the environments of the distribution we find there |t| and |ing|. These units make contrasts of the utterances in which they are used and thus the relations of their distributions in named contrastive. Units in contrastive distribution are considered to be different.
But if compare the distribution of |ing| and |s| we notice that the distribution of the former is broader. We find |ing| after all units we call "verbs" irrespective of the sound they have at the end. We find |ing| in "crossing" and "moving". In these environments we cannot find |s|. I n the environment |cros|_|# we find |t| or |iz| - "crossed", "crosses". I n the environment |mu:v|_|# we find |d| or |z|:."moved", "moves". The unit |t| is non-contrastive distribution with |s| because it can appear after, say, "jump". But neither |z|, nor |iz| can appear in any of the environments of |s|. And |s| also cannot appear in any of the environments of |z| or |iz|. But if we add together distributions of these three the sum will cover the distribution if |ing|. In fact the distributions of |z| and |iz| complement the distribution of |s| to the amount of the distribution of |ing| or the sum of distributions of |t| and |d|. We can name the relations of distributions of |s|, |z| and |iz| complementary and consider that morphs |s|, |z| and |iz| are variants of the same morpheme.
Now we come to the stage of more systematic interpretation of the data received during the analytic procedure. After identifying variants, that is discovering all units in complementary distributions, we can group together all units having common environments, that is in being in contrastive distributions, in distributional classes. After that we can describe the utterances of a language in terms of distribution of distributional classes giving each class an appropriate name. One such class has been mentioned in this section. It is "verb". Here we may define the verb as a class of units appearing before variants od |s|, |t| and |ing|. The group of variants od |s|, |t| and |ing| appearing after the verb is a distributional class, which we may call "verb inflections". We may see that at least at this stage the results of the distributional analysis is very similar to the results of categorial (or traditional) analysis. So the distributional analyses yields as the outcome the elements with which the categorial Grammar usually starts.