I've noticed responses that at face value seem to be in contradiction with each other.

For instance, here @peter-flom writes

Short answer: Cluster analysis is about grouping subjects (e.g. people). Factor analysis is about grouping variables.

Whereas, over here on p1 of this York University document it is written that

Cluster analysis is also used to group variables into homogeneous and distinct groups. This approach is used, for example, in revising a questionnaire on the basis of responses received to a draft of the questionnaire.

Are cluster analysis and factor analysis both appropriate for grouping variables and cases? If so, what would prompt me to choose one over another in a particular context? If not, why not?

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    $\begingroup$ When I go to the linked sources I can't see a contradiction, and the Flom answer that continues under the heading 'somewhat longer answer' seems a good concise high level explanation. I actually can't find the quoted phrase in the York University source, and note that they state CA has the objective 'to divide <i>observations</i> into homogeneous and distinct groups.' (last sentence of first para) which agrees entriely with Flom. $\endgroup$ – Robert de Graaf May 19 '16 at 1:36
  • $\begingroup$ I edited the OP to provide a page number, and also to sharpen the focus of the question. $\endgroup$ – user1205901 - Reinstate Monica May 19 '16 at 4:38
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    $\begingroup$ Reading the tags information might help you. Factor analysis is a latent continuous variable model. Cluster analysis is typically an unsupervised classification. The fundamental difference is that factor is a continuous characteristic, a dimension; cluster is a collection of some items, their sum, the group. FA is usually done to analyze variables, but it can be done to analyze cases (Q mode FA). Clustering is more frequently done to analyze cases, but quite often also is done to analyze variables (which are considered as "objects" then). $\endgroup$ – ttnphns Jun 8 '16 at 13:44
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    $\begingroup$ To repeat the idea what I've stressed in the post behind the link: Factor can be seen as forming a group or cluster of items (say, variables) which it loads high, because they are similar in that they correlate with each other high enough; they correlate because the factor loads them all. But factor itself is not a group or collection of something: it is a univariate trait behind the scene. $\endgroup$ – ttnphns Jun 8 '16 at 14:35
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    $\begingroup$ (You forgot to address me as @ttnphns and so I did'n get your comment in my inbox; I iust came across it coincidently). Yes, to me, PCA should not pretend to be a grouping/clustering of variables method. $\endgroup$ – ttnphns Jun 10 '16 at 8:54

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