See the article assessment section in the WikiProject Guide for a more in-depth explanation of how the assessment process functions.
What is the purpose of article assessments?
The assessment system allows a WikiProject to monitor the quality of articles in its subject areas, and to prioritize work on these articles. The ratings are also used by the Wikipedia 1.0 program to prepare for static releases of Wikipedia content.
Are these ratings official?
Not really; these ratings are meant primarily for the internal use of the project, and usually do not imply any official standing within Wikipedia as a whole.

Assessing articles

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Who can assess articles?
In general, anyone can add or change an article's rating. However, assessing an article as "A-Class" generally requires the agreement of at least two editors, and the "GA" and "FA" labels should only be used on articles that have been reviewed and are currently designated as good articles or featured articles, respectively. Individual WikiProjects may also have more formal procedures for rating an article, and please note that the WikiProject bears ultimate responsibility for resolving disputes.
How do I assess an article?
Consult the quality scale below; once you have chosen the level that seems to be closest to the article, set the class parameter in the WikiProject banner template to the level's name (omitting "Class" from the end). For example, to rate an article as "B-Class", use |class=B in the banner. Again, the "FA" and "GA" labels should not be added to articles unless they are currently designated as such.
Does this have anything to do with the Wikipedia:Article Feedback Tool, which used to appear at the end of many articles?
No, that was a completely separate system.

Common concerns

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Someone put a project banner template on an article, but it's not really within the WikiProject's scope. What should I do?
Because of the large number of articles we deal with, we occasionally make mistakes and add tags to articles that shouldn't have them. If you notice one, feel free to remove the tag, and optionally leave a note on the article's talk page (or directly with the person who tagged the article). See Wikipedia:WikiProject Council/Guide#Article_tagging for more information.
What if I don't agree with a rating?
Feel free to change it—within reason—if you think a different rating is justified; in the case of major disputes, the WikiProject as a whole can discuss the issue and come to a consensus as to the best rating.
Aren't the ratings subjective?
Yes, they are somewhat subjective, but it's the best system we've been able to devise. If you have a better idea, please don't hesitate to let us know!
Why didn't the reviewer leave any comments?
Due to the volume of articles that need to be assessed, we are unable to leave detailed comments in most cases. If you have particular questions, you might ask the person who assessed the article; they will usually be happy to provide you with their reasoning. Wikipedia:Peer review is the process designed to provide detailed comments.

Quality scale

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WikiProject article quality grading scheme

A few WikiProjects have similar FAQs that address issues more specific to their particular assessment programs:

Links for WikiProject members looking to implement assessments: