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As an aside, we avoid the use of specific keywords if possible - widget being a good replacement ;)
If Google is your target, then it's an easy test:
[google.com...]
[google.com...]
These types of searches generally return:
So, the suggestion is:
Google is IMO some distance ahead of it's competitors in terms of "translating" a search keyword so as to retrieve documents that don't necessarily contain the exact wording the searcher used (query expansion, as it's known). So you can optimise for word variations without particularly trying to do so. But equally (especially if the keywords are competitive) you want to back a winning horse, in case you don't succeed in appearing for both.
Your other consideration is whether plural or singular forms are better at driving the right visitors. For transactional keywords there can be a big difference in both traffic and conversion rate for word variations. The goal is to predict searcher behaviour. So is "Buy a widget" better than "Buy widgets"? It depends on both the conversion rate and overall traffic volume as to which is better for a particular site.
Adwords is a great playground for keyword research, if you're prepared to spend money to get reliable data. IMO it can be money well spent if you're making decisions with long-lasting implications. Otherwise, there are SERPs and free keyword tools on which to base any decisions.
Does the same apply for grammatically incorrect keywords or misspelled keywords (as adwords sometimes suggests)?
They are still different keywords, with different relevance, but it is possible for a single item of content to appear for many variations, without using them on the page itself or having incoming links with those related words.
It's spooky.
Tim
Try it now by searching the major search engines for both <a singular keyword and a plural keyword>, the results are often remarkably different:
<snip>
It is important therefore, to optimise a website for both singular and plural keywords and in proportion to their respective usages. If most people would search using a plural than more effort should be directed towards optimising the website for the search phrase involving the plural keyword.
[edited by: Receptional_Andy at 7:14 pm (utc) on Dec. 5, 2008]
[edit reason] No specific keywords, please [/edit]