This is great - a forum where you get useful answers, thanks.
It's interesting to me that my question was actually asking about something else - almost certainly my fault. Don't get me wrong, these are all great answers and are much appreciated.
In fact I spent several hours yesterday trying to answer the question that I meant to ask in the first place: the ranking of keywords, not articles in SERPs - and I found some answers.
You have to pay something like $99 - $399 per month to get seo tools such as Semrush, WordTracker etc.
The best deal I found was Market Samurai at $149 - a one off payment, not monthly recurring.
However a Google Search for 'Best SEO Tools' showed the top listing for a site called 'seotoolsreview' which listed Market Samuai as 8th in their Top Ten SEO Tools review.
Does anyone have experience of Market Samurai, and is it a dud?
Or do his Top Ten Rankings result from some Affiliate Commissions he hopes to get? I don't know if there were Affiliate links, but they weren't obvious.
His Number One choice was SEOmoz at $99 per month.
That reviewer's other SEO tools, apart from Samurai, were all high priced, Pay By The Month deals, which put them out of my league.
Or should I save my money and rely just on Webmaster Tools data and Google Keyword research?