1000 words sounds a lot, but I think the principle is correct and that articles need to be generally longer and more informative than other results for the same search, and have something unique to offer.
The presence of a significant number of short articles appears to drag down the whole site, including the articles that are of good quality. A site with 25% short poor quality articles appears to be enough to attract panda - less than that I couldn't say, but I don't think that just a few pages would do it, as sometimes suggested.
This is an observation reached by comparing my 2 panda sites with my other non-panda sites, which tend to have much fewer articles, but longer and of better quality.
Bounce rate / time on site etc taken overall for a site don't seem to a reliable indicator of whether a site is penalised - in part perhaps because these statistics only apply to articles that are shown in the results i.e. they exclude articles that google don't show because they are of too poor quality, and in part because these statistics vary a great deal between search terms.
You can start identifying low quality pages by running an 'advanced filter' in google analytics to find pages with both a high bounce rate AND a low time on site.
Improved content also seems to be the most consistently way of improving results reported by other 'panda escapees' (and should of course improve user statistics at the same time). Bit of a job if you have 1000's of pages though.