A new Twitter study from Buddy Media is detailing the facts about how marketers use Twitter – and how we’re getting it wrong in some pretty surprising ways. The study (you can get a free copy of it here), which surveyed 320 Twitter accounts for worldwide power brands, looked at a time period extending from early December 2011 through the end of February 2012.

The first – and most surprising – finding of the study was that when it comes to targeting the highest engagement rates for Twitter followers, most brands are flunking. The lowest engagement rates of followers came midway through the work week (Wednesday and Thursday) – the exact same period when the majority of brands were at their peak Tweet times. As it turns out, according to the study, “Weekends are good for relaxing and Tweeting.” Twitter engagement rates were 17% higher on Saturdays and Sundays, while a mere 19% of brands surveyed were publishing Tweets on the weekends. Furthermore, peak days were different for various industries – but across clothing, fashion, publishing, and sports, all had peak times falling on weekends, Mondays, or some combination thereof.

Not surprising were peak daily Tweet times throughout the week. Engagement rates were 30% higher from the hours of 8 am to 7 pm. Expanding further upon the details of “busy” and “non-busy” hours, the study found that Twitter and Facebook have diametrically opposed results for different time periods. Blame it on Smartphones and short attention spans, but Twitter’s peak hours are Facebook’s time for the lowest engagement rates, while Facebook’s busy times fall right during Twitter’s lull. The truly interesting part was in the numbers. From 7 am to 8 pm (“busy” hours), Twitter engagement was up 24%, while Facebook engagement was down 17%. Yet from 8 pm to 7 am (“non-busy” hours), that trend was virtually flipped upside down, with Facebook engagement climbing exactly 17% and Twitter engagement dropping exactly 24% – giving surveyors the impression that people were practically dropping Twitter at a certain point in the day and jumping over to Facebook.

Stay tuned next week for Part 2 of the findings of the study, and more cues for marketers looking to Tweet like a pro.