The text shared on social networks and interactions resulting from all virtual activities have been gaining a great impact on society. In this work, we investigate if Twitter data can be used to predict or describe stock market prices by using sentiment polarity (positive or negative). Using a Bayesian classifier and making two causality models (one with the Stock Market and another with the Twitter sentiment as dependent variable) we could relate the data from Twitter with intra-day and day-to-day stock prices. We reached four significant conclusions. First, the relationship between twitter and the stock market is, in both cases, strongly dependent on the time grouping of the twitter data. Second, using Granger Causality Analysis, we found some companies where we can use tweets to predict the stock price, and others where we can’t. Amongst those where we can, there are some where the delay between tweets and changes in price are small (Cisco, American Airlines and Microsoft), and others where those changes take a longer time (LinkedIn). Third, companies with a high number of tweets show a weaker relationship amongst the two variables. Forth, in some cases (British Petroleum), we can predict changes in Twitter sentiment using stock prices.