The relationship between quantity traded and transaction costs has been one of the main focuses among financial scholars and practitioners. The purpose of this thesis is to investigate the informational relationship between these variables. Following insights and results of Milgrom (1981), Feldman (2004), and Feldman and Winer (2004), we use New York Stock Exchange (NYSE) data and kernel estimation methods to construct the distribution of one variable conditional on the other. We then study the information in these conditional distributions: the extent to which they are ordered by first order stochastic dominance (FOSD) and by monotone likelihood ratio property (MLRP). We find that transaction size and effective spread are statistically significantly orrelated. FOSD, a necessary condition for a "separating signaling equilibrium", holds under certain conditions. We start from two-subsample case. We choose a cut-off point in transaction size and categorize the observations with transaction sizes smaller than the cut-off point into group "low". The remaining data is classified as "high". We repeat this procedure for all possible transaction size cut-off points. It turns out that FOSD holds nowhere. However, once we eliminate transactions at the quote midpoint, the "crossings" between exchange members not specialists, FOSD holds for all the cut-off points fewer than 15800 shares. MLRP, a necessary and sufficient condition for the separating equilibrium to hold point by point of the conditional density functions, does not hold but might not be ruled out considering the error in the estimates. We also find that large trades are not necessarily associated with large spread. Instead, it is more likely that larger trades are transacted at the quote midpoint (again, the non-specialist "crossings") than smaller trades. Our results confirm the findings of Barclay and Warner (1993) regarding the informativeness of medium-size transactions: we identify informational relationships between mid-size transactions and spreads but not for trades at the quote midpoint and large-size transactions. That is, we identify two regimes, an informational one and a non-informational/liquidity one.