Using a linear cue combination framework, we develop a measure of selective attention that describes the relative weight that an observer assigns to attended and unattended parts of a stimulus when making perceptual judgments. We call this measure attentional weight. We present two methods for measuring attentional weight by calculating the trial-by-trial correlation between the strength of attended and unattended parts of a stimulus and the observer's responses. We illustrate these methods in three experiments that investigate whether observers can direct selective attention according to contrast polarity when judging global direction of motion or global orientation. We find that when observers try to judge the global direction or orientation of the parts of a stimulus with a given contrast polarity (white or black), their responses are nevertheless strongly influenced by parts of the stimulus that have the opposite contrast polarity. Our measure of selective attention indicates that the influence of the opposite-polarity distractors on observers' responses is typically 65% as strong as the influence of the targets in the motion task, and typically 25% as strong as the targets in the orientation task, demonstrating that observers have only a limited ability to direct attention according to contrast polarity. We discuss some of the advantages of using a linear cue combination framework to study selective attention.