Most mental processing occurs unconsciously.
One reason anecdoes are more powerful because they are in story form; they evoke empathy, triggering an emotional reaction. With emotional reactions, people will process the data and the feelings. Emotions will also trigger the memory centers.
Information is processed more deeply and remembered longer if it has an emotional hook.
Look for ways to provide a message that will invoke emotions and empathy.
Use anecdotes in addition to or in place of factual data.