Okay, now I understand perfectly.

Nixon apparently won the debate, so the people who only heard them talk on the radio believed that Nixon won because he seemed to have a better way with words, and Kennedy on the TV screen looked better and more composed, which gave him power in front of the viewers.

This shows us once again that a good image is worth more than anything you say sometimes. I suppose that the women here were the most affected in terms of their bias for Kennedy's "good image."