Comparing two objects rated by a bipolar scale

Question

I have run an online poll on two candidates. Participants are shown both candidates and are asked to determine which one they like better. Here are the labels on my Likert scale:

• Strongly for Romney
• Leaning towards Romney
• Neutral
• Leaning towards Obama
• Strongly for Obama

I want run hypothesis testing on the results and see which candidate is more desirable. What is the proper way of designing the analysis? So far I have been just comparing the ones that are strongly for either candidate and reported the count value as the winner. But I want to be more systematic and do more rigorous hypothesis testing. The distribution of votes is like a binomial distribution.

Answer 1

Your scale shouldn't be called Likert-type scale. Likert-type scale is a unipolar intensity measuring rating scale, such as from "not at all" through "very strongly". Your scale is Osgood-type one, a bipolar rating scale measuring degree of proximity to either of the 2 poles. The poles are defined by the 2 targets with an attitude lying side-by-side the scale, whereas in Likert-type scale target is one and is side-by-side the scale, and the poles are defined by an attribute's or an attitude's intensity.

You could use any one-sample central-tendency test to check if the centre significantly departs from "Neutral" midpoint. It might be for example t-test (which is fairly robust to departures of normality) or median test or Mann-Whitney one sample test (that tests for Hodges-Lehmann pseudo-median).