If you look at the requirements, they involve the same base of math, statistics and, of course, computers.
"Requirements
Bachelor's degree in Market Research, Marketing, Business, Economics, Communications, or related field.
3 years of experience in market research
Knowledge of marketing principles and practices is required"
If your degree is in communications, you'd have to have work experience in things like survey design, recruiting, analysis and techniques like cluster or factor analysis, and so on.
Analysis of market research means taking sometimes raw data and finding the meaning. That may be by looking for correlations, useful subset trends, and so on. Depending on how deep the analysis goes, it may mean adding routines to computer programs to create additional sorts or tables or even changing sampling techniques and questionnaire design.
The job often entails taking data and presenting it for management, meaning you have to like writing reports and doing PowerPoint decks and are able to take data and express its significance for non-researchers.
I ran a radio research operation for about a decade, and in the past wrote software for a radio ratings company. That is why I say a foundation of math, computer skills (including languages) and statistics is needed.