What is the difference between a "I" or "II" after a job title? There are several job titles such as "Research Associate II" or "Research Scientist I" or "Research Scientist II" in the research institute located near my school.  

Is there a difference between the job titles and is "I" higher than "II" or vice versa?
In a job title, "I" or "II" usually denotes the level of experience.  You will also see "assistant", "senior" and similar adjectives used.  The idea is that employees can be hired at one of several levels of experience and that employees can advance through these levels as they gain experience.  

Someone hired as a "Analyst I" may be promoted to a "Analyst II" after some number of years.  Sometimes these kinds of job titles also have additional educational requirements (such as an advanced degree or certification) for the higher levels.  Typically there are different pay ranges that apply to employees as they advance through the classifications.  

The definitions of the different levels will vary from one employer to another so there's really nothing more specific that we can say in answer to this question- you'll have to check the definitions used by your employer to see what the requirements are for each level.