There are also various uses for writing case studies, from academic research schools, educators and students may select cumulative or critical case study. How to write the case study. There are two different approaches to case studies. Type 1: The Analytical Approach. The case study is examined. Case Studies. Writing @CSU. Colorado State University; Mills, Albert J., Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research.