About a year ago when I was a first-year graduate student, my advisor wanted me to follow up on a project left behind by an honors student. I agreed because, at that time, I thought the topic was important and the findings were rather interesting. However, over the past year, I was busy with other projects and my qualifying exam, so this project was put on hold for almost a year. This summer, my advisor urges me to get it done as soon as possible.
I'd be more than happy to, had I not realized the original project is not methodologically sound. My RAs who re-coded the original data share the same feeling: The experimenter made various mistakes and was overly flexible, yet all data points entered into final analyses. I don't want to spend months chasing after effects that don't exist. Moreover, due to the complex study design, I can foresee what a nightmare it can be to build computational models in the future.
I suggested radical changes that make the experiment more rigorous and subsequent modeling efforts more tractable, but my advisor refused my proposal several times, arguing that making any changes will only delay the starting time. I feel stuck: On the one hand, I don't want to pursue this project as it is since it's most definitely going to fail; on the other, I don't have the courage (or "moral capitals") to defy my advisor because I have put off this project for so long. To make matters worse, I only have one advisor, so if our relationship deteriorates, I have no one else to turn to.
Any advice on what I should do is much appreciated!