不论你是做何种工作,你无时不是在树立自己的形象。Everybody is observing you. YOu do not need to tell peopel how honest you are. You tell them by your behavior. Maintain your reputation of honesty is far more important in your whole life than any short term gain on your current work, being a scientific experiment or a marketing project. You may lose on the current assignment, but you gain by letting poeple know that you are trustworthy person.
I had a personal experience. I was upgrading our company's software. When doing the upgrade, I made a wrong choice, which put the software in a mode that could still operate but for sure needing fix. Software mostly is such a complicated product that you can not tell what went wrong. Still I reported to my manager what happened. Since it was still operational, I had time to resolve the problem. (Even if not, I still would have fixed the problem, but of course I could then have been let go, or maybe not). With this and what I had been doing before the upgrade, they know that I am up to the job, but most importantly, you feel what they think of you - that you can be trusted. When my boss'es boss (whom I actually also reported to) left the company, he asked me "when my company needs, may I call you?"