I'm eager to learn about conversions, and the best way to do it (I believe) is thru learning from others who have done it successfully.
CTA based tests are always some of the most interesting, but also provide big gains. One of the most surprising tests was when the button CTA on a form, which was aligned to the CTA on the form itself, lost with statistically significant data to just plain 'submit' and this was after several rounds of prior tests.
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One of the most significant results I've seen was for a client of mine - Switch Video. We changed one word on their call to action button and increased leads generated by 228%. How'd we do it, you ask? Well, first we surveyed their customers to find out what questions they had, and then we made an educated changed based on the survey results. It always helps to start with research so you're not just guessing about what to test.
I disagree. The best way to do it is just to get started doing testing, or hire a competent CRO firm to do it for you.
Your customers are not the same as your competitor's customers, or the customers of some case studies you've seen. Your results might vary (greatly).
The best case studies and tests which result in the greatest gain in the lifetime value of the customer are based on principles which improve the customer experience and allow you to connect and communicate with. Tactics might work in the short term, but over the longer term a strategic approach is best.