How do leading NYC SEO companies demonstrate their success and ROI?

How do the top SEO firms in NYC manage to ‘prove’ their clients that their activity was worthwhile even in terms of ROI? In particular, what indexes and key performance indicators do they apply to illustrate the growth of the organic rankings, gaining the traffic, and increasing the conversion rates from their websites? Further, how do they apply the authority of case studies and client feedback to steer the audience on their past achievements? What function do regular reporting and analytical instruments, for example, Google Analytics, execute in the reporting process? Ultimately, how do these businesses manage to exactly define the objectives of their actions in connection to their clients’ interests and present the connection of all these efforts to actual business outcomes?