As mdasen mentioned, Google Analytics probably doesn't have much of an effect on SEO due to regulatory concerns.
However, it probably does handicap you if you use other Google services, such as Adwords. Google Adwords heavily leverages Analytics data to optimize your marketing campaigns, and doesn't offer the ability to interface Adwords with a third-party like Piwik. So not using Analytics will cause Adwords to fly blind to user behavior on your site, and won't be able to tell which leads were useful and which weren't.
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As mdasen mentioned, Google Analytics probably doesn't have much of an effect on SEO due to regulatory concerns.
However, it probably does handicap you if you use other Google services, such as Adwords. Google Adwords heavily leverages Analytics data to optimize your marketing campaigns, and doesn't offer the ability to interface Adwords with a third-party like Piwik. So not using Analytics will cause Adwords to fly blind to user behavior on your site, and won't be able to tell which leads were useful and which weren't.