Steve Jobs’ medical leave of absence has the market asking hard questions:  1) Exactly how dire is Jobs’ health; and 2) if he leaves permanently, what will be the impact on Apple’s performance?

In a piece published on January 18, 2011, Steve Lohr of the New York Times framed the question this way:

For years, and across a career, knowing what consumers want has been the self-appointed task of Mr. Jobs, Apple’s charismatic co-founder. Though he has not always been right, his string of successes at Apple is uncanny. His biggest user-pleasing hits include the Macintosh, the iMac, iBook, iPod, iPhone and iPad.

But as he takes a medical leave of absence, announced on Monday, the question is: Without him at the helm, can Apple continue its streak of innovation, particularly in an industry where rapid-fire product cycles can make today’s leader tomorrow’s laggard?”

Apple itself may not know the answer to the first question and so far, it has been silent on the second one. “Mum on Jobs” read a Wall Street Journal headline above an article noting the company’s profits were up 78% on a surge in sales this past quarter.  The question of a top executive health has moved the conversation into “a sensitive area where the privacy of an individual bumps up against the disclosure of material events,” wrote John Palizza on his blog, Investor Relations Musings.

Among celebrity CEOs, Jobs floats in a stratosphere of his own. As the chart nearby demonstrates, Jobs is an order of magnitude higher than his peer group.  Since October 2010, and counting Jobs, we’ve used Vocus Social Media Monitoring to track social mentions of five CEOs including Marc Benioff, Michael Dell, Larry Ellison and Eric Schmidt.

Jobs was mentioned in social media sites, including Jack Welch’s mention on Twitter and Justin Beiber’s Facebook status, approximately 300,000 times in that time frame.  The next closest CEO was Schmidt, who has also recently made headlines, for plans to relinquish the top executive position at Google to co-founder Larry Page.  Schmidt earned approximately 20,000 mentions.  The findings were of a similar scale among top tier news and blog searches.

The noise level is clear, but what impact does all this social chatter have on business outcomes for a company?  What is the impact of the Steve Jobs Effect? The chart nearby takes a shot at correlating social media mentions to Apple’s stock price (NASDAQ: AAPL).  The stock price reflected is the closing price on Friday as reflected in Google Finance.  Social mentions were tallied counting the total number of mentions running Sunday thru Saturday.

It’s not a perfect experiment, and the correlation admittedly is weak, but then again the period reviewed is finite.  A longer period of time may yield greater insights.  Further, while the market has an abundance of anecdotal evidence, such as Jobs previous break from Apple and it’s revival in 1997 when he returned, it still suffers a paucity quantifiable data.  Such efforts are one step in a direction of estimating the potential impact one celebrity CEO might have on a brand.

What do impact do you think Steve Jobs’ absence from Apple will have on the business?