Question

Which option presents citation information in the most credible way?
According to an unknown author, the data are "flawed significantly" (90).
According to the book Counting the Beans, the data are unsound (90).
According to the book Counting the Beans, the data are "flawed."
According to a new book written by an unknown source, the data are significantly wrong.

Answer 1

I would say According to the book Counting the Beans, the data are unsound. Because you give the name of the book and the page where such information can be found.

Answer 2

The citation information in the most credible way is:

According to an unknown author, the data are "flawed significantly" (90).

Because this statement presents the quotation marks which means that was excerpted from another author and the page where this citation was taken.