Non-data tables and accessibility

Hello All,
I am wondering what happens in this scenario:

Let's say I have a table that is used for layout (yes, I know I should use 
CSS, but it's a work in progress).  This table has text and links.  The 
links are being read by JAWS, but not the text.  Could one of the reasons 
be that the table structure is a contributing factor to the text not being 
read?  Also, because the links are being read, is it because JAWS is 
looking for the <a href> and reads that?

Thanks for your help,
Anna


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