The Wool Tartan fabric produced by the big mills in Scotland use what is known as "Worsted" Wool. This means that the individual fibers are combed and stretched until they are all parallel. Then the yarns are twisted.
This results in a very tight, smooth surface to the fabric. There are no little pokey bits sticking out to itch. The resulting fabric should have a hard, smooth feel to it. You should be able to see and feel each and every yarn and find where the yarns cross in the weave.
The Fabric itself is woven in what is known as a Twill Weave. This type of weaving results in distinctive diagonal line in the Tartan Pattern.

In most Tartan fabrics, if you have it layed out on your table with the bottom or selvedge edge towards you, the Twill lines will run from your bottom right to the top left.

This photo show three different selvedge edges on Tartan fabric. All of them are of the outside or right side of the fabric.



In the X Marks Tartan fabric on the lower left side you will see what we call a tucked selvedge. If you feel this tucked edge you will feel that the fabric is slightly thicker here than in the rest of the fabric. There will also be a small line of fuzz where the individual yarns are cut off. This line of fuzz should be on the bottom side of the fabric.

BUT NOT ALWAYS!!! Some looms weave fabric by tucking the selvedge down and some tuck it up. It all depends on the loom.

But notice that the surface of the fabric itself is not fuzzy at all.

If the fabric you have is, or has a fuzzy surface you do not have Worsted Wool. You have some less or less expensive fabric.

A fuzzy surface is usually a dead give-away that the fabric you have is made somewhere other than Scotland, England, or N. America.

Please also remember this rule of Twill direction only applies to Wool Tartan fabric. Cotton Twill, Poly/Cotton Twill and other fabrics may have Twill weaves just the opposite. One is called Left-Hand Twill and one Right-hand Twill.