How to

Certainly you can just make two passes over your dado stack (set for 3/8" depth). IMO, I'd have the workpiece run against the fence with the blade set to the opposite side of the workpiece.
First pass has the edge of the dado at your 1-1/2" mark, second pass at 3/4" from the edge.

May be too much material for a pass in which case you could "nibble off" maybe 1/2" from the edge, bump the fence 1/2", nibble, bump again and be done.

You can also make two cuts with a rip blade, first cut 3/8" deep, 1-1/2" from edge. 
Second cut 1-1/2" deep, 3/8" from dado'd face (inside face?)
Though 1-1/2" deep cut probably will burn a bit.

I got my terminology wrong. I want to cut a groove , along the length of a board, 1 1/2" wide x 3/8" deep.
Actually it will be a rabbet.

I have a beautiful dado set but don't use it much. I do all my dados with hand tools. 

Groove would be the same, 2 passes.
If you want it centered, you just make the first pass, rotate 180, then cut the 2nd.
Some scrap of the same width will let you set the fence so you get the 1-1/2" rabbet when finished,
It always takes a few fence taps  to really get it perfect.

Wadeaminute, you want what is in the photo right? (rabbet down each side) 
or do you you want a groove down the center?

Pic # 2.   I want a rabbet on each side. Solid wood down the center.In the pic, those rabbets are 3/4" wide x 3/8" deep. I need to get 1 1/2" wide x 3/8" deep. I want to cut the rabbets on a long strip 4 " wide, then cut the strip into the 4 pieces to make a box.

This sounds like a perfect job for a handplane that I don't have.

That'll get tippy on the table saw bed unless you let it overhang on a piece of 3/8" whatever on the outboard side.

Insert dope slap emoji here

I haven't used my old Jet  jointer in so long I forgot it can rabbet. Thanks!!

Stand it up on edge and make the 1 1/2" cut first on the table saw.  Then lay it down and make the 3/8" cut. 
Set the fence so your cutting the outside off not trapping the off cut between the wood and the fence.

What Bent wrote on a TS. Plus his has the advantage you can use a single straight blade, and don't have to dick around setting up a Dado stack. Zip 1 1/2" then play it down and zip 3/8". I would think the cuts would be cleaner than with a Dado too.

Of late, if I have to do a 2 pass cut to make the width, as in a 1 1/2" dado/rabbet, instead of the TS and a Dado blade. I'll use a router table, and just over 1/2 the width on the bit. So I'd look for a flat bottom cutting 1" bit, and move it over enough to cover the 1 1/2" in 2 passes. 

For speed what Bent wrote is the boss. I think for accuracy the router will deliver, kinda depends on what ya are looking for as an end result. 

If I did that I could then move the fence in 1/8" and repeat twice, and it's done.
 
1 1/2" high T/S blades scare the snot out of me.

Incra fence on a right tilt saw. Biesemeyer would be better sometimes. I know, it don't matter, but it sure is different.

However I do it, it's getting a jig. NO fingers near spinning metal. I'll see what happens with the jointer.
Thanks!!

I know it can be done. Your warm and fuzzy quotient may be higher if you built a fence, or jig to support it while you sawed it on the TS. Also a major reason I have moved many tasks to a router table, easier to rig for safety, and with a big router, a 1/2 shanked bit, and nice easy feed, it comes out smooth, and most of all safe. Plus a lot less chance of kickback. :-)

I got it worked out in my head now. That last 90 degree rotation threw me.

I get locked onto a plan, until I gotta rethink it. 

Thanks for all the help,I made it way too hard.

I still don't know why I had to make it so hard. I had everything I needed.

I set up my dado blade to 3/8" wide,exposed beyond the fence. I set the blade height to 1 1/4",  I rethunk my plan of 1 1/2".

I used the board getting the rabbets to set the left side of blade fence. I think it's 3 or 4 different uses for this jig, so far.

All I had to do was push forward and down at the same time. Fingers safely away.

The 1st pic I used to start this thread was 3/4" high. I also did not use the second fence, just a featherboard.
My dado set goes up to 7/8".   This is where my train of thought got sidetracked. My thinking was for a dado,not a groove. How to go farther than the width. CRS sux.

Thanks for all the great help!

Seeing that end view shows a clean cut!

If you had a bandsaw, you could also resaw it down, narrow one slice up and then reglue in the center.

I got 3 bandsaws, and I still can't do that