Should I install an one-way valve in dishwasher drain?

I am replacing an old dishwasher. I would like to know if I should add a one-way valve to the drain hose, to help prevent water from the sink from flowing into the bottom of the washer.

I have a loop in the drain hose going up to just under the bottom of the counter, but some water still comes out of this hose if I leave the end open.

There was a blue, hex-shaped plastic connector in the old drain line, but this passes water both ways. I think it may have been just an adapter.