how to check for the presence of oxygen?

The Winkler test is used to determine the level of dissolved oxygen in water samples. The test was first developed by Lajos Winkler while working on his doctoral dissertation in 1888. The amount of dissolved oxygen is the biological activity of the water masses. Phytoplankton and macroalgae present in the water mass produce oxygen by the way of the photosynthesis. At the same time bacteria and all other organisms (zooplankton, algae, fish) consume the oxygen by respiration. The result of this two mechanisms give the concentration in dissolved oxygen.

Beside relighting the glowing splint, there are not many test for oxygen.
Just like relighting a glowing splint, you can also use BURNING SPLINT to test of oxygen, the result is THE SPLINT BURNS MORE BRIGHTLY.
Here are 3 other test of oxygen but their result are NOT UNIQUE because they can USE TO TEST OTHER GASES TOO.
Method 1: Invert a tube of oxygen. Place its mouth under water in a wash basin. Remove the stopper under water. The result is the water level does not rise inside the tube.
Method 2: Moisten a pH paper with water. The result is there are not any colour change of pH paper.
Method 3: Add 1cm^3 of limewater into a tube of oxygen. Stopper the tube immediately. Shake the tube well. The result is there are no appearance of the limewater.