"show a noticeable" is a correct and usable phrase in written English.
You can use it when you want to emphasize that something has a notable or visible impact. For example, "The new policy has shown a noticeable improvement in employee morale."
They show a noticeable predilection for the sight of the human face, and by the first or second month they are able to discriminate between different faces by attending to the internal features eyes, nose, and mouth.
The pictures do not show a noticeable change in pore diameter.
The data show a noticeable change in behaviour with the onset of plastic deformation.
Our estimates show a noticeable improvement on existing results if Markov chains contain instantaneous states or nonconservative states.
The optimum results show a noticeable improvement in the total cost in comparison with the results presented in the literature.
Nevertheless, for both TiO2 and Al2O3, an addition of AuNPs did not show a noticeable effect on the values of BET surface areas.
Soon afterward, Stacey showed up in a new pair of New Balance shoes and showed a noticeable improvement in her serve.
For evidence, Newton pointed to the example of Jupiter, which showed a noticeable flattening when seen through a telescope.
The statistical decline, in fact, has already started, with both players showing a noticeable drop-off since their strong Aprils.
The salmon-pink 2006 rosé of merlot ($14) shows a noticeable strawberry-like flavor and an alluring scent of tea roses.
The ABC/Post survey also showed a noticeable shift toward Mr. Bush when voters were asked which man they trusted more to handle major issues.
