I started a huge brouhaha with a post on this topic some time ago. If you're curious you can find it easily by searching for my prior posts.
I'm a consumer psychologist and a marketing professor who studies how people make subjective judgments about what sounds, tastes, looks, or feels better. The data on this are resoundingly clear. The only way to have confidence that a difference you are perceiving between X and Y—whether X and Y are power cords or anything else—is through a blind comparison where the person making the judgment does not know what they are listening to.
There are two very important things to know about this issue. First, the issue goes beyond confirmation bias (biasing one's judgments in favor of what one already believes to be true). Many people think that the issue is simply one of confirmation bias, so if they don't have a prior belief that power cords either do or do not make a difference in sound quality, they will approach the issue open-mindedly, and, therefore, blind listening is not needed. This makes total sense, but alas, is incorrect. If your brain knows what it is listening to, it will bias the results in all kinds of ways, even if you don't have a prior opinion and are honestly doing your best to make an accurate judgment.
Second, and this may be the most important and interesting point, if you know what you are listening to you genuinely will hear a difference. It's just that the difference is generated by your brain rather than the power cords. Here is what we used to think and after I’ll share what the research now shows.
WRONG outdated model:
(1) the stereo creates vibrations in the air.
(2) these vibrations reach your ear.
(3) your brain translates these vibrations into a sonic experience.
(4) your prior beliefs about power cords bias your judgment of this subjective experience and bias what you tell other people about it.
New, more CORRECT model:
(1) the stereo creates vibrations in the air,
(2) these vibrations reach your ear,
(3) your brain combines the information it receives from the ear with models about how the world works and motivations about how to be socially successful to actively construct your sonic experience. So, the sounds you hear in your head have already been influenced by your knowledge of what you are listening to.
(4) You judge whether power cords influence the sound quality and share that judgment with other people. You can do this in a biased way or in a more open-minded and honest way.
The important point is that knowing which power cord you are listening to will bias you at stage 3 and stage 4. If you're committed to an honest, open-minded approach, this will reduce the bias at stage 4, but the bias at stage 3 will still be there. The only way to remove the bias at stage 3 is to do a blind listening. And the bias at stage 3 will happen even if you don’t have a specific belief about power cords. Your brain will introduce biases at stage 3 for a whole host of other reasons that are too complicated to get into in this post.
At the time of my previous post on this issue I searched the Internet to find examples of blind listening tests using different power cords. I was only able to find a few examples, but all of them provided strong evidence that power cords make zero difference in what people hear if the people don't know what power cord they are listening to. This does not mean that all stereo sound the same or that spending money on stereo equipment is always a waste. There are many ways that you can spend money improving the sound of your stereo that hold up in blind listening tests. But from the evidence available last time I checked, spending money on power cords is not a good way to improve the sound quality of your system.