Because of the way our hearing works, critical and objective comparing of two nearly identical performances is difficult. Some people go as far as to claim that certain changes in the audio system (such as swapping cables, for example) have no audible effect at all. In my opinion, with thorough understanding of the way human hearing works, a procedure can be established, that will allow anyone who has healthy ears to perceive even very minute differences with minimal difficulty.
Perception
Listening is a very special way of perceiving the world. Unlike vision, hearing is strictly connected with time - you cannot stop and carefully examine a sound with a magnifying glass. Our first goal then, if we are to critically and objectively assess the sound, is to maximise our auditory perception abilities.
Minimising background noises is an obvious first step. Ideal conditions for listening tend to be late in the night, when there is less traffic (if you live in a city), and less animal noises (if you live in the countryside). Also, there is usually less noise in the electrical grid during the night-time, and less electromagnetic noise in the air, from mobile phones and such - both of which influence (degrade) the performance of a hi-fi system.
Minimise all sensory input to the brain, except for hearing. Night-time is again favourable. Dim or switch off the lights, make yourself comfortable in your listening position. Make sure you are not very hungry or thirsty (being slightly hungry might actually help you focus, while eating a big meal will typically induce drowsiness). Our senses are not truly independent, and there is actually a good amount of sensory cross-talk in our perception. See this interesting article in Scientific American: source.
I did a "scientific experiment" with a few friends, on the influence of light on our ability to focus on the music. In the end, we all agreed that it was easiest to concentrate on the sound in near-darkness (absolute darkness we found a bit unsettling). Dim, diffuse light was very good also, especially for those of us who listen with their eyes closed. The most distracting we thought was a strong, point light source somewhere in the peripheral field of vision (such as a bare bulb hanging from the ceiling above your head).
Make sure you fell well. Your mood might have an influence on your perception, and having a cold or catarrh will affect your hearing capabilities (as well as your mood).
Make sure you have all the time you need, and that you will not be interrupted. Do everything that needs to be done in advance so that, as soon as you start listening, you can dismiss all other thoughts from your brain and focus on the sound.
Of course, the circumstances will never be truly perfect, so you can take the preparations as far as you like. So long as you are well, and you conduct your auditions at more or less the same time of the day, you should get reliable (and repeatable) results.
Listening methodology
Once you have prepared your listening environment, you can commence the actual testing. The procedure described below is applicable to testing single components, as well as entire devices.
The crucial condition for reliable evaluation is that you must be able to swap between your reference and test components quickly - under 30 seconds, ideally. This is because sonic memory is very volatile, and quickly degrades - it becomes infused with moods, other memories, in other words, becomes unreliable. One can memorise melodies and rhythms easily enough for a long time, but it is very difficult to memorise exact sounds: their precise timbre, attack, decay etc. You can probably remember certain sounds very well - the way you bedroom door creaks, your car engine starts and so on - they are the sounds you are exposed to every day. Remembering one-off sounds is much more difficult, hence the necessity to cut the wait time to minimum.
This condition is easily met for entire devices (you just swap cables or switch inputs at the amplifier). For single components such as resistors or capacitors, it usually requires a dedicated system in place, that will allow such quick swapping.
My preferred method is to install a "3-pin fan connector" socket in place of a component (see picture on the right). These sockets are cheap or free if you cut them off a broken PC fan. They accept virtually all commonly used wire diameters - although you may have to drill out the socket holes slightly to accommodate some big electrolytic caps. These sockets have the same hole spacing as many standard components (all TO-220 devices for example), and can be either soldered directly onto PCB, or with an extension cable for ease of access. Once a socket is installed, all I need to do is power-off my test setup, take out one test component, plug in the other one and power back on, which typically takes under 30 seconds.
Another crucial condition for the test is that you listen in exactly the same conditions, so as to eliminate all other variables. Use the same seating position, same lighting conditions, etc.
Once you are satisfied that you will be able to conduct the swaps quickly and effortlessly, it is time for the actual audition:
Listen to one "revealing" song a few times over on your reference setup (my personal all-time favourite is "Dragon Boy" by Joe Hisaishi from the "Spirited Away" soundtrack, you probably have your own favourite).
It is important to "brainwash" oneself in this manner, as after a few repetitions the mind gives up trying to listen to the music and naturally (out of boredom) focuses on the sound and nuances instead. This also establishes a "baseline" sonic signature, which allows the listener to easier perceive the difference, rather than the absolute sound quality.
It is hard or downright impossible to follow all the sounds simultaneously, so make a decision what instrument or voice you will be analysing in each song section, and stick to that choice for the duration of the test. If you want to scrutinise a certain phrase from a few different angles, listen to the whole section again - analyse and memorise one instrument or voice at a time.
Swap a device / component that is the subject of the test. Listen for changes in the passages you were focusing on in step 2.
If the auditioned component sounds clearly inferior or clearly superior, this evaluation is done; if this is a part of a bigger test, remember to write down your impressions.
If the component demands further investigation, repeat p.1-2 with different songs, including at least one with prominent vocals.
If the audition is still inconclusive, give up for now as you are probably tired and resume the audition after a day or two; absolute 100% focus is paramount. If you are still unable to hear a difference in repeated auditions - it is probably because there is no difference, and the components / devices in question can be considered sonically equivalent.
Following this procedure will allow you to discern relatively small characteristics reliably to the point that blind or non-blind testing making will make negligible difference. It is not easy - it can be actually quite an exhausting activity, as it requires perfect focus throughout the entire audition. But with practise and over time, you will tire less. More importantly, you will increase trust in your ears because you will notice your observations are accurate and consistent.
