In any listening test, listeners' responses are YES or NO. How do you make that semi-quantitative?
If positive controls are carefully selected, they can be used to make a standard curve. For those who need an illustration, here is how to use added pink noise to make a standard curve for the listening test. I've made up some numbers for 5 imaginary listeners (A through E), put them in Excel, and I made and X-Y graph of it. For the listener's answers, YES = 1 and NO = 0.
| Pink Noise | A | B | C | D | E | Total | % of Total |
| 0.0% | 0 | 0 | 0 | 0 | 0 | 0 | 0% |
| 0.1% | 1 | 0 | 0 | 0 | 0 | 1 | 20% |
| 0.3% | 1 | 1 | 0 | 0 | 0 | 2 | 40% |
| 1.0% | 1 | 1 | 1 | 0 | 0 | 3 | 60% |
| 3.0% | 1 | 1 | 1 | 1 | 0 | 4 | 80% |
| 10.0% | 1 | 1 | 1 | 1 | 1 | 5 | 100% |
On the graph, the horizontal axis shows
% Listeners That Hear Added Pink Noise, and the vertical axis shows
% Added Pink Noise on a log scale.
I drew two extra lines in red. The vertical red line is drawn from the 50% of listeners point, and the horizontal red line shows what % Added Pink Noise corresponds to the 50% listeners point. It's a little more than 0.5% Pink Noise.
In the speaker cable listening test, for each listener, you have multiple repeats of two different tests, the actual test where two different cables are compared, and the negative control where two identical cables are compared. Subtract the negative control value from the cable comparison. If, on the negative control test, a listener says 50% of the time that he hears a difference, you must subtract 50% from his answers for the cable comparison test. Ignore the results from any listener that result in zero or negative values after subtracting the negative control. Once you've done this for all the listeners in the test, look of the pink noise standard curve, and find where the 50% listener's point is.
For example, let's say that point is 0.5% Pink Noise. You can conclude that, under conditions where half the listeners can reliably report hearing 0.5% added pink noise, listeners can also hear sounds due to different speaker cables.
Of course, if most or all of the listeners produce results that are zero or negative values after subtracting the negative control, you can conclude that listeners could not hear sounds due to different speaker cables. And you can describe what levels of added pink noise they could hear with the audio gear and the room used for the test.
If anyone wants to repeat the test, they can compare standard curves to see whose test was more sensitive.
I deliberately chose my example to make a simple looking graph where the points generate a straight line. In a real listening test, there will be more listeners, and the resulting graph won't be so clean looking. Each listener will hear 3 to 5 repeats of every level of added pink noise, the negative control, and the cable comparison, so each point will represent an average of the repeats. The resulting graph will probably be an S shaped or
sigmoid curve instead of a straight line. But it will contain a linear portion that can be used for this purpose.
