Human factor

You may be looking for the audio story The Human Factor.

The human factor was the distillation of the essence of what distinguished humans from other species (primarily Daleks).

History

Operation Human Factor

While known as Genetic Variant Two-One-Zero and in a period of testing, the Dalek Emperor was inspired to seek the human factor through an encounter with Steven Taylor. Intrigued by his behaviour, the Emperor gave the Daleks a prime directive to discover, study, and understand the human factor. (AUDIO: Across the Darkened City)

In what they termed Operation Human Factor, (AUDIO: The Dalek Conquests) the Daleks recruited the Second Doctor, against his will, to isolate and identify the human factor, using Jamie McCrimmon as a test subject. The Daleks claimed that they wished to distill the most important qualities from the factor and use it to make themselves more deadly. The Emperor's true plan, however, was to use the Doctor's work to identify the Dalek factor by contrast.

Once the human factor was identified, it was experimentally transferred to test Daleks, creating three humanised Daleks. The Doctor gave them the names Alpha, Beta, and Omega. He later sabotaged a Dalek machine so that it instilled the human factor into any Dalek that passed through it, converting them into humanised Daleks as well. (TV: The Evil of the Daleks)

Later history

Fleeing Skaro in the aftermath of the Dalek Civil War, the "human factor Daleks" created by the gateway took refuge on the planet Kyrol, with Alpha acting as their leader. The Eighth Doctor learned of their existence a short time before they were destroyed, not by their Emperor-loyal brethren as they had feared, but in rebellion against the malevolent entity Kata-Phobus. (COMIC: Children of the Revolution)

During the Last Great Time War, the Time Lords made a tactical analysis on Human Factor. With the Doctor having granted them access to the details of his experimental results via the telepathic circuits of his TARDIS, they conducted tests to determine the possibility of distilling a similar "Gallifreyan Factor" whilst research was under way to determine whether any of Humanised Daleks survived, with operatives following up on reports of their potential presence on Kyrol. (PROSE: Dalek Combat Training Manual)

When the "Metaltron" Dalek imprisoned in the Vault by Henry van Statten drained artron energy from Rose Tyler via her touch as a way to regenerate itself, it accidentally absorbed her DNA, (TV: Dalek) "infecting" it with the human factor. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe) The "Metaltron" consequently began feeling mercy and compassion, even towards its own torturer Van Statten, and to question the very purpose of the Daleks. Maddened and debilitated by its new freedom of thought, the Dalek eventually died by suicide. (TV: Dalek)

Behind the scenes

The Discontinuity Guide speculates that, whilst under interrogation during his incursion on Skaro, the Fourth Doctor had told Davros about the Human Factor Incident, which later influenced the Dalek creator as he converted humans into Daleks on Necros, Davros' conclusion being that, by possessing some of the Human Factor, the Daleks will not be slaves to logic and thus not be drawn into an impasse as they had with the Movellans.