Even if readers agree that a reason is well supported by evidence, they may not see why it should lead them to accept your claim. They will ask why that reason, though factually true, is relevant to the claim.
Your argument: Children who are exposed to large amounts of violent entertainment tend to become adults who think violence is a legitimate component of daily life (claim) because as children they tend to adopt the violent values in what they see (reason).
Reader question: Why should children who adopt violent values necessarily become adults who tend to accept violence as a legitimate component of everyday life? I don't see how your claim follows from your reason.
To answer your readers' questions of relevance, you must offer a general principle that shows why you believe your particular reason is relevant to your particular claim so that you are justified in connecting them.
Example: Whenever children adopt particular values, as adults they tend to accept as "normal" any behavior that reflects those values.
Let's connect that principle as a warrant through the larger argument:
Example: Violence on television and in video games can have harmful psychological effects (main claim). Few of us question that when children are repeatedly exposed to particular values in graphic and attractive form, they use those values to structure their understanding of the world (warrant). In the same way, children constantly exposed to violent entertainment tend to adopt the values of what they see...
It is not easy to decide where to put warrants in the sequence of an argument, or even whether you need them at all. In fact, writers state warrants rarely, only when they think readers might question the relevance of a reason to their claim.
Example: Watch out going down the stairs, because the light is out.
You wouldn't need to add the warrant --
Example: When it's dark, you have to be careful not to misstep (warrant). So watch out going down the stairs (claim), because the light is out (reason).
That would just seem condescending.