"evident connection" is correct and can be used in written English.
It is used to describe a clear link between two things. For example, "The evident connection between the rise in fuel prices and the decrease in car sales could not be ignored."
Some apparently inaccurate bombs destroyed houses with no evident connection to the Taliban or Al Qaeda.
Roth's client was Alfred N. Cohen, a laundry operator with no evident connection to E. Yancey Cohen.
Despite its evident connection with contemporary Surrealism, the de Pisis could not be more different in its distinctive brushwork and color scheme, and, above all, in its alacrity.
In general, he excludes knowledge claims in which there is no evident connection or exclusion between the ideas of which the claim is composed.
Throughout much of the action percussion is played offstage but with no sustained meter and no evident connection to the movement or the music on view.
Her claim has no evident connection to an acid attack on Sergei Filin, the ballet's artistic director, two weeks ago that severely burned his eyes and face.
Tony Blair cuts a pitiable figure as he denies the self-evident connection between his violent occupation of Iraq and the barbarism being unleashed today.
Indeed the impression is given that talking about teachers is to focus on inputs, when we should now be solely focused on outcomes - without seeing the self-evident connections between them.
And in Mackie's formulation it has the desirable feature that it makes evident the connection between a miracle and supernatural agency.
The screening is followed by an interactive workshop that makes evident the connections between care work and all of our lives.
The screening will be followed by an interactive workshop that will make evident the connections between care work and all of our lives.
