Directive ngRepeat creates a new scope for each iteration, so you need to reference your variables in parent scope.
Use $parent.selected = value
, as in:
<p ng-repeat="value in values" ng-click='$parent.selected = value'>{{value}}</p>
Note: Function call propagates due to prototypal inheritance.
If you want to learn more: The Nuances of Scope Prototypal Inheritance.