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A tester might even test differently with a parent present (e.g., maybe being more patient and allowing more time than if the parent weren't in the room).

This. And the child might test differently, too. Better or worse. My DD knows I hate it when she punts and says "I don't know," so she might have been less likely to do that with me there. OTOH, on a day when she was irked with me, she might have been MORE likely.