First Samuel 6.7-6.9. Instructions from the Philistines' priests, on how to determine whether the plagues their people had been suffering were due to their having captured the ark of the Lord from the Israelites.
"... Now therefore take and prepare you a new cart, and two milch kine, on which there hath come no yoke, and tie the kine to the cart, ... And take the ark of the Lord, and lay it upon the cart ... and send it away, that it may go. And see; if it goeth up on the way to its own border to Beth-shemesh, then He hath done us this great evil; but if not, then we shall know that it is not His hand that smote us, it was a chance that happened to us."
Not a modern scientific test; but the null hypothesis is explicitly stated.
The outcome, by the way, is "... And the kine took the straight way by the way to Beth-shemesh; they went along the highway, lowing as they went, and turned not aside to the right hand or to the left; ..." (6.12).