Your quads work hard during squats no matter how heavy the weight, but your glutes really kick in only when the weights are heavy or you're almost too tired to keep going.
Evidence from Studies
Supporting (2)
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Effect of external load on muscle activation during the barbell back squat
The study found that leg muscles (quadriceps) work hard even with light squats, but the butt muscle (gluteus maximus) really kicks in only when the weight is heavy, which supports the claim.
The effect of back squat depth and load on lower body muscle activity in group exercise participants
The study shows that your quads work hard during squats no matter how light the weight, but your glutes kick in more when the weight gets heavier. This matches the claim.
Contradicting (0)
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Gold Standard Evidence Needed
According to GRADE and EBM methodology, here is what ideal scientific evidence would look like to definitively prove or disprove this specific claim, ordered from strongest to weakest evidence.