To solve his mystery, Dave turned to a legendary tool known as . He carefully selected ten trees from each grove and recorded their harvests. He found that: The Apple trees averaged 200 fruits. The Orange trees averaged 180 fruits. The Mango trees averaged 220 fruits.
Dave calculated his , a magical ratio. If the variation between his groves was much larger than the variation within them, his F-statistic would be high, signaling a real difference. After crunching the numbers, Dave found a high F-value and a tiny p-value of 0.03, meaning there was only a 3% chance these differences were just a fluke.
With his ANOVA complete, Dave finally had his answer: his groves weren't just varying by chance; the type of tree really did matter. He celebrated by planting more of his high-yielding Mango trees, confident that his decision was backed by the power of variance. What Is Analysis of Variance (ANOVA)? - Investopedia
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