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Why does Example 2 lead to rejecting the null hypothesis?

In Example 2, the scores within each group are very close together, but the groups are very different from one another. Because between-group variation is large and within-group variation is small, the video concludes that the type of drink makes a big difference, leading to rejecting the null hypothesis.

Conditions

  • The displayed Example 2 data are used.
  • Between-group variation is much larger than within-group variation.

Reasoning, step by step

  1. Observe that values inside each column are tightly clustered (small within-group variation).
  2. Observe that the three columns occupy clearly separated value ranges (large between-group variation).
  3. Conclude that the drink makes a big difference.
  4. Reject the null hypothesis.

Example

Water group: 29, 29, 30, 31, 31. Juice group: 17, 18, 19, 19, 20. Coffee group: 10, 11, 12, 12, 13. Conclusion text: "it's the drink that makes the difference, not the people."

Common misconceptions

  • Assuming that because the numbers vary a lot overall, the groups must differ meaningfully without checking the balance of variance.

Watch the explanation

1:47 – 2:15Watch this moment ↗

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Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.