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Understanding Probabilistic Equivalence in Experimental Design

Probabilistic equivalence is a critical concept in experimental design, indicating that while we can determine the likelihood of observing pretest differences between two groups, it does not guarantee identical pretest means. For instance, with an alpha level of 0.05, we expect to see a pretest difference 5 times out of 100 due to chance. Even with observed differences, these results do not impact posttest outcomes. Random assignment means any differences arise from luck, emphasizing the importance of controlling for chance in experimental studies.

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Understanding Probabilistic Equivalence in Experimental Design

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  1. Probabilistic Equivalence in Experimental Design

  2. What Is Probabilistic Equivalence? • It means that we know perfectly the odds that we will find a pretest difference between the two groups. • It doesn’t mean that the two groups will have identical pretest means.

  3. What Is Probabilistic Equivalence? Group 1 49

  4. What Is Probabilistic Equivalence? Group 1 Group 2 51 49

  5. What Is Probabilistic Equivalence? Group 1 Group 2 51 49 With  = .05, we expect that we will observe a pretest difference 5 times out of 100.

  6. What Is Probabilistic Equivalence? • Even if we observe a pretest difference, it must be due to chance because we assigned by chance (so it’s one of the 5 out of 100 cases).

  7. What Is Probabilistic Equivalence? • If we observe a pretest difference, what does this mean for the posttest? • NOTHING! • The odds we will observe a posttest difference by chance are still 5 out of a 100 (with =.05).

  8. What Is Probabilistic Equivalence? • Because we assigned randomly, we could observe differences on either the pretest or posttest, but these must be due to chance (or the luck of the draw). • We know perfectly the odds of observing a chance difference. • We can control this (through ).

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