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# Probabilistic Equivalence in Experimental Design

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Probabilistic Equivalence in Experimental DesignWhat Is Probabilistic Equivalence?Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Probabilistic Equivalence in Probabilistic Equivalence in Experimental DesignExperimental DesignWhat Is Probabilistic Equivalence?What Is Probabilistic Equivalence?It means that we know It means that we know perfectlyperfectly the the odds that we will find a pretest odds that we will find a pretest difference between the two groups.difference between the two groups.It It does n’tdoes n’t mean that the two groups will mean that the two groups will have identical pretest means.have identical pretest means.What Is Probabilistic Equivalence?What Is Probabilistic Equivalence?49Group 1What Is Probabilistic Equivalence?What Is Probabilistic Equivalence?4951Group 1 Group 2What Is Probabilistic Equivalence?What Is Probabilistic Equivalence?4951With  = .05, we expect that we will observe a pretest difference 5 times out of 100.Group 1 Group 2What Is Probabilistic Equivalence?What Is Probabilistic Equivalence?Even if we observe a pretest difference, Even if we observe a pretest difference, it must be due to it must be due to chanc echanc e because we because we assigned by chance (so it’s one of the 5 assigned by chance (so it’s one of the 5 out of 100 cases).out of 100 cases).What Is Probabilistic Equivalence?What Is Probabilistic Equivalence?If we observe a pretest difference, what If we observe a pretest difference, what does this mean for the does this mean for the posttes tposttes t??NOTHINGNOTHING!!The odds we will observe a posttest The odds we will observe a posttest difference by chance are difference by chance are stillstill 5 out of a 5 out of a 100 (with 100 (with =.05).=.05).What Is Probabilistic Equivalence?What Is Probabilistic Equivalence?Because we assigned randomly, we Because we assigned randomly, we couldcould observe differences on either the observe differences on either the pretest or posttest, but these must be pretest or posttest, but these must be due to due to chanc echanc e (or the luck of the draw). (or the luck of the draw).We know We know perfectlyperfectly the odds of the odds of observing a chance difference.observing a chance difference.We can control this (through We can control this (through Unlocking...