10-18 math - Notation and Equations for Effect Size Lecture...

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Notation’and’Equations’for’Effect’Size’Lecture 10/18’ Notation:’ d :’ Cohen±s’ d ,’which’measures’effect’size’relative’to’the’standard’deviation’of’raw’scores Point’estimates’of’effect’size’with’t -tests.’In’a’t -test,’we’are’looking’for’differences’in’ means.’ ’ The’assoc iated’effect’size’is’just’that —the’difference’in’means.’The’true’effect’ sizes’are’based’on’the’true’population’means: One’sample:’ ’ μ ’ -’ μ 0 (1)’ Independent’samples:’ ’ μ A ’ –’ μ B (2)’ Paired’samples:’ ’ μ diff (3)’ Notice’that’for’each’t -test’the’null’hypot hesis’is’equivalent’to’the’assumption’that’the’effect’ size’equals’zero.’Therefore,’you’can’also’think’of’the’effect’size’as’how’much’the’null’ hypothesis’is’violated. ’ In’an’actual’experiment,’we’don±t’know’the’population’mean(s).’Therefore,’we’estimate’ the’effect’size’using’the’sample’mean(s). ’ This’gives’the’point’estimate’of’the’effect’size. One’sample:’ ’ M ’ -’ μ 0 (4)’ Independent’samples:’ ’ M A ’ –’ M B (5)’ Paired’samples:’ ’ M diff (6)’ Critical’v alue’ for’a’confidence’interval .’ The’critical’value’of’any’inferential’statistic’is’the’ cutoff’value’between’retaining’and’rejecting’the’null’hypothesis.’If’ the’statistic’you’ compute’from’your’sample’is’more’extreme’than’the’critical’value,’you’reject’the’null’ hypothesis;’otherwise’you ’ retain’the’null.’ For’computing’confidence’intervals,’you’always’want’the’critical’value’for’a’two -tailed’test.’ A’two -tailed’test’actually’has’two’critical’values’ –’ one’positive’and’one’negative’ –’ but’these’ have’the’same’absolute’value’(i.e.,’one’is’the ’ negative’of’the’other),’so’for’confidence’ intervals’we’just’think’about’the’positive’one.’ For’t -tests,’we’call’this’positive’critical’value’ t crit .’
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