Estimating the Standardized Mean Difference in Intervention Studies

Fowler, Robert L.

doi:10.2307/1164708

Cited by 4 publications

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“…Active discussion in the literature has not yet yielded a general consensus on preferred measures. Nevertheless, with some exceptions, proposed effect size statistics can be placed into two broad categories (Fowler, 1988;Plucker, 1997;Snyder & Lawson, 1993;Vacha-Haase & Nilsson, 1998;Young, 1993). One approach derives from estimating effect size based on a standardized difference between group means.…”

Section: When Is An Effect Size Not An Effect Size?mentioning

confidence: 99%

“…In this case, they used baseline and treatment means rather than control and experimental group means, respectively. As Fowler (1988) and Friedman (1968) have pointed out, this approach assumes equal variances across the populations represented by the groups. Fowler further recommended that because of this assumed equality of variances, a pooled standard deviation should be used as the best estimate of the true standard deviation.…”

Section: Issues Concerning Standardizedmentioning

confidence: 99%

“…However, correlational measures of effect sizes have stimulated much more interest in bias adjustments than standardized mean difference effect size measures have, so there are few specific recommendations for bias adjustments to the latter. Fowler (1988) has suggested an empirically derived adjustment for standardized mean differences to estimate population effect sizes. Fowler compared his adjustment with one proposed by Hedges (1982) and found his adjustment to be more precise for sample sizes in the range of 6 ≤ N ≤ 40 and population standardized mean differences in the range of .25 ≤ δ ≤ 1.5.…”

Section: Issues Concerning Standardizedmentioning

confidence: 99%

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Effect Size Use in Studies of Learning Disabilities

Ives

2003

J Learn Disabil

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The misinterpretation and overuse of significance testing in the social sciences has been widely criticized. This criticism is reviewed, along with several recommendations found in the literature, including the use of effect size measures to enhance the interpretation of significance testing. A review of typical effect size measures and their application is followed by an analysis of the extent to which effect size measures have been applied in three prominent journals on learning disabilities over a 10-year period. Specific recommendations are offered for using effect size measures to improve the quality of reporting on quantitative research in the field of learning disabilities.

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Section: When Is An Effect Size Not An Effect Size?mentioning

confidence: 99%

Section: Issues Concerning Standardizedmentioning

confidence: 99%

Section: Issues Concerning Standardizedmentioning

confidence: 99%

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Effect Size Use in Studies of Learning Disabilities

Ives

2003

J Learn Disabil

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“…These were chosen based on relative values of d outlined by Cohen (1988) as "small," "medium," and "large" benchmark effect sizes; these benchmarks are also embraced by some social scientists in practice. Fowler (1988) considered somewhat similar levels but extended the number of levels to include 1.0 and 1.5.…”

Section: Methodsmentioning

confidence: 99%

The Efficacy of Two Improvement-Over-Chance Effect Sizes for Two-Group Univariate Comparisons Under Variance Heterogeneity and Nonnormality

Hess¹,

Olejnik²,

Huberty³

2001

educ psychol meas

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Hypothesis tests and confidence interval estimates for the overlap of two normal distributions with equal variances

Inman

Bradley

1994

Environmetrics

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A special case of the overlapping coefficient, the common area under two probability density curves. that has received intermittent attention in the scientific and statistical literature concerns the overlap of two normal distributions with equal variances. Here we consider the problem of constructing tests of hypotheses and interval estimation for the true overlap in this special situation. Direct and conditional tests for the true value of the overlap are discussed. A method of constructing an exact confidence interval estimator for the true overlap is presented. Several alternative methods of obtaining confidence intervals for the true overlap are compared in a Monte Carlo investigation. In an example, we use the normal theory results discussed and an invariance property of the overlapping coefficient to estimate the overlap between two log-normal distributions from sample data.Given two univariate probability (density) functions fi (x) andf2(x), the general form of the index of dissimilarity or separation coefficient can be defined as the following: --ooThis measure of separation represents the area under whichfi (x) orf2(x) are not common to the other distribution. It can easily be shown that the value of this index is zero when the two distributions are identical; its value is unity when the two distributions are totally disjoint. This measure of the separation between fi (x) and f 2 ( x ) is also a Hellinger or Matusita distance measure.We prefer to work with the complement of this separation index, which we call the overlapping coefficient 0 VL:-oo This measure of the agreement between two distributions meets the usual convention for measures of association noted by Goodman and Kruskal (Reference 5, p. 8): O V L = 1 signifies the perfect identity of the two distributions, and O V L = 0 indicates their complete separation. Since, O V L = 1 -C,, properties determined for one of these measures apply immediately to the other. In the context of two normal distributions with means p2 and p2 and common variance a', OVL=2iP ( --;"11 , , , I ) = 2 @ ( -$ q ) ,where @( -) represents the standard normal distribution function and 6 = (plp 2 ) / o . In this distributional setting, 0 V L can be viewed as a transformation applied to the Mahalanobis distance b2 or the Kulback discrimination information b 2 / 2 . The parameter 6 itself is known as the standard mean difference and has become widely accepted as a measure of effect size in metaanalysis (for example, see Reference 7, pp. 76).A sample estimator for O V L based on independent random samples from the two normal distributions defined above can be obtained by replacing the parameters pI , p2 and 0 in (2) with appropriate sample estimators. Let n l and n2 indicate the sizes of the random samples from the two normal distributions; let XI and Xz denote the usual sample means and S: and S: the unbiased estimators for the common variance o2 computed from the two samples. If we insert XI, X2 and for p l , p2 and 0 in expression (2) for 0 VL, we obtain the maximum-likeli...

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Estimating the Standardized Mean Difference in Intervention Studies

Cited by 4 publications

References 0 publications

Effect Size Use in Studies of Learning Disabilities

Effect Size Use in Studies of Learning Disabilities

The Efficacy of Two Improvement-Over-Chance Effect Sizes for Two-Group Univariate Comparisons Under Variance Heterogeneity and Nonnormality

Hypothesis tests and confidence interval estimates for the overlap of two normal distributions with equal variances

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