effect size discussion

7/26/2019 Effect Size Discussion

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$orrelations

Ho do &ou interpret 'alues %eteen 0 and @A i$$erent authors suggest di$$erentinterpretations* hoe'er, ohen (4988, pp. :984) suggests the $olloing guidelines

• 1mall r = .40 to .29

• Bedium r = .!0 to .9

• Carge r = ."0 to 4.0

&ultiple 'eression

1o ho man& cases or su%ects do &ou needA i$$erent authors tend to gi'e di$$erentguidelines concerning the num%er o$ cases re#uired $or multiple regression. 1te'ens(4996, p. :2) recommends that -for social science research, about 5 sub*ectsper predictor are needed for a reliable e+uation -. 7a%achnic+ and idell (200:, p.42!) gi'e a $ormula $or calculating sample si;e re#uirements, ta+ing into account thenum%er o$ independent 'aria%les that &ou ish to use N D "0 3 8 k (here k =num%er o$ independent 'aria%les). @$ &ou ha'e $i'e independent 'aria%les, &ou illneed 90 cases. &ore cases are needed if the dependent variable is sewed or stepise regression, there should %e a ratio o$ 0 cases $or e'er& independent'aria%le.

@ndi'idual predictors then the sample si;e = 40! 3 k (Ereen, 4994)

Ereen, 1. F. (4994). Ho man& su%ects does it ta+e to do a regression anal&sisAMultivariate Behavioral Research, 26, 995"40.

7a%achnic+, F. E., G idell, C. 1. (200:). Using multivariate statistics ("th ed.).Foston ll&n G Facon



"ormality and .ransformation

Not e'er&one agrees that trans$orming data is a good idea* $or e<ample, Elass,?ec+ham, and 1anders (49:2) in a 'er& e<tensi'e re'ie commented that /thepayoff of normalizin transformations in terms of more valid probability

statements is low, and they are seldom considered to be worth the effort (p.24). @n hich case, should e %otherA

7he issue is #uite complicated (especiall& $or this earl& in the %oo+), %ut essentiall&e need to +no hether the statistical models e appl& per$orm %etter ontrans$ormed data than the& do hen applied to data that 'iolate the assumption thatthe trans$ormation corrects. @$ a statistical model is still accurate e'en hen itsassumptions are %ro+en it is said to %e a robust test. @m not going to discusshether particular tests are ro%ust here, %ut @ ill discuss the issue $or particular tests in their respecti'e chapters. 7he #uestion o$ hether to trans$orm is lin+ed tothis issue o$ ro%ustness (hich in turn is lin+ed to hat test &ou are per$orming on&our data). good case in point is the F-test in NIJ, hich is o$ten claimed to %ero%ust (Elass et al., 49:2). /arl& $indings suggested that F per$ormed as it should ins+eed distri%utions and that trans$orming the data helped as o$ten as it hinderedthe accurac& o$ F (Eames G Cucas, 4966). Hoe'er, in a li'el& %ut in$ormati'ee<change Ce'ine and unlap (4982) shoed that trans$ormations o$ s+e didimpro'e the per$ormance o$ F * hoe'er, in a response Eames (498!) argued thattheir conclusion as incorrect, hich Ce'ine and unlap (498!) contested in aresponse to the response. inall&, in a response to the response o$ the response,Eames (498) pointed out se'eral important #uestions to consider

4. 7he central limit theorem tells us that in %ig samples the sampling distri%utionill %e normal regardless, and this is whats actually important so thedebate is academic in anythin other than small samples (ield, 2009)Cots o$ earl& research did indeed sho that ith samples o$ 0 the normalit&o$ the sampling distri%ution as, as predicted, normal. Hoe'er, this research$ocused on distri%utions ith light tails and su%se#uent or+ has shon thatith hea'&tailed distri%utions larger samples ould %e necessar& to in'o+ethe central limit theorem (Wilco<, 200"). 7his research suggests thattrans$ormations might %e use$ul $or such distri%utions.

2. F& trans$orming the data &ou change the h&pothesis %eing tested (hen using

a log trans$ormation and comparing means &ou change $rom comparingarithmetic means to comparing geometric means). 7rans$ormation also meansthat &oure no addressing a di$$erent construct to the one originall&measured, and this has o%'ious implications $or interpreting that data(Era&son, 200).

!. @n small samples it is tric+& to determine normalit& one a& or another (testssuch as K51 ill ha'e lo poer to detect de'iations $rom normalit& andgraphs ill %e hard to interpret ith so $e data points).

. 7he conse#uences $or the statistical model o$ appl&ing the Lrong

trans$ormation could %e orse than the conse#uences o$ anal&;ing theuntrans$ormed scores.



7here is an e<tensi'e li%rar& o$ ro%ust tests that can %e used and hich ha'econsidera%le %ene$its o'er trans$orming data. 7he de$initi'e guide to these isWilco<s (200") outstanding %oo+.

Eames, ?. . (498!). ur'ilinear trans$ormations o$ the dependent 'aria%le.Psychological Bulletin, 93(2), !825!8:.

Eames, ?. . (498). ata trans$ormations, poer, and s+e re%uttal to Ce'ineand unlap. Psychological Bulletin,

95 (2), !"5!:.Eames, ?. ., G Cucas, ?. . (4966). ?oer o$ the anal&sis o$ 'ariance o$

independent groups on nonnormal and normall& trans$ormed data.Educational and Psychological Measurement, ! , !445!2:.

Elass, E. J. (4966). 7esting homogeneit& o$ 'ariances. "merican Educational Research #ournal, 3(!), 48:5490.

Elass, E. J., ?ec+ham, ?. ., G 1anders, M. >. (49:2). onse#uences o$ $ailure to

meet assumptions underl&ing the $i<ed e$$ects anal&ses o$ 'ariance andco'ariance. Revie$ o% Educational Research, & (!), 2!:5288.

Era&son, . (200). 1ome m&ths and legends in #uantitati'e ps&cholog&.Understanding 'tatistics, 3(4), 40454!

Ce'ine, . W., G unlap, W. ?. (4982). ?oer o$ the test ith s+eed data 1houldone trans$orm or notA Psychological Bulletin, 9 (4), 2:25280.

Wilco<, >. >. (200"). (ntroduction to ro)ust estimation and hy*othesis testing (2nded.). Furlington, B /lse'ier.

effect size discussion

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