Sampling Characteristics of Kelley's ε and Hays' ω

Carroll, Robert M.; Nordholm, Lena A.

doi:10.1177/001316447503500304

Cited by 75 publications

(74 citation statements)

References 7 publications

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“…Vaughan and Corballis (1969) cautioned against the use of omega squared in these situations. Carroll and Nordholm (1975), however, found that in a single-factor design, unequal n had little effect on the estimation of Kelley's ε 2 or Hay's ω 2 if variances are equal, and with equal n heterogeneous variances had little impact on the estimation of these effect sizes. But unequal n and heterogeneous variances lead to an overestimation of the effect size, and Carroll and Nordholm cautioned against their use in these situations.…”

Section: Cautionary Notesmentioning

confidence: 90%

“…But unequal n and heterogeneous variances lead to an overestimation of the effect size, and Carroll and Nordholm cautioned against their use in these situations. Carroll and Nordholm (1975) also showed empirically that the standard errors for both ε 2 and ω 2 can be large when sample sizes are small. Even when the total sample size from three populations equaled 90 the standard errors for these effect size measures were unacceptably large.…”

Section: Cautionary Notesmentioning

confidence: 91%

“…Generally epsilon squared and omega squared will only differ slightly (Carroll & Nordholm, 1975). Estimated epsilon squared and estimated omega squared can be negative and negative estimates are typically set equal to zero.…”

Section: Contrastsmentioning

confidence: 99%

See 2 more Smart Citations

Measures of Effect Size for Comparative Studies: Applications, Interpretations, and Limitations

Olejnik¹,

Algina

2000

Contemporary Educational Psychology

578

370

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Although dissatisfaction with the limitations associated with tests for statistical significance has been growing for several decades, applied researchers have continued to rely almost exclusively on these indicators of effect when reporting their findings. To encourage an increased use of alternative measures of effect, the present paper discusses several measures of effect size that might be used in group comparison studies involving univariate and/or multivariate models. For the methods discussed, formulas are presented and data from an experimental study are used to demonstrate the application and interpretation of these indices. The paper concludes with some cautionary notes on the limitations associated with these measures of effect size.

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Section: Cautionary Notesmentioning

confidence: 90%

Section: Cautionary Notesmentioning

confidence: 91%

See 1 more Smart Citation

Measures of Effect Size for Comparative Studies: Applications, Interpretations, and Limitations

Olejnik¹,

Algina

2000

Contemporary Educational Psychology

578

370

View full text Add to dashboard Cite

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“…Thus, although the ordinal relationship shown in Equation 8 holds, it is possible thatω 2 underestimates the population effect size more thanε 2 does. Second, another Monte Carlo study by Carroll and Nordholm (1975) produced results that somewhat contradicted those of Keselman (1975). Putting aside the fact that their study used a smaller number of replications per condition than Keselman's which may have resulted in more sampling errors, Carroll and Nordholm's (1975) results implied that while "ω 2 is slightly negatively biased" (p.548), "any bias inε 2 is not evident" (p.549).…”

Section: (Equationmentioning

confidence: 97%

Is Omega Squared Less Biased? a Comparison of Three Major Effect Size Indices in One-Way Anova

Okada

2013

Behaviormetrika

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The purpose of this study is to find less biased effect size index in one-way analysis of variance (ANOVA) by performing a thorough Monte Carlo study with 1,000,000 replications per condition. Our results show that contrary to common belief, epsilon squared is the least biased among the threemajorindices, while omega squared produces the least root mean squared errors, for all conditions. Although eta squared results in the least standard deviation, this does not necessarily make it a good estimator because a considerable amount of bias still occurs when the sample size is small.

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“…A 2 differs qualitatively from an F statistic because it is insensitive to changes in sample size (9,30). This index is often referred to as the proportion of variation "accounted for" by the experimental manipulation, or "explained variance."…”

Section: Analyses Of Effect Sizesmentioning

confidence: 99%

Gonadal hormone-dependent and -independent regulation of immune function by photoperiod in Siberian hamsters

Prendergast¹,

Baillie²,

Dhabhar³

2008

American Journal of Physiology-Regulatory, Integrative and Comp

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Siberian hamsters (Phodopus sungorus) exhibit changes in reproductive and immune function in response to seasonal variations in day length. Exposure to short days induces gonadal regression and inhibits testosterone secretion. In parallel, short days enhance immune function: increasing leukocyte numbers and attenuating cytokine and behavioral responses to infection. We examined whether photoperiodic changes in leukocyte phenotypes and sickness behaviors are dependent on concurrent photoperiodic changes in gonadal function. Male hamsters were gonadectomized or sham-gonadectomized and either exposed to short days (9 h light/day; SD) or kept in their natal long-day (15 h light/day; LD) photoperiod for 10 -13 wk. Blood samples were obtained for leukocyte enumeration, and hamsters were challenged with bacterial LPS, which induced behavioral (anorexia, reductions in nest building) and somatic (weight loss) sickness responses. Among gonad-intact hamsters, exposure to SD increased total and CD62Lϩ lymphocytes and CD3ϩ T lymphocytes in blood and significantly attenuated LPSinduced sickness responses. Independent of photoperiod, castration alone increased total and CD62Lϩ lymphocyte and CD3ϩ T lymphocyte numbers and attenuated somatic and anorexic sickness responses. Among castrated hamsters, SD exposure increased lymphocyte numbers and suppressed sickness behaviors. In castrated hamsters, the magnitude of most immunological effects of SD were diminished relative to those evident in gonad-intact hamsters. The SD phenotype in several measures of immunity can be instated via elimination of gonadal hormones alone; however, photoperiodic effects on immune function persist even in castrated hamsters. Thus, photoperiod affects the immune system and neural-immune interactions underlying sickness behaviors via gonadal hormone-dependent and -independent mechanisms. seasonality; sickness behaviors; infection; neural-immune interactions SEASONAL CHANGES IN PHYSIOLOGY and behavior are legion, most notably in reproductive function (8). Many mammals have evolved mechanisms that permit cessation of reproduction during intervals of the year when environmental conditions of food availability and ambient temperature are unfavorable for successful weaning of offspring (44,47). In nonequatorial regions, changes in day length (photoperiod) predict these environmental constraints (46) and function as proximate cues for triggering anticipatory changes in reproductive physiology and behavior. In long-day breeders, decreasing photoperiods of late-summer trigger gonadal atrophy, withdrawal of gonadal hormone secretion, and cessation of sex behaviors (8). The full complement of changes in the reproductive system can be elicited in the laboratory by exposing reproductively photoperiodic animals to winter-like day lengths (Ͻ12 h of light/day) (22).Seasonal changes in immune function also occur in wild and laboratory animals (34), and a growing body of research indicates photoperiod likewise drives these cycles. Among long-day breeding rodents, many a...

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Sampling Characteristics of Kelley's ε and Hays' ω

Cited by 75 publications

References 7 publications

Measures of Effect Size for Comparative Studies: Applications, Interpretations, and Limitations

Measures of Effect Size for Comparative Studies: Applications, Interpretations, and Limitations

Is Omega Squared Less Biased? a Comparison of Three Major Effect Size Indices in One-Way Anova

Gonadal hormone-dependent and -independent regulation of immune function by photoperiod in Siberian hamsters

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