On the Exact Variance of Products

Goodman, Leo A.

doi:10.2307/2281592

Cited by 481 publications

(460 citation statements)

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“…Under the assumptions of maximum likelihood and ordinary least squares, O a 1 and O b 1 are asymptotically independent and normally distributed. When it is further assumed that the product O a 1 O b 1 is normally distributed, the exact SE (Aroian, 1947;Craig, 1936;Goodman, 1960) is:…”

Section: Product Of Coefficients Strategiesmentioning

confidence: 99%

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

Preacher

Rucker²,

Hayes

2007

Multivariate Behavioral Research

8,079

6,813

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This article provides researchers with a guide to properly construe and conduct analyses of conditional indirect effects, commonly known as moderated mediation effects. We disentangle conflicting definitions of moderated mediation and describe approaches for estimating and testing a variety of hypotheses involving conditional indirect effects. We introduce standard errors for hypothesis testing and construction of confidence intervals in large samples but advocate that researchers use bootstrapping whenever possible. We also describe methods for probing significant conditional indirect effects by employing direct extensions of the simple slopes method and Johnson-Neyman technique for probing significant interactions. Finally, we provide an SPSS macro to facilitate the implementation of the recommended asymptotic and bootstrapping methods. We illustrate the application of these methods with an example drawn from the Michigan Study of Adolescent Life Transitions, showing that the indirect effect of intrinsic student interest on mathematics performance through teacher perceptions of talent is moderated by student math self-concept.

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Section: Product Of Coefficients Strategiesmentioning

confidence: 99%

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

Preacher

Rucker²,

Hayes

2007

Multivariate Behavioral Research

8,079

6,813

View full text Add to dashboard Cite

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“…Consequently, variances for these products were calculated as described previously (19,32). Annual fungal production and microbial respiration (per gram of plant litter and per m 2 of stream bottom) were estimated by interpolating between sampling dates and summing up daily production or respiration estimates over the year.…”

Section: Methodsmentioning

confidence: 99%

Comparison of Fungal Activities on Wood and Leaf Litter in Unaltered and Nutrient-Enriched Headwater Streams

Gulis

Suberkropp

Rosemond

2008

Appl Environ Microbiol

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Fungi are the dominant organisms decomposing leaf litter in streams and mediating energy transfer to other trophic levels. However, less is known about their role in decomposing submerged wood. This study provides the first estimates of fungal production on wood and compares the importance of fungi in the decomposition of submerged wood versus that of leaves at the ecosystem scale. We determined fungal biomass (ergosterol) and activity associated with randomly collected small wood (<40 mm diameter) and leaves in two southern Appalachian streams (reference and nutrient enriched) over an annual cycle. Fungal production (from rates of radiolabeled acetate incorporation into ergosterol) and microbial respiration on wood (per gram of detrital C) were about an order of magnitude lower than those on leaves. Microbial activity (per gram of C) was significantly higher in the nutrient-enriched stream. Despite a standing crop of wood two to three times higher than that of leaves in both streams, fungal production on an areal basis was lower on wood than on leaves (4.3 and 15.8 g C m ؊2 year ؊1 in the reference stream; 5.5 and 33.1 g C m ؊2 year ؊1 in the enriched stream). However, since the annual input of wood was five times lower than that of leaves, the proportion of organic matter input directly assimilated by fungi was comparable for these substrates ( Terrestrial detritus in the form of leaves and wood is an important carbon and energy source for microorganisms and food webs in freshwaters. Detritus-associated microorganisms also control important processes in aquatic ecosystems, including the uptake and sequestration of dissolved inorganic nutrients (33, 37). Fungi, rather than bacteria, dominate the microbial biomass on coarse particulate organic matter (CPOM), such as leaves and wood in streams, and fungal production on submerged leaves is also greater than that of bacteria (10,14,23,28,56). A recent study suggests that fungal ribotype richness levels (as determined by denaturing gradient gel electrophoresis) may be higher than those of bacteria and actinomycetes on submerged leaves (10). Thus, fungi are likely the most important biological driver of processes such as CPOM carbon dynamics and detritus-associated nutrient uptake in headwater streams.Both allochthonous leaf litter and submerged wood in streams harbor diverse communities of fungi, mainly ascomycetes and their anamorphs (hyphomycetes) (see, e.g., references 4, 39, and 51) though chytrids, zygomycetes, and basidiomycetes have also been detected by using molecular techniques (35). Communities can be species rich. For example, more than 200 species from wood in a single river have been reported (51), whereas the diversity of aquatic hyphomycetes that colonize mostly leaves is considerably lower (e.g., see reference 5). Aquatic fungi also show some substrate preferences (13, 22), so leaves and wood harbor different communities that may result in different biomass and activity. While several studies have quantified biomass and production of fungi associate...

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“…This observation led us to statistically test whether the between group differences in SBP were partially explained by parental variations in reporting of social support. Accordingly, we tested for mediation using the Goodman test (Goodman, 1960) and found that social support mediated this association, z = 2.04, p =.04. Thus, it would seem that social support was not only associated with daytime SBP independently of parental group in these models but it accounted, at least in part, for some of the variation in group differences in SBP.…”

Section: Contribution Of Potential Psychosocial Variables To Group DImentioning

confidence: 99%

Social support is associated with blood pressure responses in parents caring for children with developmental disabilities

Gallagher

Whiteley

2012

Research in Developmental Disabilities

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Highlights► Caregiving is associated with high blood pressure in parents.► Caregiving is associated with high stress and low social support in parents.► Social support is associated with blood pressure responses in parents.► The importance of the social support for these families was discussed. AbstractThe present study tested whether parents caring for children with developmental disabilities would have higher blood pressure compared to parents of typically developing children (controls). It also examined the psychosocial factors underlying this observation. Thirty-five parents of children with developmental disability and thirty controls completed standard measures of perceived stress, child challenging behaviours and social support and wore an ambulatory blood pressure (BP) monitor throughout the day, for one day. Relative to controls, parents caring for children with developmental disabilities reported poorer psychosocial functioning and had a higher mean systolic BP. Of the psychosocial predictors, only social support was found to be predictive. Moreover, variations in social support accounted for some of the between group differences with the β for parental group attenuated from .42 to .34 in regressionanalyses. It appears that social support may influence blood pressure responses in parental caregivers. Finally, our findings underscore the importance of providing psychosocial interventions to improve the health of family caregivers.

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On the Exact Variance of Products

Cited by 481 publications

References 0 publications

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

Comparison of Fungal Activities on Wood and Leaf Litter in Unaltered and Nutrient-Enriched Headwater Streams

Social support is associated with blood pressure responses in parents caring for children with developmental disabilities

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