A Primer of Multivariate Statistics

Harris, Richard

doi:10.4324/9781410600455

Cited by 484 publications

(539 citation statements)

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“…The univariate tests do not account for relations among the cognitive dimensions, and they confound level and measure effects. A traditional multivariate analysis of variance determines how a set of measures can be combined into a set of K -1 univariate composites (discriminant functions), which maximally separates groups (Bernstein, Garbin, & Teng, 1988;Harris, 1975). However, each composite comprises elements that involve differences not only in elevation but also in shape, both of which seem apparent in the profiles shown in Figure 1.…”

Section: Group Comparisons On Cognitive Dimensionsmentioning

confidence: 99%

Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?

Fuchs¹,

Fuchs²,

Stuebing³

et al. 2008

Journal of Educational Psychology

215

275

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The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains, or neither domain; and measured on 9 cognitive dimensions. Difficulty occurred across domains with the same prevalence as difficulty with a single domain; specific difficulty was distributed similarly across domains. Multivariate profile analysis on cognitive dimensions and chi-square tests on demographics showed that specific computational difficulty was associated with strength in language and weaknesses in attentive behavior and processing speed; problem-solving difficulty was associated with deficient language as well as race and poverty. Implications for understanding mathematics competence and for the identification and treatment of mathematics difficulties are discussed. Keywordscalculations; word problems; cognitive predictors; mathematics Mathematics, which involves the study of quantities as expressed in numbers or symbols, comprises a variety of related branches. In elementary school, for example, mathematics is conceptualized in strands such as concepts, numeration, measurement, arithmetic, algorithmic computation, and problem solving. In high school, curriculum offerings include algebra, geometry, trigonometry, and calculus. Little is understood, however, about how different aspects of mathematical cognition relate to one another (i.e., which aspects of performance are shared or distinct, or how difficulty in one domain corresponds with difficulty in another). SuchCorrespondence concerning this article should be addressed to Lynn S. Fuchs, Peabody College, Box 228, Vanderbilt University, Nashville, TN 37203. lynn.fuchs@vanderbilt.edu. NIH Public AccessAuthor Manuscript J Educ Psychol. Author manuscript; available in PMC 2010 January 6. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript understanding would provide theoretical insight into the nature of mathematics competence and practical guidance about the identification and treatment of mathematics difficulties.The purpose of the present study was to explore the overlap of difficulty with two aspects of primary-grade mathematical cognition and to examine how characteristics differ among subgroups with difficulty in one, the other, both, or neither. The first aspect of performance was computation, including skill with number combinations (e.g., 2 + 5; 8 − 3) and procedural computation (e.g., 25 + 38; 74 − 22). The second aspect of performance was problem solving, including one-step, contextually straightforward word problems (e.g., John had 9 pennies. He spent 3 pennies at the store. How many pennies did he have left?) and multistep, contextually more complex problems (e.g., Fred went to the ballgame with 2 friends. He left his house with $42. While at the game, he bought 5 h...

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Section: Group Comparisons On Cognitive Dimensionsmentioning

confidence: 99%

Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?

Fuchs¹,

Fuchs²,

Stuebing³

et al. 2008

Journal of Educational Psychology

215

275

View full text Add to dashboard Cite

show abstract

“…The variable defined by the first linear combination is the first canonical variable or canonical component or yet, Fisher linear discriminant function, whose effectiveness increases in proportion to the percentage of the total variance attributed to it (Harris, 1975). The second canonical variable is obtained by defining the linear combination of the original variables, not correlated with the first canonical variable, which has the highest possible multiple correlation.…”

Section: Introductionmentioning

confidence: 99%

Canonical discriminant analysis applied to broiler chicken performance

Rosário

Silva

Coelho

et al. 2008

Animal

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The mechanisms involved in the control of growth in chickens are too complex to be explained only under univariate analysis because all related traits are biologically correlated. Therefore, we evaluated broiler chicken performance under a multivariate approach, using the canonical discriminant analysis. A total of 1920 chicks from eight treatments, defined as the combination of four broiler chicken strains (Arbor Acres, AgRoss 308, Cobb 500 and RX) from both sexes, were housed in 48 pens. Average feed intake, average live weight, feed conversion and carcass, breast and leg weights were obtained for days 1 to 42. Canonical discriminant analysis was implemented by SAS R CANDISC procedure and differences between treatments were obtained by the F-test (P , 0.05) over the squared Mahalanobis' distances. Multivariate performance from all treatments could be easily visualised because one graph was obtained from two first canonical variables, which explained 96.49% of total variation, using a SAS R CONELIP macro. A clear distinction between sexes was found, where males were better than females. Also between strains, Arbor Acres, AgRoss 308 and Cobb 500 (commercial) were better than RX (experimental). Evaluation of broiler chicken performance was facilitated by the fact that the six original traits were reduced to only two canonical variables. Average live weight and carcass weight (first canonical variable) were the most important traits to discriminate treatments. The contrast between average feed intake and average live weight plus feed conversion (second canonical variable) were used to classify them. We suggest analysing performance data sets using canonical discriminant analysis.

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“…To complement the analysis, the first canonical discriminant function was used; according to Harris (1975), it results in higher value for the F test, considering any linear combination involving the variables analyzed. Bionutritional efficiency was determined from the coefficients generated by the analysis of the first canonical variable, forming the following equation: coefficient of bionutritional efficiency = 6.2172*(ADG) -0.4836*(DMI).…”

Section: Introductionmentioning

confidence: 99%

Animal performance and carcass characteristics of Nellore young bulls fed coated or uncoated urea slaughtered at different weights

Pazdiora

Resende

Faria³

et al. 2013

R. Bras. Zootec.

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-The objective of this study was to evaluate animal performance and carcass characteristics of 64 Nellore young bulls at 22 months of age finished in a feedlot and slaughtered at five body weights (350; 455; 485; 555 and 580 kg) fed diets containing coated or uncoated urea. The experimental design adopted was completely randomized, set in a 4 × 2 factorial arrangement, and for the variables assessed in the control animals, it was 5 × 2. No effect of interaction between slaughter weights and diets were observed, so the variables were analyzed separately, compared by polynomial contrasts and by the F test, respectively. The time animals remained in the feedlot to reach slaughter weights was 66, 88, 145 and 194 days. Average daily gain (ADG) showed quadratic behavior, with a maximum of 1.44 kg/day with animals of 491.7 kg. Dry matter intake (DMI) (kg/day) was similar in all the treatments, but it decreased linearly as body weight increased. The bionutritional efficiency worsened linearly as body weight rose. The elevation in slaughter weight resulted in linear decrease in the percentage of beef round and increase in forequarter. Backfat thickness and rib eye area of the longissimus increased linearly and the percentages of muscle and protein in the carcass reduced and those of fat and ether extract increased linearly as body weight increased. Average daily gain, DMI, feed efficiency and carcass characteristics were not affected by diets containing coated or uncoated urea. However, animals fed coated urea presenter better crude fiber and neutral detergent fiber intake.

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A Primer of Multivariate Statistics

Cited by 484 publications

References 0 publications

Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?

Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?

Canonical discriminant analysis applied to broiler chicken performance

Animal performance and carcass characteristics of Nellore young bulls fed coated or uncoated urea slaughtered at different weights

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