Analysis of Covariance

Jul 14, 2014

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Analysis of Covariance. The function of Experimental design is to explain the effect of a IV or DV while controlling for the confounding effect of extraneous variables. Analysis of Covariance.

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different teachings situations
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Analysis of Covariance

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Analysis of Covariance The function of Experimental design is to explain the effect of a IV or DV while controlling for the confounding effect of extraneous variables.
Analysis of Covariance When extraneous variable are not controlled the results of the measurement can not be attributed to solely the experiment treatment.
Analysis of Covariance ANOCOVA - combination of ANOVA and linear regression present a covariant as another variable that the groups may differ on.
Analysis of Covariance • Effect of two different teachings situations on clinical performances in clinical • Previous GPA may be a factor if not controlled • Control for GPA to find true effects of teaching strategies.
Analysis of Covariance

Analysis of Covariance

Analysis of Covariance.

678 views • 31 slides

Covariance structures in longitudinal analysis

Covariance structures in longitudinal analysis. Which one to choose?. Repeated Measures. Importance of Covariance Structures. variability not explained by the fixed effects are model in the covariance structure represent the background variability that the fixed effects are tested against

1.12k views • 39 slides

Covariance

Covariance. And portfolio variance. The states of nature model. Time zero is now. Time one is the future. At time one the possible states of the world are s = 1,2,…,S. Mutually exclusive, collectively exhaustive states. This IS the population. No sampling. The states of nature model.

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Analysis of Covariance

Analysis of Covariance. 46-512: Statistics for Graduate Study in Psychology. Learning Outcomes. What is an ANCOVA? How does it relate to what we have done already? When would we use it? What are the issues & assumptions? What are some limitations and alternatives?.

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One-Way Analysis of Covariance

One-Way Analysis of Covariance. One-Way ANCOVA. ANCOVA. Allows you to compare mean differences in 1 or more groups with 2+ levels (just like a regular ANOVA), while removing variance from a 3 rd variable What does this mean?. ANCOVA. ANCOVA.

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Analysis of Covariance

Analysis of Covariance. Goals:. Reduce error variance. Remove sources of bias from experiment. Obtain adjusted estimates of population means. Analysis of Covariance. Y. Y. X .1. X . X .2. X. X .1. X. X .2. X . Random assignment conditional distribution is less variable.

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Analysis of Covariance (Chapter 16)

Analysis of Covariance (Chapter 16). A procedure for comparing treatment means that incorporates information on a quantitative explanatory variable, X , sometimes called a covariate . The procedure, ANCOVA, is a combination of ANOVA with regression. Example: Calf Weight Gain.

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Maximum Covariance Analysis

Maximum Covariance Analysis. Canonical Correlation Analysis. FIG. 6. The CCA mode 1 for (a) SLP and (b) SST . The pattern in (a) is scaled by [max(u )-min (u)]/2, and (b) by [max ( v )-min( v ) ]/2 . Contour interval is 0.5 mb in (a) and 0.5C in (b).

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LECTURE 13 ANALYSIS OF COVARIANCE AND COVARIANCE INTERACTION

LECTURE 13 ANALYSIS OF COVARIANCE AND COVARIANCE INTERACTION. and ATI (Aptitude-Treatment Interaction). ANCOVA. ANCOVA model The simplest ANCOVA model includes a covariate C , an exogenous treatment variable X , and an outcome Y : y ij =  y +  i  ij +  c ij + e ij

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Analysis of Variance and Covariance

Analysis of Variance and Covariance. 16- 1. Chapter Outline. Overview Relationship Among Techniques 3) One-Way Analysis of Variance 4) Statistics Associated with One-Way Analysis of Variance 5) Conducting One-Way Analysis of Variance

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Analysis of Covariance, ANCOVA (GLM2)

Analysis of Covariance, ANCOVA (GLM2). Aims. When and Why do we use ANCOVA? Partitioning Variance Carrying out on PASW/SPSS Interpretation Main Effects Covariates. When And Why.

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Analysis of Covariance (ANCOVA)

Analysis of Covariance (ANCOVA) Analysis of variance conducted after removing the relationship of some extraneous variable (covariate) with the dependent variable (Y) What variability in DV can be explained by IV, AFTER removing variability explained by the covariate?.

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One-Way Analysis of Covariance (ANCOVA)

One-Way Analysis of Covariance (ANCOVA). Extension of Analysis of Variance (ANOVA) One categorical independent (grouping) variable One continuous dependent variable Add additional continuous covariate(s) Covariates hypothesized to have potential effect on outcome of interest

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Analysis of Covariance

Analysis of Covariance. Harry R. Erwin, PhD School of Computing and Technology University of Sunderland. Resources. Crawley, MJ (2005) Statistics: An Introduction Using R. Wiley. Freund, RJ, and WJ Wilson (1998) Regression Analysis, Academic Press.

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REVIEW OF COVARIANCE

REVIEW OF COVARIANCE. Consider an asset A, whose expected return is k a . k a is an unknown variable, BUT with a known probability distribution. e.g. Treasury Bill Amazon.com. Probability distribution. Amazon. T-Bill. Rate of return (%). -70. 2. 15. 100. Expected Rate of Return.

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Analysis of Covariance

Analysis of Covariance. David Markham djmarkham@bsu.edu. Analysis of Covariance. Analysis of Covariance (ANCOVA) is a statistical test related to ANOVA It tests whether there is a significant difference between groups after controlling for variance explained by a covariate

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Definition of Covariance

Definition of Covariance. The covariance of X & Y , denoted Cov ( X , Y ), is the number where m X = E ( X ) and m Y = E ( Y ). Computational Formula:. Variance of a Sum. Covariance and Independence. If X & Y are independent, then Cov ( X , Y ) = 0.

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Analyses of Covariance

Analyses of Covariance. Comparing k means adjusting for 1 or more other variables (covariates) Ho: u 1 = u 2 = u 3 (Adjusting for X) Combines ANOVA and regression u y = u k + b X Assumptions are same as ANOVA + regression Y normally distributed, constant variance across groups

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Analysis of Covariance

Analysis of Covariance. Combines linear regression and ANOVA Can be used to compare g treatments, after controlling for quantitative factor believed to be related to response (e.g. pre-treatment score)

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The Analysis of Covariance

The Analysis of Covariance. ANACOVA. Multiple Regression. Dependent variable Y (continuous) Continuous independent variables X 1 , X 2 , …, X p. The continuous independent variables X 1 , X 2 , …, X p are quite often measured and observed (not set at specific values or levels).

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Analysis of Covariance

Analysis of Covariance. Comparison of Head-Lengths for Trout from 2 Lakes Source: C. McC. Mottley (1941). “The Covariance Method of Comparing the Head-Lengths of Trout From Different Environments,” Copeia , Vol.1941, #3, pp.154-159. Analysis of Covariance.

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Analysis of Covariance Experimental Designs

Analysis of Covariance Experimental Designs. Design Notation. R O X O R O O. Uses a pre-measure Can be a pretest, but doesn’t have to be Can have multiple covariates. 1. 0. 0. 9. 0. 8. 0. 7. 0. 6. 0. 5. 0. 4. 0. 3. 0. 2. 0. 2. 0. 3. 0. 4. 0. 5. 0. 6. 0. 7. 0.

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