Applied Univariate, Bivariate, and Multivariate Statistics - Daniel J. Denis

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2.9 Randomized Block Design

      2 Chapter 3Table 3.1 Achievement as a Function of TeacherTable 3.2 Hypothetical Achievement DataTable 3.3 Summary Table for One‐Way Fixed Effects Analysis of VarianceTable 3.4 Hypothetical Data on Two Independent SamplesTable 3.5 Hypothetical Data on Dependent Variable Y and Independent Variable XTable 3.6 Pairwise Differences Between Achievement Means for Respective Teacher A...Table 3.7 R2 →f2 → f Conversions4Table 3.8 Number of Bacteria Colonies by Plate and Sample (Fisher, 1925/1934)

      3 Chapter 4TABLE 4.1 Achievement as a Function of Teacher and TextbookTABLE 4.2 Cell Means of Sleep Onset as a Function of Melatonin Dose and Noise Lev...TABLE 4.3 Cell Means Layout for 2 × 3 Factorial Analysis of Variance...TABLE 4.4 Deviations Featured in One‐way and Two‐way Analysis of Variance...TABLE 4.5 ANOVA Summary Table for Two‐Way Factorial DesignTABLE 4.6 Nested Design: Teacher is Nested Within TextbookTABLE 4.7 Learning as a Function of Trial (Hypothetical Data)TABLE 4.8 Achievement Cell Means Teacher*Textbook

      4 Chapter 5TABLE 5.1 Achievement as a Function of TeacherTABLE 5.2 Cell Layout for 6 × 3 Mixed Model Analysis of VarianceTABLE 5.3 Cell Layout of Data on Factors A and B

      5 Chapter 6TABLE 6.1 Matched-Pairs DesignTABLE 6.2 Fictional Data on Y, A, and BlockTABLE 6.3 Cell Layout of Data on Y, A, and BlockTABLE 6.4 Learning as a Function of Trial (Hypothetical Data)TABLE 6.5 Learning as a Function of Trial and Treatment (Hypothetical Data)TABLE 6.6 Nitrogen in Blood Plasma

      6 Chapter 7TABLE 7.1 Analysis of Variance for Linear RegressionTABLE 7.2 Analysis of Variance Summary Table in MatricesTABLE 7.3 Quantitative and Verbal Scores on Nine Subjects (Hypothetical Data)TABLE 7.4 Mean Ability Scores and Final Grades for 14 Mathematics Classes

      7 Chapter 9TABLE 9.1 Cell Means Layout for 2 × 3 Factorial Analysis of Variance...

      8 Chapter 10TABLE 10.1 Hypothetical Data on Quantitative and Verbal Ability for Those Receivi...

      9 Chapter 11TABLE 11.1 Hypothetical Data on Quantitative and Verbal Ability for Those Receivi...TABLE 11.2 Cross‐Product Matrices in 2 × 3 Multivariate Factorial Analysis of Var...TABLE 11.3 Hypothetical Data on Quantitative and Verbal Ability as a Function of ...

      10 Chapter 12Table 12.1 Comparison of Typical Response and Predictor Variables for MANOVA vers...Table 12.2 Hypothetical Data on Binary Response and Continuous PredictorsTable 12.3 Posterior Probabilities and Predicted Group Membership (Posterior G), ...Table 12.4 Eigenvalue and Significance Test for Discriminant FunctionTable 12.5 Unstandardized Coefficients (Left), Standardized Coefficients (Middle)...Table 12.6 Decision Table for Discriminant Analysis with Binary Dependent Variabl...

      11 Chapter 14TABLE 14.1 Estimated Loadings for Varimax and Quartimax Rotations of CormatrixTABLE 14.2 Fictional Data for Simple Cluster AnalysisTABLE 14.3 Hypothetical Data for Cluster Analysis on Two Variables Using Euclidea...

      List of Illustrations

      1 Chapter 1Figure 1.1 Observing the behavior of a pigeon in a Skinner box.Figure 1.2 “Model fit” as an overlap of data with theory.Figure 1.3 Hebbian Yerkes–Dodson performance–arousal curve.Figure 1.4 Number of O‐ring incidents on boosters as a function of temperatu...Figure 1.5 The “pilot criterion” must be met for any pilot to be permitted t...

      2 Chapter 2Figure 2.1 Standard normal distribution with shaded area from −1 to +1 stand...Figure 2.2 Shaded area under the standard normal distribution at a z‐score o...Figure 2.3 Fisher's overlay of normal density on empirical observations.Figure 2.4 Binomial distribution for the probability of the number of heads ...Figure 2.5 Binomial distributions approximated by normal densities for 5 (fa...Figure 2.6 Bivariate density. Source: Data from Plotting bivariate normal di...Figure 2.7 A 3D scatterplot with density contour and points (Image is taken ...Figure 2.8 Because the sum of deviations about the arithmetic mean is always...Figure 2.9 The “Beautiful Triangle” as a way to understanding degrees of fre...Figure 2.10 F distribution on 2 and 5 degrees of freedom. It is positively s...Figure 2.11 Student's t versus normal densities for 3 (left), 10 (middle), a...Figure 2.12 Power curves for detecting parameters C1 and C2.Figure 2.13 G*Power output for estimating required sample size for r = 0.10....Figure 2.14 Power curves generated by G*Power for detecting correlation coef...Figure 2.15 Relationship between Cohen's d and R‐squared.

      3 Chapter 3FIGURE 3.1 Sleep onset as a function of melatonin dose (hypothetical). Circl...FIGURE 3.2 Power analysis for fixed effects analysis of variance.FIGURE 3.3 Power curves for fixed effects analysis of variance.

      4 Chapter 4FIGURE 4.1 (a) Cell means for teacher*textbook on achievement. (b) Distances...FIGURE 4.2 Generic two‐way analysis of variance layout. The two‐way factoria...FIGURE 4.3 A simple main effect: Mean difference of textbook at level 1 of t...

      5 Chapter 7FIGURE 7.1 Francis Galton. Innovator of correlation and regression.FIGURE 7.2 Galton’s 1886 correlational surface.FIGURE 7.3 Regression line of child on parent.FIGURE 7.4 Linear regression of Y on X, where sy and sx are the standard dev...FIGURE 7.5 Galton data adjusted to show no correlation.FIGURE 7.6 Linear regression of child height on parent height.FIGURE 7.7 Least‐squares regression line of Y on X (a). Dotted line is the n...FIGURE 7.8 Absence of correlation between residuals and predicted values (a)...FIGURE 7.9 Evidence of heteroscedasticity of errors.

      6 Chapter 8FIGURE 8.1 Model selection unofficially begins with the selection of p candi...FIGURE 8.2 Classic single‐variable mediation model.

      7 Chapter 9FIGURE 9.1 Hypothesized slope of treatment success on length of treatment fo...FIGURE 9.2 Length of treatment and age interact in predicting treatment succ...FIGURE 9.3 Relationship between sales and price using OLS (a) versus mixed m...

      8 Chapter 10Figure 10.1 Hypothetical nonlinear relationship between suicide attempts and...Figure 10.2 Logistic “sigmoid” function.Figure 10.3 Example of a simple exponential function.Figure 10.4 Exponential functions with increasing base b > 1 (a) and 0 < b <...Figure 10.5 Graph of f(x) = 2x (solid line) and f(x) = 2−x (dotted lin...Figure 10.6 Graph of y = log2(x). Note the steep rise then plateau.Figure 10.7 Effect plot for predicting O‐ring failure as a function of tempe...

      9 Chapter 11FIGURE 11.1 (a) Collinear vectors. (b) Noncollinear vectors.

      10 Chapter 12FIGURE 12.1 Fisher’s

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