Bivariate Analysis: Relationships Between Two Variables
Hamilton (Lawrence)
Source: Hamilton (Lawrence) - Modern Data Analysis, Part III
Paper - Abstract

Paper StatisticsNotes Citing this PaperColour-ConventionsDisclaimer


Sections

  1. Two Categorical Variables: Crosstabulation and the Chi-Square Test – 359
    • 12.1 Cell Frequencies and Percentages in Crosstabulation – 360
    • 12.2 The Independence Hypothesis and Expected Frequencies – 364
    • 12.3 The Chi-Square Test – 366
    • 12.4 Degrees of Freedom and the Chi-Square Distribution – 370
    • 12.5 Parenthood and Opinions About Water Quality – 374
    • 12.6 Chi-Square as a "Badness-of-Fit" Test – 377
    • 12.7 The Problem of Thin Cells – 381
    • 12.8 Continuity Correction for Thin Cells – 384
    • 12.9 Sample Size and Significance In Chi-Square Analysis – 386
      Summary – 388
      Problems – 389
      Notes – 393
  2. One Categorical and One Measurement Variable: Comparisons – 397
    • 13.1 Overview of Comparison Issues – 398
    • 13.2 Testing Hypotheses About Means – 403
    • 13.3 Two-Sample Problems: Difference-of-Means Tests – 407
    • 13.4 Confidence Intervals for Differences of Means – 413
    • 13.5 Paired-Difference Tests – 415
    • 13.6 K-Sample Problems: Analysis of Variance – 420
    • 13.7 Error-Bar Plots – 428
    • 13.8 IQ1 Scores and Reading Ability – 432
    • 13.9 Dealing with Distributional Problems – 439
    • 13.10 Nonparametric Tests and Rank Transformations – 440
      Summary – 446
      Problems – 447
      Notes – 454
  3. Two Measurement Variables: Regression Analysis – 457
    • 14.1 Scatter Plots – 458
    • 14.2 Regression Line and Regression Equation – 462
    • 14.3 Summary Statistics for Two Measurement Variables – 468
    • 14.4 Predicted Values and Residuals – 473
    • 14.5 Assessing Fit in Regression – 477
    • 14.6 Correlation Coefficients – 480
    • 14.7 Physician Problems and Hospital Size – 483
    • 14.8 Predicting State SAT Scores – 488
    • 14.9 Outliers and influence in Regression Analysis – 492
    • 14.10 Notes on Calculation – 495
      Summary – 498
      Problems – 498
      Notes – 502
  4. Inference and Criticism in Two-Variable Regression – 503
    • 15.1 Inference In Regression – 504
    • 15.2 Standard Errors in Regression – 505
    • 15.3 Income and Homicide Rate – 508
    • 15.4 t Tests for Regression Coefficients – 513
    • 15.5 t Tests for Hypotheses Other Than beta = 0 – 516
    • 15.6 Confidence Intervals for Regression Coefficients – 517
    • 15.7 Confidence intervals for Regression Predictions – 521
    • 15.8 F Tests in Two-Variable Regression – 523
    • 15.9 Assumptions and Problems In Regression Analysis – 526
    • 15.10 Scatter Plots for Regression Criticism – 529
    • 15.11 Coping with Problems in Regression – 535
    • 15.12 Understanding Curvilinear Regression – 541
    • 15.13 Alternative Explanations – 550
      Summary – 552
      Problems – 553
      Notes – 559

Text Colour Conventions (see disclaimer)

  1. Blue: Text by me; © Theo Todman, 2021
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)



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