Handbook Of Parametric And Nonparametric Statistical Procedures

Cover
Title Page
Half Title
Copyright Page
Dedication
Preface
Table of Contents
Introduction
Descriptive Versus Inferential Statistics
Statistic Versus Parameter
Levels of Measurement
Continuous Versus Discrete Variables
Measures of Central Tendency (Mode, Median, Mean, Weighted Mean, Geometric Mean, and the Harmonic Mean)
Measures of Variability (Range; Quantiles, Percentiles, Quartiles, and Deciles; Variance and Standard Deviation; The Coefficient of Variation)
Measures of Skewness and Kurtosis
Visual Methods for Displaying Data (Tables and Graphs, Exploratory Data Analysis (Stem-and-leaf Displays and Boxplots))
The Normal Distribution
Hypothesis Testing
A History and Critique of the Classical Hypothesis Testing Model
Estimation in Inferential Statistics
Relevant Concepts, Issues, and Terminology in Conducting Research (The Observational Method; The Experimental Method; The Correlational Method)
Experimental Design (Pre-experimental Designs; Quasi-experimental Designs; True Experimental Designs; Single-subject Designs)
Sampling Methodologies
Basic Principles of Probability
Parametric Versus Nonparametric Inferential Statistical Tests
Univariate Versus Bivariate Versus Multivariate Statistical Procedures
Selection of the Appropriate Statistical Procedure
References
Endnotes
Outline of Inferential Statistical Tests and Measures of Correlation/Association
Guidelines and Decision Tables for Selecting the Appropriate Statistical Procedure
Inferential Statistical Tests Employed with a Single Sample
Test 1: The Single-Sample z Test
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Single-Sample z Test and/or Related Tests
VII. Additional Discussion of the Single-Sample z Test
1. The Interpretation of a Negative z value
2. The Standard Error of the Population Mean and Graphical Representation of the Results of the Single-Sample z test
3. Additional Examples Illustrating the Interpretation of a Computed z Value
4. The z Test for a Population Proportion
VIII. Additional Examples Illustrating the Use of the Single-Sample z Test
References
Endnotes
Test 2: The Single-Sample t Test
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Single-Sample t Test and/or Related Tests
1. Determination of the Power of the Single-Sample t test and the Single Sample z test, and the Application of Test 2a: Cohen's d Index
2. Computation of a Confidence Interval for the Mean of the Population Represented by a Sample
VII. Additional Discussion of the Single-Sample t Test
Degrees of freedom
VIII. Additional Examples Illustrating the Use of the Single-Sample t Test
IX. Addendum
Statistical Quality Control
Process Control
Acceptance Sampling
References
Endnotes
Test 3: The Single-Sample Chi-Square Test for a Population Variance
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Single-Sample Chi-SquareTest for a Population Variance and/or Related Tests
1. Large Sample Normal Approximation of the Chi-Square Distribution
2. Computation of a Confidence Interval for the Variance of a Population Represented by a Sample
3. Sources for Computing the Power of the Single-Sample Chi-Square Test for a Population Variance
VII. Additional Discussion of the Single-Sample Chi-Square Test for a Population Variance
VIII. Additional Examples Illustrating the Use of the Single-Sample Chi-Square Test for a Population Variance
References
Endnotes
Test 4: The Single-Sample Test for Evaluating Population Skewness
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Single-sample Test for Evaluating Population Skewness and/or Related Tests
VII. Additional Discussion of the Single-Sample Test for Evaluating Population Skewness
1. Exact Tables for the Single-Sample Test for Evaluating Population Skewness
2. Note on a Nonparametric Test for Evaluating Skewness
VIII. Additional Examples Illustrating the Use of the Single-Sample Test for Evaluating Population Skewness
References
Endnotes
Test 5: The Single-Sample Test for Evaluating Population Kurtosis
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Single-sample Test for Evaluating Population Kurtosis and/or Related Tests
1. Test 5a: The D' Agostino-Pearson Test of Normality
2. Test 5b: The Jarque-Bera Test of Normality
VII. Additional Discussion of the Single-Sample Test for Evaluating Population Kurtosis
1. Exact Tables for the Single-Sample Test for Evaluating Population Kurtosis
2. Additional Comments on Tests of Normality
VIII. Additional Examples Illustrating the Use of the Single-Sample Test for Evaluating Population Kurtosis
References
Endnotes
Test 6: The Wilcoxon Signed-Ranks Test
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Wilcoxon Signed RanksTest and/or Related Tests
I. The Normal Approximation of the Wilcoxon Tstatistic for Large Sample Sizes
2. The Correction for Continuity for the Normal Approximation of the Wilcoxon Signed-Ranks Test
3. Tie Correction for the Normal Approximation of the Wilcoxon Test Statistic
4. Computation of a Confidence Interval for a Population Median
VII. Additional Discussion of the Wilcoxon Signed-Ranks Test
l. Power-Efficiency of the Wilcoxon Signed-Ranks Test and the Concept of Asymptotic Relative Efficiency
2. Note on Symmetric Population Concerning Hypotheses Regarding Median and Mean
VIII. Additional Examples Illustrating the Use of the Wilcoxon Signed-Ranks Test
References
Endnotes
Test 7: The Kolmogorov-Smirnov Goodness-of-Fit Test for a Single Sample
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Kolmogorov-Smirnov Goodness-of-Fit Test for a Single Sample and/or Related Tests
l. Computing a Confidence Interval for the Kolmogorov-Smirnov Goodness-of-Fit Test for a Single Sample
2. The Power of the Kolmogorov-Smirnov Goodness-of-Fit Test for a Single Sample
3. Test 7a: The Lilliefors Test for Normality
VII. Additional Discussion of the Kolmogorov-Smirnov Goodness-of-Fit Test for a Single Sample
1. Effect of Sample size on the Result of a Goodness-of-Fit Test
2. The Kolmogorov-Smirnov Goodness-of-Fit Test for a Single Sample Versus the Chi-Square Goodness-of-Fit Test and Alternative Goodness-of-Fit Tests
VIII. Additional Example Illustrating the Use of the Kolmogorov-Smirnov Goodness-of-Fit Test for a Single Sample
References
Endnotes
Test 8: The Chi-Square Goodness-of-Fit Test
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Examples
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Chi-Square Goodness-of-Fit Test and/or Related Tests
1. Comparisons Involving Individual Cells when k > 2
2. The Analysis of Standardized Residuals
3. The Correction for Continuity for the Chi-Square Goodness-of-Fit Test
4. Computation of a Confidence Interval for the Chi-Square Goodness-of-Fit Test/Confidence Interval for a Population Proportion
5. Brief Discussion of the z Test for a Population Proportion (Test 9a) and the Single-Sample Test for the Median (Test 9b)
6. Application of the Chi-Square Goodness-of-Fit Test for Assessing Goodness-of-Fit for a Theoretical Population Distribution
7. Sources for Computing of the Power of the Chi-Square Goodness-of-Fit Test
8. Heterogeneity Chi-Square Analysis
VII. Additional Discussion of the Chi-Square Goodness-of-Fit Test
1. Directionality of the Chi-Square Goodness-of-Fit Test
2. Additional Goodness-of-Fit Tests
VIII. Additional Examples Illustrating the Use of the Chi-Square Goodness-of-Fit Test
References
Endnotes
Test 9: The Binomial Sign Test for a Single Sample
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Examples
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Binomial Sign Test for a Single Sample and/or Related Tests
1. Test 9a: The z Test for a Population Proportion (with Discussion of Correction for Continuity; Computation of a Confidence Interval; Procedure for Computing Sample Size for Test of Specified Power; Additional Comments on Computation of the Power of the Binomial Sign Test for a Single Sample)
2. Extension of the z Test for a Population Proportion to Evaluate the Performance of m Subjects on n Trials on a Binomially Distributed Variable
3. Test 9b: The Single-Sample Test for the Median
VII. Additional Discussion of the Binomial Sign Test for a Single Sample
1. Evaluating Goodness-of-Fit for a Binomial Distribution
VIII. Additional Example Illustrating the Use of the Binomial Sign Test for a Single Sample
IX. Addendum
1. Discussion of Additional Discrete Probability Distributions and the Exponential Distribution
a. The Multinomial Distribution
b. The Negative Binomial Distribution
c. The Hypergeometric Distribution
d. The Poisson Distribution
Computation of a Confidence Interval for a Poisson Parameter
Test 9c: Test for Comparing Two Poisson Counts
Evaluating Goodness-of-Fit for a Poisson Distribution
e. The Exponential Distribution
f. The Matching Distribution
2. Conditional Probability, Bayes' Theorem, Bayesian Statistics, and Hypothesis Testing
Conditional Probability
Bayes' Theorem
Bayesian Hypothesis Testing
Bayesian Analysis of a Continuous Variable
References
Endnotes
Test 10: The Single-Sample Runs Test (and Other Tests of Randomness)
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Single-Sample Runs Test and/or Related Tests
1. The Normal Approximation of the Single-Sample Runs Test for Large Sample Sizes
2. The Correction for Continuity for the Normal Approximation of the Single-Sample Runs Test
3. Extension of the Runs Test to Data with More than Two Categories
4. Test lOa: The Runs Test for Serial Randomness
VII. Additional Discussion of the Single-Sample Runs Test
1. Additional Discussion of the Concept of Randomness
VII. Additional Examples Illustrating the Use of the Single-Sample Runs Test
IX. Addendum
1. The Generation of Pseudorandom Numbers (The Midsquare Method; the Midproduct Method; the Linear Congruential Method)
2. Alternative Tests of Randomness
Test 10b: The Frequency test
Test 10c: The Gap Test
Test 10d: The Poker Test
Test 10e: The Maximum Test
Test 10f: The Coupon Collector's Test
Test 10g: The Mean Square Successive Difference Test (For Serial Randomness)
Additional Tests of Randomness Test; The d 2 Square Test of Random Numbers; Tests of Trend Analysis/Time Series Analysis)
References
Endnotes
Inferential Statistical Tests Employed with Two Independent Samples (and Related Measures of Association/Correlation)
Test 11: The t Test for Two Independent Samples
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the t Test for Two Independent Samples and/or Related Tests
1. The Equation for the t Test for Two Independent Samples when a Value for a Difference other than Zero is Stated in the Null Hypothesis
2. Test 11a: Hartley's Fmax Test for Homogeneity of Variance/F Test for Two Population Variances: Evaluation of the Homogeneity of Variance Assumption of the t Test for Two Independent Samples
3. Computation of the Power of the t Test for Two Independent Samples and the Application of Test 11b: Cohen's d Index
4. Measures of Magnitude of Treatment Effect for the t Test for Two Independent Samples: Omega Squared (Test 11c) and Eta Squared (Test 11d)
5. Computation of a Confidence Interval for the t Test for Two Independent Samples
6. Test 11e: The z Test for Two Independent Samples
VII. Additional Discussion of the t Test for Two Independent Samples
1. Unequal Sample Sizes
2. Robustness of the t Test for Two Independent Samples
3. Outliers (Procedures for Identifying Outliers: Box-and-Whiskerplot Criteria; Standard Deviation Score Criterion; Test 11f: Median Absolute Deviation Test for Identifying Outliers; Test 11g: Extreme Studentized Deviate Test for Identifying Outliers; Trimming Data; Winsorization) and Data Transformation
4. Missing Data
5. Clinical Trials
6. Tests of Equivalence: Test 11h: The Westlake-Schuirmann Test of Equivalence of Two Independent Treatments (and Procedure for Computing Sample Size in Reference to the Power of the Test)
7. Hotelling's T2
VIII. Additional Examples Illustrating the Use of the t Test for Two Independent Samples
References
Endnotes
Test 12: The Mann-Whitney U Test
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Mann-Whitney U Test and/or Related Tests
I. The Normal Approximation of the Mann-Whitney U Statistic for Large Sample Sizes
2. The Correction for Continuity for the Normal Approximation of the Mann-Whitney Utest
3. Tie Correction for the Normal Approximation of the Mann-Whitney Ustatistic
4. Computation of a Confidence Interval for a Difference Between the Medians of Two Independent Populations
VII. Additional Discussion of the Mann-Whitney U Test
1. Power-Efficiency of the Mann-Whitney U Test
2. Equivalency of the Normal Approximation of the Mann-Whitney U Test and the t Test for Two Independent Samples with Rank Orders
3. Alternative Nonparametric Rank-Order Procedures for Evaluating a Design Involving Two Independent Samples
VIII. Additional Examples Illustrating the Use of the Mann-Whitney U Test
IX. Addendum
1. Computer-Intensive Tests (Randomization and Permutation Tests: Test 12a: The Randomization Test for Two Independent Samples; Test12b: The Bootstrap; Test 12c: The Jackknife; Final Comments on Computer-Intensive Procedures)
2. Survival Analysis (Test 12d: Kaplan-Meier Estimate)
3. Procedures for Evaluating Censored Data in a Design Involving Two Independent Samples (Permutation Test Based on the Median, Gehan's Test for Censored Data (Test 12e), and the Log-Rank Test (Test 12f))
References
Endnotes
Test 13: The Kolmogorov-Smirnov Test for Two Independent Samples
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Kolmogorov-Smirnov Test for Two Independent Samples and/or Related Tests
1. Graphical Method for Computing the Kolmogorov-Smirnov Test Statistic
2. Computing Sample Confidence Intervals for the Kolmogorov-Smirnov Test for Two Independent Samples
3. Large Sample Chi-Square Approximation for a One-Tailed Analysis of the Kolmogorov-Smimov Test for Two Independent Samples
VII. Additional Discussion of the Kolmogorov-Smirnov Test for Two Independent Samples
1. Additional Comments on the Kolmogorov-Smirnov Test for Two Independent Samples
VIII. Additional Examples Illustrating the Use of the Kolmogorov-Smirnov Test for Two Independent Samples
References
Endnotes
Test 14: The Siegel-Tukey Test for Equal Variability
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Siegel-Tukey Test for Equal Variability and/or Related Tests
1. The Normal Approximation of the Siegel-Tukey Test Statistic for Large Sample Sizes
2. The Correction for Continuity for the Normal Approximation of the Siegel-Tukey Test for Equal Variability
3. Tie Correction for the Normal Approximation of the Siegel-Tukey Test Statistic
4. Adjustment of Scores for the Siegel-Tukey Test for Equal Variability when Q1=Q2
VII. Additional Discussion of the Siegel-Tukey Test for Equal Variability
1. Analysis of the Homogeneity of Variance Hypothesis for the Same Set of Data with Both a Parametric and Nonparametric Test, and the Power Efficiency of the Siegel-Tukey Test for Equal Variability
2. Alternative Nonparametric Tests of Dispersion
VIII. Additional Examples Illustrating the Use of the Siegel-Tukey Test for Equal Variability
References
Endnotes
Test 15: The Moses Test for Equal Variability
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Moses Test for Equal Variability and/or Related Tests
1. The Normal Approximation of the Moses Test Statistic for Large Sample Sizes
VII. Additional Discussion of the Moses Test for Equal Variability
1. Power-Efficiency of the Moses Test for Equal Variability
2. Issue of Repetitive Resampling
3. Alternative Nonparametric Tests of Dispersion
VIII. Additional Examples Illustrating the Use of the Moses Test for Equal Variability
References
Endnotes
Test 16: The Chi-Square Test for r x c Tables (Test 16a: The Chi-Square Test for Homogeneity; Test 16b: The Chi-Square Test of lndependence (Employed with a Single Sample))
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Examples
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Chi-Square Test for r x c Tables and/or Related Tests
1. Yates' Correction for Continuity
2. Quick Computational Equation for a 2 x 2 table
3. Evaluation of a directional Alternative Hypothesis in the Case of a 2 x2 Contingency Table
4. Test 16c: The Fisher Exact Test
5. Test 16d: The z Test for Two Independent Proportions(and Computation of Sample Size in Reference to Power)
6. Computation of a Confidence Interval for a Difference Between Two Proportions
7. Test 16e: The Median Test for Independent Samples
8. Extension of the Chi-Square Test for r x c Tables to Contingency Tables Involving More than Two Rows and/or Columns, and Associated Comparison Procedures
9. The analysis of Standardized Residuals
10. Sources for Computing the Power of the Chi-Square Test for r x c Tables
11. Measures of Association for r x c Contingency Tables
Test 16f: The Contingency Coefficient
Test 16g: The Phi Coefficient
Test 16h: Cramer's Phi Coefficient
Test 16i: Yule's Q
Test 16j: The odds ratio (and the concept of relative risk)(and Test 16j-a: Test of Significance for an Odds Ratio and Computation of a Confidence Interval for an Odds Ratio)
Test 16k: Cohen's Kappa (and Computation of a Confidence Interval for Kappa, Test 16k-a: Test of Significance for Cohen's Kappa, and Test 16k-b: Test of Significance for Two Independent Values of Cohen's Kappa)
12. Combining the Results of Multiple 2 x 2 Contingency Tables: Heterogeneity Chi-Square Analysis for a 2 x 2 Contingency Table
Heterogeneity Chi-Square Analysis for a 2 x 2 Contingency Table
Test 16L: The Mantei-Haenszel Analysis/Test (Test 161-a:Test of Homogeneity of odds ratios for Mantel-Haenszel analysis, Test 161-b: Summary Odds Ratio for Mantei Haenszel analysis, and Test 161-c: Mantel-Haenszel Test of Association)
VII. Additional Discussion of the Chi-Square Test for r x c Tables
1. Equivalency of the Chi-Square Test for r x c Tables when c = 2 with the t Test for Two Independent Samples (when r = 2) and the Single-Factor Between-Subjects Analysis of Variance (when r > 2)
2. Test of Equivalence for Two Independent Proportions: Test 16m: The Westlake-Schuirmann test of Equivalence of Two Independent Proportions (and Procedure for Computing Sample Size in Reference to the Power of the Test)
3. Test 16n: The Log-Likelihood Ratio
4. Simpson's Paradox
5. Analysis of Multidimensional Contingency Tables Through use of a Chi-Square Analysis
6. Test 16O: Analysis of Multidimensional Contingency Tables with Log-Linear Analysis
VIII. Additional Examples Illustrating the Use of the Chi-Square Test for r x c Tables
References
Endnotes
Inferential Statistical Tests Employed with Two Dependent Samples (and Related Measures of Association/Correlation)
Test 17: The t Test for Two Dependent Samples
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the t Test for Two Dependent Samples and/or Related Tests
1. Alternative Equation for the t Test for Two Dependent Samples
2. The Equation for the t Test for Two Dependent Samples when a Value for a Difference Other than Zero is Stated in the Null Hypothesis
3. Test 17a: The t Test for Homogeneity of Variance for Two Dependent Samples: Evaluation of the Homogeneity of Variance Assumption of the t Test for Two Dependent Samples
4. Computation of the Power of the t Test for Two Dependent Samples and the Application of Test 17b: Cohen's d Index
5. Measure of Magnitude of Treatment Effect for the t Test for Two Dependent Samples: Omega Squared (Test 17c)
6. Computation of a Confidence Interval for the t Test for Two Dependent Samples
7. Test 17d: Sandler's A Test
8. Test 17e: The z Test for Two Dependent Samples
VII. Additional Discussion of the t Test for Two Dependent Samples
1. The Use of Matched Subjects in a Dependent Samples Design
2. Relative Power of the t Test for Two Dependent Samples and the t Test for Two Independent Samples
3. Counterbalancing and Order Effects
4. Analysis of a One-Group Pretest-Posttest Design with the t Test for Two Dependent Samples
5. Tests of Equivalence: Test 17f: The Westlake-Schuirmann Test of Equivalence of Two Dependent Treatments (and Procedure for Computing Sample Size in Reference to the Power of the Test)
VIII. Additional Example Illustrating the Use of the t Test for Two Dependent Samples
References
Endnotes
Test 18: The Wilcoxon Matched-Pairs Signed-Ranks Test
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Wilcoxon Matched-Pairs Signed-Ranks Test and/or Related Tests
1. The Normal Approximation of the Wilcoxon T Statistic for Large Sample Sizes
2. The Correction for Continuity for the Normal Approximation of the Wilcoxon Matched-Pairs Signed-Ranks Test
3. Tie Correction for the Normal Approximation of the Wilcoxon Test Statistic
4. Computation of a Confidence Interval for a Median Difference Between Two Dependent Populations
VII. Additional Discussion of the Wilcoxon Matched-Pairs Signed-RanksTest
1. Power-Efficiency of the Wilcoxon Matched-Pairs Signed-Ranks Test
2. Probability of Superiority as a Measure of Effect Size
3. Alternative Nonparametric Procedures for Evaluating a Design Involving Two Dependent Samples
VIII. Additional Examples Illustrating the Use of the Wilcoxon Matched-Pairs Signed-Ranks Test
References
Endnotes
Test 19: The Binomial Sign Test for Two Dependent Samples
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Binomial Sign Test for TwoDependent Samples and/or Related Tests
I. The Normal Approximation of the Binomial Sign Test for Two Dependent Samples with and without a Correction for Continuity
2. Computation of a Confidence Interval for the Binomial Sign Test for Two Dependent Samples
3. Sources for Computing the Power of the Binomial Sign Test for Two Dependent Samples, and Comments on the Asymptotic Relative Efficiency of the Test
VII. Additional Discussion of the Binomial Sign Test for Two Dependent Samples
1. The Problem of an Excessive Number of Zero Difference Scores
2. Equivalency of The Binomial Sign Test for two Dependent Samples and the Friedman Two-way Analysis of Variance By Ranks When K = 2
VIII. Additional Examples Illustrating the Use of the Binomial Sign Test for two Dependent Samples
References
Endnotes
Test 20: The McNemar Test
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Examples
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Mcnemar Test and/or Related Tests
1. Alternative Equation for the Mcnemar Test Statistic Based on the Normal Distribution
2. The Correction for Continuity for the Mcnemar Test
3. Computation of the Exact Binomial Probability for the Mcnemar Test Model with a Small Sample Size
4. Computation of the Power of the Mcnemar Test
5. Computation of a Confidence Interval for the McNemar Test
6. Computation of an Odds Ratio for the McNemar Test
7. Additional Analytical Procedures for the Mcnemar Test
8. Test 20a: The Gart Test for Order Effects
VII. Additional Discussion of the Mcnemar Test
1. Alternative Format for the Mcnemar Test Summary Table and Modified Test Equation
2. The Effect of Disregarding Matching
3. Alternative Nonparametric Procedures for Evaluating a Design with two Dependent Samples Involving Categorical Data
4. Test of Equivalence for two Independent Proportions: Test 20b: The Westlake-schuirmann Test of Equivalence of two Dependent Proportions
VIII. Additional Examples Illustrating the Use of The Mcnemar Test
Ix. Addendum
Extension of the Mcnemar Test Model Beyond 2 X 2 Contingency Tables
1. Test 20c: The Bowker Test of Internal Symmetry
2. Test 20d: The Stuart-maxwell Test of Marginal Homogeneity
References
Endnotes
Inferential Statistical Tests Employed with Two or More Independent Samples (and Related Measures of Association/Correlation)
Test 21: The Single-Factor Between-Subjects Analysis of Variance
I. Hypothesis Evaluated with Test And Relevant Background Information
II. Example
Ill. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Single-Factor Between- Subjects Analysis of Variance and/or Related Tests
I. Comparisons Following Computation of the Omnibus F Value for the Single-Factor Between-Subjects Analysis of Variance (Planned Versus Unplanned Comparisons (Including Simple Versus Complex Comparisons); Linear Contrasts; Orthogonal Comparisons; Test 21a: Multiplet tests/Fisher's LSD test; Test 2lb: The BonferroniDunntest; Test 21c: Tukey's HSD test; Test 2ld: The Newman-Keuls Test Test 21e: The Scheffe Test; Test 21f: The Dunnett Test; Additional Discussion of Comparison Procedures and Final Recommendations; The Computation of a Confidence Interval for a Comparison
2. Comparing the Means of Three or More Groups When k>4
3. Evaluation of the Homogeneity of Variance Assumption of the Singlefoctor between-Subjects Analysis of Variance (Test lla: Hartley's Fmax Test for Homogeneity of Variance, Test 21g: The Levene Test for Homogeneity of Variance, Test 21h: The Brown-Forsythe Test for Homogeneity of Variance)
4. Computation of the Power of the Single-Factor Between-Subjects Analysis of Variance
5. Measures of Magnitude of Treatment Effect for the Single-Factor Between-Subjects analysis of Variance: Omega Squared (Test 21i), Eta Squared (Test 21j), and Cohen's f index (Test 21k)
6. Computation of a Confidence Interval for the Mean of a Treatment Population
7. Trend Analysis
VII. Additional Discussion of the Single-Factor Between-Subjects Analysis of Variance
I. Theoretical Rationale Underlying the Single-Factor Between-Subjects Analysis of Variance
2. Defmitional Equations for the Single-Factor Between-Subjects Analysis of Variance
3. Equivalency of the Single-Factor Between-Subjects Analysis of Variance and the Test for two Independent Samples When k = 2
4. Robustness of the Single-Factor Between-Subjects Analysis of Variance
5. Equivalency of the Single-Factor Between-Subjects Analysis of Variance and the Test for two Independent Samples with the Chi-Square Test for r x c Tables When c= 2
6. The General Linear Model
7. Fixed-Effects Versus Random-Effects Models for the Single-Factor Between-Subjects Analysis of Variance
8. Multivariate Analysis of Variance (MANOVA)
VIII. Additional Examples Illustrating the Use ofthe Single-Factor Between Subjects Analysis of Variance
IX. Addendum
I. Test 211: The Single-Factor Between-Subjects Analysis of Covariance
References
Endnotes
Test 22: The Kruskal-Wallis One-Way Analysis of Variance by Ranks
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Kruskal-Wallis One-Way Analysis of Variance by Ranks and/or Related Tests
I. Tie Correction for the Kruskal-Wallis One-Way Analysis of Variance by Ranks
2. Pairwise Comparisons Following Computation of the Test Statistic for the Kruskal-Wallis One-Way Analysis of Variance by Ranks
VII. Additional Discussion of the Kruskal-Wallis One-Way Analysis of Variance by Ranks Variance by Ranks
I. Exact Tables of the Kruskal-Wallis Distribution
2. Equivalency of the Kruskal-Wallis One-Way Analysis of Variance by Ranks and the Mann-Whitney U Test When k = 2
3. Power-Efficiency of the Kruskal-Wallis One-Way Analysis of Variance by Ranks
4. Alternative Nonparametric Rank-Order Procedures for Evaluating a Design Involving k Independent Samples
VIII. Additional Examples Illustrating the Use of the Kruskal-Wallis One- Way Analysis of Variance by Ranks
IX. Addendum
1. Test 22a: The Jonckheere-Terpstra Test for Ordered Alternatives
References
Endnotes
Test 23: The Van Der Waerden Normal-Scores Test for k Independent Samples
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the van der Waerden Normal-Scores Test for k Independent Samples and/or Related Tests
1. Pairwise Comparisons Following Computation of the Test Statistic for the Van Der Waerden Normal-Scores Test Fork Independent Samples
VII. Additional Discussion of the Van Der Waerden Normal-Scores Test for k Independent Samples
I. Alternative Normal-Scores Tests
VIII. Additional Examples Illustrating the Use of the van der Waerden Normal-Scores Test fork Independent Samples
References
Endnotes
Inferential Statistical Tests Employed with Two or More Dependent Samples (and Related Measures of Association/Correlation)
Test 24: The Single-Factor Within-Subjects Analysis of Variance
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Single-Factor Within-Subjects Analysis of Variance and/or Related Tests
1. Comparisons Following Computation of the Omnibus F Value for the Single-Factor Within-Subjects Analysis of Variance (Test 24a: Multiple t Tests/Fisher's LSD Test; Test 24b: The Bonferroni- Dunn Test; Test 24c: Tukey's HSD Test; Test 24d: The Newman-Keuls Test; Test 24e: The Scheffe Test; Test 24f: The Dunnett Test; The Computation of a Confidence Interval for a Comparison; Alternative Methodology for Computing MSres for a Comparison)
2. Comparing the Means of Three or More Conditions when k >4
3. Evaluation of the Sphericity Assumption Underlying the Single-Factor Within-Subjects Analysis of Variance
4. Computation of the Power of the Single-Factor Within-Subjects Analysis of Variance
5. Measures of Magnitude of Treatment Effect for the Single-Factor Within-Subjects Analysis of Variance: Omega Squared (Test 24g) and Cohen's! index (Test 24h)
6. Computation of a Confidence Interval for the Mean of a Treatment Population
7. Test 24i: The Intraclass Correlation Coefficient
VII. Additional Discussion of the Single-Factor Within-Subjects Analysis of Variance
1. Theoretical Rationale Underlying the Single-Factor Within-Subjects Analysis of Variance
2. Definitional Equations for the Single-Factor Within-Subjects Analysis of Variance
3. Relative Power of the Single-Factor Within-Subjects Analysis of Variance
4. Equivalency of the Single-Factor Within-Subjects Analysis of Variance and the t Test for two Dependent Samples When k = 2
5. The Latin Square Design
VIII. Additional Examples Illustrating the Use of the Single-Factor Within- Subjects Analysis of Variance
References
Endnotes
Test 25: The Friedman Two-Way Analysis of Variance by Ranks
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Friedman Two-Way Analysis Variance by Ranks and/or Related Tests
1. Tie Correction for the Friedman two-way Analysis Variance by Ranks
2. Pairwise Comparisons Following Computation of the test Statistic for the Friedman two-way Analysis of Variance by Ranks
VII. Additional Discussion of the Friedman Two-Way Analysis of Variance by Ranks
1. Exact Tables of the Friedman Distribution
2. Equivalency of the Friedman two-way Analysis of Variance by Ranks and the Binomial Sign Test for two Dependent Samples When k=2
3. Power-Eficiency of the Friedman two-way Analysis of Variance by Ranks
4. Alternative Nonparametric Rank-Order Procedures for Evaluating a Design Involving k Dependent Samples
5. Relationship Between the Friedman two-way Analysis of Variance by Ranks and Kendall's Coefficient of Concordance
VIII. Additional Examples Illustrating the Use of the Friedman Two-Way Analysis of Variance by Ranks
IX. Addendum
1. Test 25a: The Page Test for Ordered Alternatives
References
Endnotes
Test 26: The Cochran Q Test
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Cochran Q Test and/or Related Tests
1. Pairwise Comparisons Following Computation of the test Statistic for the Cochran Q Test
VII. Additional Discussion of the Cochran Q Test
1. Issues Relating to Subjects who Obtain the Same Score Under all of the Experimental Conditions
2. Equivalency of the Cochran Q Test and the McNemar Test When k=2
3. Alternative Nonparametric Procedures with Categorical Data for Evaluating a Design Involving k Dependent Samples
VIII. Additional Examples Illustrating the Use of the Cochran Q Test
References
Endnotes
Inferential Statistical Test Employed with a Factorial Design (and Related Measures of Association/Correlation)
Test 27: The Between-Subjects Factorial Analysis of Variance
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Between-Subjects Factorial Analysis of Variance and/or Related Tests
1. Comparisons Following Computation of the F Values for the Between-Subjects Factorial Analysis of Variance (Test 27a: Multiple t Tests/ Fisher's LSD Test; Test 27b: The Bonferroni-Dunn Test; Test 27c: Tukey's HSD Test; Test 27d: The Newman-Keuls Test; Test 27e: The Scheffe Test; Test 27f: The Dunnett Test; Comparisons Between the Marginal Means; Evaluation of an Omnibus Hypothesis Involving More Than Two Marginal Means; Comparisons Between Speciic Groups That are a Combination of Both Factors; The Computation of a Confidence Interval for a Comparison; Analysis of Simple Effects)
2. Evaluation of the Homogeneity of Variance Assumption of the Between Subjects Factorial Analysis of Variance
3. Computation of the Power of the Between-Subjects Factorial Analysis of Variance
4. Measures of Magnitude of Treatment Effect for the Between-Subjects Factorial Analysis of Variance: Omega Squared (Test 27g) and Cohen's /index (Test 27h)
5. Computation of a Confidence Interval for the Mean of a Population Represented by a Group
VII. Additional Discussion of the Between-Subjects Factorial Analysis of Variance
1. Theoretical Rationale Underlying the Between-Subjects Factorial Analysis of Variance
2. Definitional Equations for the Between-Subjects Factorial Analysis of Variance
3. Unequal Sample Sizes
4. The Randomized-Blocks Design
5. Additional Comments on the Between-Subjects Factorial Analysis of Variance (Fixed-Effects Versus Random-Effects Versus Mixed-Effects Models; Nested Factors/Hierarchical Designs and Designs Involving More Than two Factors; Screening Designs)
VIII. Additional Examples Illustrating the Use of the Between-Subjects Factorial Analysis of Variance
IX. Addendum
Discussion of and Computational Procedures for Additional Analysis of Variance Procedures for Factorial Designs
1. Test 27i: The Factorial Analysis of Variance for a Mixed Design
Analysis of a Crossover Design with a Factorial Analysis of Variance for a Mixed Design
2. Test 27j: Analysis of Variance for a Latin Square Design
3. Test 27k: The Within-Subjects Factorial Analysis of Variance
4. Analysis of Higher-Order Factorial Designs
References
Endnotes
Measures of Association/Correlation
Test 28: The Pearson Product-Moment Correlation Coefficient
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results (Test 28a: Test of Significance for a Pearson Product-Moment Correlation Coefficient; The Coefficient of Determination)
VI. Additional Analytical Procedures for the Pearson Product-Moment Correlation Coefficient and/or Related Tests
I. Derivation of a Regression line
2. The Standard Error of Estimate
3. Computation of a Confidence Interval for the Value of the Criterion Variable
4. Computation of a Confidence Interval for a Pearson Product-Moment Correlation Coefficient
5. Test 28b: Test for Evaluating the Hypothesis That the True Population Correlation is a Specific Value Other Than Zero
6. Computation of Power for the Pearson Product-Moment Correlation Coefficient
7. Test 28c: Test for Evaluating a Hypothesis on Whether There is a Significant Difference Between two Independent Correlations
8. Test 28d: Test for Evaluating a Hypothesis on Whether k Independent
9. Test 28e: Test for Evaluating the Null Hypothesis H0: Pxz = Prz
10. Tests for Evaluating a Hypothesis Regarding One or More Regression Coefficients (Test 28f: Test for Evaluating the Null Hypothesis H0:B = 0; Test 28g: Test for Evaluating the Null Hypothesis H0: B1=B2
11. Additional Correlational Procedures
VII. Additional Discussion of the Pearson Product-Moment Correlation Coefficient
I. The Definitional Equation for the Pearson Product-Moment Correlation Coefficient
2. Covariance
3. The Homoscedasticity Assumption of the Pearson Product-Moment Correlation Coefficient
4. Residuals, Analysis of Variance for Regression Analysis, and Regression Diagnostics
5. Autocorrelation (and Test 28h: Durbin-Watson test)
6. The Phi Coefficient as a Special Case of the Pearson Product-Moment Correlation Coefficient
7. Ecological Correlation
8. Cross-Lagged Panel and Regression-Discontinuity Designs
VIII. Additional Examples Illustrating the Use of the Pearson Product- Moment Correlation Coefficient
IX. Addendum
1. Bivariate Measures of Correlation That are Related to the Pearson Productmoment Correlation Coefficient (Test 28i: The Point-Biserial Correlation Coefficient); Test 28j: The biserial Correlation Coefficient (and Test 28j-a: Test oF Significance for a Biserial Correlation Coefficient); Test 28k: The Tetrachoric Correlation Coefficient (and Test 28k-a: Test of Significance for a Tetrachoric Cor-Relation Coefficient))
2. Data Mining
3. Time Series Analysis
References
Endnotes
Test 29: Spearman's Rank-Order Correlation Coefficient
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results (Test 29a: Test of Significance for Spearman's Rank-Order Correlation Coefficient)
VI. Additional Analytical Procedures for Spearman's Rank-Order Correlation Coefficient and/or Related Tests
1. Tie Correction for Spearman's Rank-Order Correlation Coefficient
2. Spearman's Rank-Order Correlation CoeffiCient as a Special Case of the Pearson Product-Moment Correlation Coefficient
3. Regression analysis and Spearman's Rank-Order Correlation Coefficient
4. Partial Rank Correlation
5. Use of Fisher's zr, Transformation with Spearman's Rank-Order Correlation Coefficient
VII. Additional Discussion of Spearman's Rank-Order Correlation Coefficient
1. The Relationship Between Spearman's Rank-Order Correlation Coefficient, Kendall's Coefficient of Concordance, and the Friedman two-way Analysis of Variance by Ranks
2. Power Efficiency of Spearman's Rank-Order Correlation Coefficient
3. Brief Discussion of Kendall' s tau: An Alternative Measure of Association for Two Sets of Ranks
4. Weighted Rank/top-Down Correlation
VIII. Additional Examples Illustrating the Use of the Spearman's Rank-Order Correlation Coefficient
References
Endnotes
Test 30: Kendall's Tau
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results (Test 30a: Test of Significance for Kendall's tau)
VI. Additional Analytical Procedures for Kendall's Tau and/or Related Tests
1. Tie Correction for Kendall's Tau
2. Regression Analysis and Kendall's Tau
3. Partial Rank Correlation
4. Sources for Computing a Confidence Interval for Kendall's Tau
VII. Additional Discussion of Kendall's Tau
1. Power Efficiency of Kendall's Tau
2. Kendall's Coefficient of Agreement
VIII. Additional Examples Illustrating the Use of Kendall's Tau
References
Endnotes
Test 31: Kendall's Coefficient of Concordance
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results (Test 31a: Test of Significance for Kendall's Coefficient of Concordance)
VI. Additional Analytical Procedures for Kendall's Coefficient of Concordance and/or Related Tests
1. Tie Correction for Kendall's Coefficient of Concordance
VII. Additional Discussion ofKendall's Coefficient of Concordance
1. Relationship Between Kendall's Coefficient of Concordance and Spearman's Rank-Order Correlation Coefficient
2. Relationship Between Kendall's Coefficient of Concordance and the Friedman Two-way Analysis of Variance by Ranks
3. Weighted Rank/top-Down Concordance
4. Kendall's Coefficient of Concordance Versus the Intraclass Correlation Coefficient
VIII. Additional Examples Illustrating the Use of Kendall's Coefficient of Concordance
References
Endnotes
Test 32: Goodman and Kruskal's Gamma
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results (Test 32a: Test of Significance for Goodman and Kruskal's Gamma)
VI. Additional Analytical Procedures for Goodman and Kruskal's Gamma and/or Related Tests
1. The Computation of a Confidence Interval for the Value of Goodman and Kruskal's Gamma
2. Test 32b: Test for Evaluating the Null Hypothesis H0: y1 = y2
3. Sources for Computing a Partial Correlation Coefficient for Goodman and Kruskal's Gamma
VII. Additional Discussion of Goodman and Kruskal's Gamma
1. Relationship Between Goodman and Kruskal's Gamma and Yule's Q
2. Somers' Delta as an Alternative Measure of Association for an Ordered Contingency Table
VIII. Additional Examples Illustrating the Use of Goodman and Kruskal's Gamma
References
Endnotes
Multivariate Statistical Analysis
Matrix Algebra and Multivariate Analysis
I. Introductory Comments on Multivariate Statistical Analysis
II. Introduction to Matrix Algebra
References
Endnotes
Test 33: Multiple Regression
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Examples
III. Null versus Alternative Hypotheses
IVN. Test Computations and Interpretation of the Test Results
A. Test Computations and Interpretation of Results for Example 33.1 (Computation of the Multiple Correlation Coefficient; The Coefficient of Multiple Determination; Test of Significance for a Multiple Correlation Coefficient; The Multiple Regression Equation; The Standard Error of Multiple Estimate; Computation of a Confidence Interval for Y'; Evaluation of the Relative Importance of the Predictor Variables; Evaluating the Significance of a Regression Coefficient; Computation of a Confidence Interval for a Regression Coefficient; Analysis of Variance for Multiple Regression; Semipartial and Partial Correlation (Test 33a: Computation of a Semipartial Correlation Coefficient; Test of Significance for a Semipartial Correlation Coefficient; Test Coefficient; Test of Significance for a Partial Correlation Coefficient)
B. Test Computations and Interpretation of Results for Example 33.2 with SPSS
VI. Additional Analytical Procedures for Multiple Regression and/or Related Tests
1. Cross-Validation of Sample Data
VII. Additional Discussion of Multiple Regression
1. Final Comments on Multiple Regression Analysis
2. Causal Modeling: Path Analysis and Structural Equation Modeling
3. Brief Note on Logistic Regression
VIII. Additional Examples Illustrating the Use of Multiple Regression
References
Endnotes
Test 34: Hotelling's T2
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for Hotelling's T2 and/or Related Tests
1. Additional Analyses Following the Test of the Omnibus Null Hypothesis
2. Test 34a: The Single-Sample Hotelling's T2
3. Test 34b: The Use of the Single-Sample Hotelling's T2 to Evaluate a Dependent Samples Design
VII. Additional Discussion ofHotelling's T 2
1. Hotelling's T 2 and Mahalanobis' D2 Statistic
VIII. Additional Examples Illustrating the Use of Hotelling's T 2
References
Endnotes
Test 35: Multivariate Analysis of Variance
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Multivariate Analysis ofV ariance and/or Related Tests
VII. Additional Discussion of the Multivariate Analysis of Variance
1. Conceptualizing the Hypothesis for the Multivariate Analysis of Variance Within the Context of a Linear Combination
2. Multicollinearity and the Multivariate Analysis of Variance
VIII. Additional Examples Illustrating the Use of the Multivariate Analysis of Variance
References
Endnotes
Test 36: Multivariate Analysis of Covariance
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for the Multivariate Analysis of Covariance and/or Related Tests
VII. Additional Discussion of the Multivariate Analysis of Covariance
1. Multiple Covariates
VIII. Additional Examples Illustrating the Use of the Multivariate Analysis of Covariance
References
Endnotes
Test 37: Discriminant Function Analysis
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Examples
Ill. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
Analysis of Example 37.1
Analysis of Example 37.2
VI. Additional Analytical Procedures for Discriminant Function Analysis and/or Related Tests
VII. Additional Discussion of Discriminant Function Analysis
VIII. Additional Examples Illustrating the Use of Discriminant VIII. Additional Examples Illustrating the Use of Discriminant
References
Endnotes
Test 38: Canonical Correlation
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
Ill. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for Canonical Correlation and/or Related Tests
VII. Additional Discussion of Canonical Correlation
VIII. Additional Examples Illustrating the Use of Canonical Correlation
References
Endnotes
Test 39: Logistic Regression
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
Results for a Binary Logistic Regression with One Predictor Variable
Results for a Binary Logistic Regression with Multiple Predictor Variables
VI. Additional Analytical Procedures for Logistic Regression and/or Related Tests
VII. Additional Discussion of Logistic Regression
VIII. Additional Examples Illustrating the Use of Logistic Regression
References
Endnotes
Test 40: Principal Components Analysis and Factor Analysis
I. Hypothesis Evaluated with Test and Relevant Background Information
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
VI. Additional Analytical Procedures for Principal Components Analysis and Factor Analysis and/or Related Tests
1. Principal Axis Factor Analysis of Example 40.1
VII. Additional Discussion of Principal Components Analysis and Factor Analysis
1. Criticisms of factor analytic Procedures
2. Cluster Analysis
3. Multidimensional Scaling
VIII. Additional Examples Illustrating the Use of Principal Components Analysis and Factor Analysis
References
Endnotes
Test 41: Path Analysis
I. Hypothesis Evaluated with Test and Relevant Background Information
Additional Discussion of Basic Terminology Employed in Path Analysis
Assumptions Underlying Bath Analysis
II. Example
III. Null versus Alternative Hypotheses
IV. Test Computations
Decomposition of Correlations Among Pairs of Variables
Model Identification
Computation of Degrees of Freedom for a Bath Model
Determination of the Number of Observations
Determination of the Number of Parameters to be Estimated
Guidelines for Evaluating Effect Values
Decomposition of Correlations Among Pairs of Variables in Models A and B
V. Interpretation of the Test Results
Goodness-of-Fit Indices for a Path Analysis Model
VI. Additional Analytical Procedures for Path Analysis
VII. Additional Discussion of Path Analysis
VIII. Additional Examples Illustrating the Use or Path analysis
References
Endnotes
Test 42: Structural Equation Modeling
I. Hypothesis Evaluated with Test and Relevant Background Information
Assumptions Underlying SEM
Elements Employed in a Structural Equation Model
Methods for Summarizing a Structural Model
II. Example
III. Null Versus Alternative Hypotheses
IV. Test Computations
V. Interpretation of the Test Results
Guidelines for Determining Degrees of Freedom
Assessing Model Fit
Analysis of Example 42.1
VI. Additional Analytical Procedures for Structural Equation Modeling
VII. Additional Discussion of Structural Equation Modeling
SEM Software
Additional Sources of Information on SEM
VIII. Additional Examples Illustrating the Use of Structural Equation Modeling
References
Endnotes
Test 43: Meta-Analysis
I. Hypothesis Evaluated with Test and Relevant Background Information Relevant Background Information on Meta-Analysis Measures of Effect Size
Relevant Background Information on Meta-Analysis
Measures of Effect Size
II. Examples
III. Null versus Alternative Hypotheses
IV /V. Test Computations and Interpretation of Test Results
Meta-Analytic Procedures Employing Significance Level and Effect Size
Test 43a: Procedure for Comparing k Studies with Respect to Significance Level
Test 43b: The Stouffer Procedure for Obtaining a Combined Significance Level (P Value) Fork Studies
The File Drawer Problem
Test 43c: Homogeneity Analysis for Comparing k Studies with respect to Effect Size
Test 43d: ProCedure for Obtaining a Combined Effect Size for k Studies
Meta-Analytic Procedures Based on Weighting Effect Sizes with Inverse Variance Weights
Test 43e: Procedure for Obtaining a Weighted Mean Effect Size Fork Studies
Test 43f: Procedure for Evaluating the Null Hypothesis That the True Value of the Overall Effect Size in the Underlying Population Equals 0
Test 43g: Procedure for Computing a Confidence Interval for the Mean Effect Size
Test 43h: Homogeneity Analysis for Comparing k Studies with Respect to Effect Size Through Use of Inverse Variance Eeights
VI. Additional Analytical Procedures for Meta-Analysis
Graphing techniques for meta-analysis
Alternative Meta-Analytic Procedures
Practical implications of magnitude of effect size value
Test 43i: Binomial effect size display
VII. Additional Discussion of Meta-Analysis
Meta-Analysis Software
The Significance Test Controversy
The Minimum-Effect Hypothesis Testing model
VIII. Additional Examples Illustrating the Use of Meta-Analysis
References
Endnotes
Appendix: Tables
Table Al. Table of the Normal Distribution
Table A2. Table of Student's t Distribution
Table A3. Power Curves for Student's t Distribution
Table A4. Table of the Chi-Square Distribution
Table A5. Table of Critical T Values for Wilcoxon's Signed Ranks and Matched-Pairs Signed-Ranks Tests
Table A6. Table of the Binomial Distribution, Individual Probabilities
Table A7. Table of the Binomial Distribution, Cumulative Probabilities
Table A8. Table of Critical Values for the Single-Sample Runs Test
Table A9. Table of the Fmax Distribution
Table A10. Table of the F Distribution
Table A11. Table of Critical Values for Mann-Whitney U Statistic
Table A12. Table of Sandler's A Statistic
Table A13. Table of the Studentized Range Statistic
Table A14. Table of Dunnett's Modified t Statistic for a Control Group Comparison
Table A15. Graphs of the Power Function for the Analysis of Variance
Table A16. Table of Critical Values for Pearson r
Table A17. Table of Fisher's Zr Transformation
Table A18. Table of Critical Values for Spearman's Rho
Table A19. Table of Critical Values for Kendall's Tau
Table A20. Table of Critical Values for Kendall's Coefficient of Concordance
Table A21. Table of Critical Values for the Kolmogorov-Smirnov Goodness-of-Fit Testfor a Single Sample
Table A22. Table of Critical Values for the Lilliefors Test for Normality
Table A23. Table of Critical Values for the Kolmogorov-Smirnov Test for Two Independent Samples
Table A24. Table of Critical Values for the Jonckheere-Terpstra Test Statistic
Table A25. Table of Critical Values for Page Test Statistic
Table A26. Table of Extreme Studentized Deviate Outlier Statistic
Table A27. Table of Durbin-Watson Test Statistic
Table A28. Constants Used for Estimation and Construction of Control Charts
Index