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Introduction | |

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Types of Statistics | |

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Parameters and Statistics | |

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Sampling and Independent Observations | |

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Types of Variables | |

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Independent and Dependent Variables | |

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Selection of the Appropriate Statistical Test | |

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Procedures for Inferential Statistical Tests | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Probability | |

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Classic Probability | |

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Probability Involving Two Variables | |

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Conditional Probability | |

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Probability Distribution | |

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Counting Techniques | |

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Binomial Distribution | |

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Poisson Distribution | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Sampling | |

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Random Sampling | |

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Other Probability Sampling Procedures | |

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Precision, Accuracy, and Bias | |

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Reliability and Validity | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Presentation Modes | |

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Tabulation of Data | |

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Visual Displays for Discrete Variables | |

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Visual Displays for Continuous Variables | |

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Visual Displays for Two or More Continuous Variables | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Measures of Central Tendency | |

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Centers of a Continuous Distribution | |

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Dispersion within a Continuous Distribution | |

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Population versus Sample Measures of Central Tendency | |

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Measurements Related to the Sample Standard Deviation | |

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Trimmed Mean | |

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Alternative Computational Methods for Calculating Central Tendency | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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The Normal Distribution and Data Transformation | |

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The Normal Distribution | |

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Determining if the Distribution is Normal | |

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Data Transformations: An Overview | |

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Lognormal Transformation and the Geometric Mean | |

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Other Types of Transformations | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Confidence Intervals and Tolerance Limits | |

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Sampling Distribution | |

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Standard Error of the Mean versus the Standard Deviation | |

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Confidence Intervals | |

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Statistical Control Charts | |

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Process Capability Indices | |

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Tolerance Limits | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Hypothesis Testing | |

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Hypothesis Testing | |

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Types of Errors | |

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Type I Error | |

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Type II Error and Power | |

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Experimental Errors and Propagation of Errors | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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t-Tests | |

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Parametric Procedures | |

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The t-Distribution | |

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One-Tailed vs. Two-Tailed Tests | |

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One-Sample t-Tests | |

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Two-Sample t-Tests | |

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Corrected Degrees of Freedom for Unequal Variances | |

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One-Sample t-Test Revisited for Critical Value | |

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Matched Pair t-Test (Difference t-Test) | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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One-Way Analysis of Variance (ANOVA) | |

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Hypothesis Testing with the One-Way ANOVA | |

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The F-Distribution | |

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Test Statistic | |

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ANOVA Definitional Formula | |

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ANOVA Computational Formula | |

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Randomized Block Design | |

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Homogeniety of Variance | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Multiple Comparison Tests | |

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Error Associated with Multiple t-Tests | |

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Overview of Multiple Comparison Tests | |

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The q-Statistic | |

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Planned Multiple Comparisons | |

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Bonferroni Adjustment | |

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Sidak Test | |

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Dunn's Multiple Comparisons | |

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Dunnett's Test | |

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Post hoc Procedures | |

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Tukey HSD Test | |

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Student Newman-Keuls Test | |

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Fisher LSD Test | |

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Scheffe Procedure | |

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Scheffe Procedure for Complex Comparisons | |

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Unbalanced Designs | |

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Lack of Homogeneity | |

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Other Post hoc Tests | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Factorial Designs: An Introduction | |

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Factorial Designs | |

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Two-Way Analysis of Variance | |

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Computational Formula with Unequal Cell Size | |

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Post Hoc Procedures | |

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Repeated Measures Design | |

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Repeatability and Reproducibility | |

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Latin Square Designs | |

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Other Designs | |

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Fixed, Random and Mixed Effect Models | |

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Beyond a Two-Way Factorial Design | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Correlation | |

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Graphic Representation of Two Continuous Variables | |

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Pearson Product-Moment Correlation Coefficient | |

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Correlation Line | |

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Statistical Significance of a Correlation Coefficient | |

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Correlation and Causality | |

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In vivo - In vitro Correlation | |

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Other Types of Bivariate Correlations | |

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Pairwise Correlations Involving More Than Two Variables | |

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Multiple Correlations | |

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Partial Correlations | |

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Nonlinear Correlations | |

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Assessing Independence and Randomness | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Linear Regression | |

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The Regression Line | |

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Coefficient of Determination | |

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ANOVA Table | |

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Confidence Intervals and Hypothesis Testing for the Population Slope ([beta]) | |

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Confidence Intervals for the Regression Line | |

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Inverse Prediction | |

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Multiple Data at Various Points on the Independent Variable | |

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Assessing Parallelism of the Slopes of Two Samples | |

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Multiple Linear Regression Models | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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z-Tests of Proportions | |

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z-Test of Proportions - One-Sample Case | |

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z-Test of Proportions - Two-Sample Case | |

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Estimating Power and Desired Sample size for Two-Sample z-Test of Proportions | |

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z-Tests for Proportions - Yates' Correction for Continuity | |

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Proportion Testing for More Than Two Levels of a Discrete Independent Variable | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Chi Square Tests | |

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Chi Square Statistic | |

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Chi Square for One Discrete Independent Variable | |

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Chi Square Goodness-of-Fit Test | |

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Chi Square Test of Independence | |

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Yates' Correction for 2 x 2 Contingency Table | |

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Comparison of Chi Square to the Z-Test of Proportions | |

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Fisher's Exact Test | |

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McNemar's Test | |

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Cochran's Q Test | |

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Mantel-Haenszel Test | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Measures of Association | |

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Introduction | |

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Dichotomous Associations | |

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Nominal Associations | |

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Ordinal Associations | |

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Nominal-by-Interval Associations | |

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Reliability Measurements | |

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Summary | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problem | |

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Odds Ratios and Relative Risk Ratios | |

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Probability, Odds, and Risk | |

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Odds Ratio | |

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Relative Risk | |

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Graphic Display for Odds Ratios and Relative Risk Ratios | |

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Mantel-Haenszel Estimate of Relative Risk | |

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Logistic Regression | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Evidence-Based Practice: An Introduction | |

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Sensitivity and Specificity | |

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Two-by-Two Contingency Table | |

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Defining Evidence-Based Practice | |

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Frequentist versus Bayesian Approaches to Probability | |

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Predictive Values | |

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Likelihood Ratios | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Survival Statistics | |

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Censored Survival Data | |

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Life Table Analysis | |

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Survival Curve | |

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Kaplan-Meier Procedure | |

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Visual Comparison of Two Survival Curves | |

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Tests to Compare Two Levels of an Independent Variable | |

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Hazard Ratios | |

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Multiple Regression with Survival Data: Proportional Hazards Regression | |

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Other Measures and Tests of Survival | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Nonparametric Tests | |

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Use of Nonparametric Tests | |

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Ranking of Information | |

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Mann-Whitney U Test | |

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Median Test | |

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Wilcoxon Matched-Pairs Test | |

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Sign Test | |

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Kruskal-Wallis Test | |

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Post hoc Comparisons Using Kruskal-Wallis | |

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Friedman Two-Way Analysis of Variance | |

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Spearman Rank-Order Correlation | |

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Theil's Incomplete Method | |

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Kolmogorov-Smirnov Goodness-of-Fit Test | |

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Anderson-Darling Test | |

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Runs Tests | |

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Range Tests | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Statistical Tests for Equivalence | |

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Bioequivalence Testing | |

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Experimental Designs for Bioequivalence Studies | |

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Two-Sample t-Test Example | |

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Power in Bioequivalence Tests | |

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Rules for Bioequivalence | |

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Creating Confidence Intervals | |

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Comparison Using Two One-Sided t-Tests | |

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Clinical Equivalence and Noninferiority | |

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Dissolution Testing | |

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SUPAC-IR Guidance | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Outlier Tests | |

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Regulatory Considerations | |

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Outliers on a Single Continuum | |

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Plotting and the Number of Standard Deviations from the Center | |

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The "Huge" Rule | |

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Grubbs' Test for Outlying Observations | |

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Dixon Q Test | |

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Hampel's Rule | |

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Multiple Outliers | |

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Bivariate Outliers in Correlation and Regression Analysis | |

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References | |

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Suggested Supplemental Readings | |

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Example Problems | |

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Answers to Problems | |

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Statistical Errors in the Literature | |

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Errors and the Peer Review Process | |

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Problems with Experimental Design | |

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Standard Deviations versus Standard Error of the Mean | |

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Problems with Hypothesis Testing | |

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Problems with Parametric Statistics | |

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Errors with the Chi Square Test of Independence | |

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Summary | |

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References | |

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Suggested Supplemental Readings | |

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Flow Charts for the Selection of Appropriate Tests | |

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Statistical Tables | |

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Random Numbers Table | |

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Normal Standardized Distribution | |

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K-Values for Calculating Tolerance Limits (two-tailed) | |

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K-Values for Calculating Tolerance Limits (one-tailed) | |

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Student t-Distribution (1 - [alpha]/2) | |

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Comparison of One-tailed vs. Two-Tailed t-Distributions | |

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Analysis of Variance F-Distribution | |

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Upper Percentage Points of the F[subscript max] Statistic | |

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Upper Percentage Points of the Cochran C Test for Homogeneity of Variance | |

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Percentage Points of the Standardized Range (q) | |

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Percentage Points of the Dunn Multiple Comparisons | |

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Critical Values of q for the Two-Tailed Dunnett's Test | |

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Critical Values of q for the One-Tailed Dunnett's Test | |

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Values of r at Different Levels of Significance | |

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Chi Square Distribution | |

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Critical Values for Kolmogorov Goodness-of-Fit Test ([alpha] = 0.05) | |

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Critical Values for Smirnov Test Statistic ([alpha] = 0.05) | |

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Critical Values for the Runs Test ([alpha] = 0.05) | |

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Critical Values for T[subscript I] Range Test ([alpha] = 0.05) | |

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Critical Values for the F[subscript R] Test for Dispersion | |

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Values for Use in Grubbs Test for Outlier ([alpha]) | |

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Values for Use in Dixon Test for Outlier ([alpha]) | |

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Index | |