Introductory Statistics for Psychology

One Introduction Relationships Between Variables Restricting Questions to Two Variables at a Time Controlling a Variable Experimental Manipulation of the Controlled Variable Classification of the Controlled Variable Independent and Dependent Variables The Degree of Relationship Between Variables The Goals of Psychological Research The Place of Statistics in Psychology Descriptive Statistics Inferential StatisticsTwo the Average The Mean The Median The Middle Rank and the Median Choosing Between the Mean and the Median The Mode Summary Comparison The Symbols in Statistical Formulas The Variables X and Y Subscripts for Variables The Rules of Summation The First Rule of Summation The Second Rule of Summation The Third Rule of Summation The Sum of the Deviations from the Mean Equals Zero The Logic and Purpose of a ProofThree Frequency Distributions Advantages of Frequency Distributions Computing the Mean of a Frequency Distribution Graphs Modal Peaks Skewness Continuous Distributions Histograms Improper Uses of Graphs Graphing Relationships Between Variables Grouped Data The Interval Size in a Grouped Frequency Distribution The Range of a Distribution Choosing the Size and Number of Intervals Zero Frequencies Unequal Intervals Graphing Grouped Data Computing the Mean with Grouped Data Cumulative Frequency Distributions Graphs of Cumulative Frequency DistributionsFour Percentiles Computing Percentile Ranks of Raw Scores Computing Percentile Ranks in Grouped Frequency Distributions The Use of Percentile Ranks The Use of Percentiles Deciles Quartiles Computing Percentiles Computing the Median as the 50th PercentileFive Variability Populations versus Samples Infinite Populations Parameters versus Statistics Random Samples Measures of Variability from the Complete Population The Range The Mean Deviation The Variance The Standard Deviation Sample Estimates of Variability Degrees of Freedom The Estimate of the Variance The Estimate of the Standard Deviation Computational Formulas for Variance and Standard Deviation Proving the Equality of Defining and Computational Formulas Computational Formulas for Samples Contrasting Defining and Computational Formulas Computations with Frequency DistributionsSixz Scores and Effects of Linear Transformations Adding a Constant Value to the Scores of a Distribution The Variance and Standard Deviation are Unchanged by Addition of a Constant Multiplying the Scores of a Distribution by a Constant Changes in the Variance and Standard Deviation Effects of z Score TransformationsSeven Probability The Sample Space Events and Sample Points The Axioms of Probability Probability as a Closed System Equal Probabilities, Theoretically Assigned Complementary Events Summing Mutually Exclusive Events ("Or Relations") Joint Events ("And Relations") Comparing Theoretical and Empirical Probabilities Empirical Basis of ProbabilityEight the Binomial Distribution Reaching Conclusions from Unlikely Events An Empirical Model of Chance Rejecting Initial Assumptions The Null Hypothesis A Theoretical Probability Distribution for Coin Tossing Stating the Distribution as an Equation The Binomial Coefficient Theoretical Analysis of the Binomial Distribution Assumptions of the Binomial Distribution The Binomial Distribution as a Model of Survival in Illness Critical Values Type I Errors Type II Errors Uncertainty About Errors Statistical Significance Controlling the Probability of Being Wrong Verbalizing Statistically-Based ConclusionsNine The Normal Distribution Defining Probabilities in Continuous Distributions The Defining Equation for the Normal Distribution The Normal Distribution of z Scores Using the Table of Probabilities Under the Normal Curve Sample Means as Estimates of Population Means The Standard Error of the Mean The Normal Distribution of Sample Means The Central Limit Theorem Using the Normal Distribution for Statistical Inference Directional versus Nondirectional Hypotheses Nondirectional Hypotheses (Two-Tailed Tests of Significance) Graphic Presentation of Type II Error Probabilities Conditions for Using a One-Tailed Test of Significance Doubt About the Use of One-Tailed Tests of Significance Defense of One-Tailed Tests Summary of the Issues in One- versus Two-Tailed Tests of SignificanceTen The t Distribution Using the t Distribution for Statistical Inference The Table for the t Distribution Matched-Pair t Tests Paired Scores from Different Subjects t Test for the Difference Between Two Means The Null Hypothesis when Comparing Two Means The Standard Error of the Difference Between Two Means Degrees of Freedom when Testing the Difference Between Means Working with Different Sample Sizes The Power of t Tests Sample Size and Power of a t Test A Note on AssumptionsEleven Correlation Degree of Relationship Linear Relationships Correlation and Slope Negative Correlation The Correlation Coefficient and Its Values Cross Products and the Covariance Correlation with z Scores An Interpretation of Correlation Correlation and Causation The Point Biserial Correlation Coefficient Statistical Inference in Correlation Testing Sampled Correlations for Significance Prediction from Regression Lines Obtaining the Slope with ρxy Regression Toward the Mean A Note About AssumptionsTwelve Correlation and Tests Reliability Values for Reliability Coefficients Sample Size in the Assessment of Reliability Reliability and Number of Test Items Test-Retest Reliability The Alternate Test Form Reliability Coefficient The Split-Half Reliability Coefficient Coefficient Alpha Comparisons of the Reliability Coefficients Validity Testing Validity Through Tests of Significance Reliability versus ValidityThirteen Analysis of Variance Experimental Manipulation versus Classification Summary of When to Use Analysis of Variance Control of the Independent Variable Conclusions About Cause and Effect The Group Mean as an Index of Treatment Effects The Null Hypothesis in Analysis of Variance Random Variability Within a Group Random Variability Between Means Using Variability to Detect Treatment Effects Two Different Variance Estimates as Measures of Variability The F Distribution Double Subscript Notation in Analysis of Variance The Within-Groups Variance The Within-Groups Sum of Squares The Within-Groups Degrees of Freedom The Computational Formula for the Within-Groups Mean Square The Between-Groups Variance The Between-Groups Mean Square The Computational Formula for the Between-Groups Mean Square The F Ratio and Mean Squares The Table for Critical Values of F The Total Sum of Squares and Total Degrees of Freedom A Summary Table for Analysis of Variance Computations with Unequal n A Note on Assumptions A Note on the Importance of This ChapterFourteen Statistics Following Significance Degree of Relationship in Analysis of Variance Sources of Variance in the Population of Dependent Variable Scores Estimating the Variance Due to Treatment Effects An Estimate of the Intraclass Correlation Coefficient Computational Form for Estimating the Intraclass Correlation Coefficient Omega-Squared Multiple Comparisons The t Test as a Basis for Multiple Comparisons Adjusting the Type I Error Probability When to Use the Experimentwise Criterion for the Type I ErrorFifteen Two-Factor Analysis of Variance Subscript Notation in Multifactor Analysis of Variance Cells Means of Cells, Columns, and Rows Main Effects Simple Effects Interactions Interpreting Interactions MSw in the Two-Factor Design F Tests in the Two-Factor Design Computation in the Two-Factor Design Designs with More than Two Factors Repeated Measures Statistical Models in Analysis of Variance Omega Squared in the Two-Factor Design Multiple Comparisons in the Two-Factor Design Illustration of Multiple Comparisons for a Main Effect Illustration of Multiple Comparisons for Simple EffectsSixteen Chi-Square The Chi-Square Statistic and the Null Hypothesis Expected Frequencies in Chi-Square Computing the Chi-Square The Chi-Square Distribution and Degrees of Freedom Chi-Square with a 2 x 2 Contingency Table Single Variable Problems (The Goodness of Fit Test) Restrictions on the Use of Chi-Square Single Subject Chi-Square Degree of Relationship in Chi-Square Computing the Degree of RelationshipSeventeen Postscript (Choosing a Statistic) Appendix A: Some Useful Principles of Elementary Algebra Appendix B: Tables Table 1: Table of Squares, Square Roots, and Reciprocals Table 2: Table of Random Numbers Table 3: Table of Probabilities Under the Normal Curve Table 4: The Critical Values of t Table 5: The Critical Values of the Pearson r Table 6: The Critical Values of F Table 7: The Critical Values of the Dunn Multiple Comparison Test Table 8: The Critical Values of Chi-Square Appendix C: Answers to Chapter ProblemsGlossary of SymbolsIndex