Introductory Statistics for Psychology
The Logic and the Methods
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Introductory Statistics for Psychology: The Logic and the Methods presents the concepts of experimental design that are carefully interwoven with the statistical material. This book emphasizes the verbalization of conclusions to experiments, which is another means of communicating the reasons for statistical analyses. Organized into 17 chapters, this book begins with an overview of alternative ways of stating the conclusions from a significant interaction. This text then presents the analysis of variance and introduces the summation sign and its use. Other chapters consider frequency distribution as any presentation of data that offers the frequency with which each score occurs. This book discusses as well the differences in and among people, which are a constant source of variability in test scores, and in most other measurements of people. The final chapter deals with the working knowledge of arithmetic and elementary algebra. This book is a valuable resource for students and psychologists.
Table of Contents
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 Statistics
Two 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 Proof
Three 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 Distributions
Four 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 Percentile
Five 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 Distributions
Sixz 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 Transformations
Seven 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 Probability
Eight 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 Conclusions
Nine 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 Significance
Ten 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 Assumptions
Eleven 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 Assumptions
Twelve 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 Validity
Thirteen 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 Chapter
Fourteen 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 Error
Fifteen 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 Effects
Sixteen 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 Relationship
Seventeen 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 Problems
Glossary of Symbols
Index
Product details
- No. of pages: 512
- Language: English
- Copyright: © Academic Press 1981
- Published: January 1, 1981
- Imprint: Academic Press
- eBook ISBN: 9781483257860
About the Author
Gustav Levine
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