Introductory Statistics for Psychology

Introductory Statistics for Psychology

The Logic and the Methods

1st Edition - January 1, 1981

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  • Author: Gustav Levine
  • eBook ISBN: 9781483257860

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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


    Modal Peaks


    Continuous Distributions


    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



    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


    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


    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


    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


    Means of Cells, Columns, and Rows

    Main Effects

    Simple Effects


    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


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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