# Introductory Statistics for the Behavioral Sciences

## 1st Edition

**Authors:**Joan Welkowitz Robert B. Ewen Jacob Cohen

**eBook ISBN:**9781483258157

**Imprint:**Academic Press

**Published Date:**1st January 1971

**Page Count:**288

## Description

Introductory Statistics for the Behavioral Sciences provides an introduction to statistical concepts and principles. This book emphasizes the robustness of parametric procedures wherein such significant tests as t and F yield accurate results even if such assumptions as equal population variances and normal population distributions are not well met.

Organized into three parts encompassing 16 chapters, this book begins with an overview of the rationale upon which much of behavioral science research is based, namely, drawing inferences about a population based on data obtained from a sample. This text then examines the primary goal of descriptive statistics to bring order out of chaos. Other chapters consider the concept of variability and its applications. This book discusses as well the essential characteristics of a group of scores. The final chapter deals with the chi-square analysis.

This book is a valuable resource for students of statistics as well as for undergraduates majoring in psychology, sociology, and education.

## Table of Contents

Preface

Acknowledgments

Glossary of Symbols

Part I. Introduction

1. Introduction

Descriptive and Inferential Statistics

Populations, Samples, Parameters, and Statistics

Summation Notation

Summary

Part II. Descriptive Statistics

2. Frequency Distributions and Graphs

The Purpose of Descriptive Statistics

Regular Frequency Distributions

Cumulative Frequency Distributions

Grouped Frequency Distributions

Graphic Representations

Shapes of Frequency Distributions

Summary

3. Transformed Scores I: Percentiles

Definition of Percentiles

Deciles, Quartiles, and the Median

Summary

4. Measures of Central Tendency

The Mean

The Median

The Mode

Summary

5. Measures of Variability

The Concept of Variability

The Range

The Standard Deviation and Variance

Summary

6. Transformed Scores II: Z and T Scores

Rules for Changing X and σ

Standard Scores (Z Scores)

T Scores

SAT Scores

Summary

Appendix to Chapter 6: Proofs of Rules for Changing X and σ

Part III. Inferential Statistics

7. The General Strategy of Inferential Statistics

The Goals of Inferential Statistics

The Strategy of Inferential Statistics

Statistical Models

Summary

8. The Normal Curve Model

Score Distributions

Characteristics of the Normal Curve

Illustrative Examples

Summary

9. Inferences About the Mean of a Single Population

The Standard Error of the Mean

Hypothesis Testing

The Statistical Test for the Mean of a Single Population when σ Is Known

The Statistical Test for the Mean of a Single Population when σ Is Not Known: The t Distributions

Interval Estimation

The Standard Error of a Proportion

One-Tailed Tests of Significance

Summary

10. Testing Hypotheses About the Difference Between the Means of Two Populations

The Standard Error of the Difference

Estimating the Standard Error of the Difference

The t Test for Two Sample Means

Measures of the Strength of the Relationship Between the Two Variables

Confidence Intervals for μ1—μ2

Using the t Test for Two Sample Means: Some General Considerations

The t Test for Matched Samples

Summary

11. Linear Correlation and Prediction

Describing the Linear Relationship Between Two Variables

Testing the Significance of the Correlation Coefficient

Prediction and Linear Regression

Measuring Prediction Error: The Standard Error of Estimate

Summary

Appendix to Chapter 11 : Equivalence of the Various Formulas for r

12. Other Correlational Techniques

The Relationship Between Ranked Variables: The Spearman Rank-Order Correlation Coefficient

The Relationship Between One Dichotomous and One Continuous Variable

The Relationship Between Two Dichotomous Variables

Summary

13. Introduction to Power Analysis

Concepts of Power Analysis

The Test of the Mean of a Single Population

The Significance Test of the Proportion of a Single Population

The Significance Test of a Pearson r

Testing the Significance of the Difference Between Independent Means

Summary

14. One-Way Analysis of Variance

The General Logic of ANOVA

Computational Procedures

One-Way ANOVA with Unequal Sample Sizes

Some Comments on the Use of ANOVA

Summary

Appendix to Chapter 14: Proof That Total Variance Is Equal to the Sum of Between-Group and within-Group Variance

15. Introduction to Factorial Design: Two-Way Analysis of Variance

Computational Procedures

The Meaning of Interaction

Summary

16. Chi Square

Chi Square and Goodness of Fit: One-Variable Problems

Chi Square as a Test of Independence: Two-Variable Problems

Measures of Strength of Association in Two-Variable Tables

Summary

Appendix

Index

## Details

- No. of pages:
- 288

- Language:
- English

- Copyright:
- © Academic Press 1971

- Published:
- 1st January 1971

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483258157