# Fundamental Statistics For The Behavioral Sciences

**by**Howell, David C.

### 9780495811251

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## Summary

**David Howell**'s practical approach focuses on the context of statistics in behavioral research, with an emphasis on looking before leaping; investigating the data before jumping into a test. This provides you with an understanding of the logic behind the statistics: why and how certain methods are used rather than just doing techniques by rote.

Formulas used in the book are definitional rather than for purposes of calculation, as **Howell** believes formulas are there to help students define the concepts. This textbook offers hundreds of exercises, most of which are based on data from published research, promote student interest and provide the context of statistics in behavioral research.

Learn faster and understand more because **Howell**'s texts moves you beyond number crunching, allowing you to discover the meaning of statistical results and how they relate to the research questions being asked.

## Table of Contents

Introduction | |

The importance of Context | |

Basic Terminology | |

Selection among Statistical Procedures | |

Using Computers | |

Summary | |

Exercises | |

Basic Concepts | |

Scales of Measurement | |

Variables | |

Random Sampling | |

Notation | |

Summary | |

Exercises | |

Displaying Data | |

Plotting Data | |

Stem-and-Leaf Displays | |

Histograms | |

Reading Graphs | |

Alternative Methods of Plotting Data | |

Describing Distributions | |

Using Computer Programs to Display Data | |

Summary | |

Exercises | |

Measures of Central Tendency | |

The Mode | |

The Median | |

The Mean | |

Relative Advantages of the Mode, the Median, and the Mean | |

Obtaining Measures of Central Tendency Using SPSS | |

A Simple Demonstration-Seeing Statistics | |

Summary | |

Exercises | |

Measures of Variability | |

Range | |

Interquartile Range and Other Range Statistics | |

The Average Deviation | |

The Variance | |

The Standard Deviation | |

Computational Formulae for the Variance and the Standard eviation | |

The Mean and the Variance as Estimators | |

Boxplots: Graphical Representations of Dispersion and Extreme Scores | |

A Return to Trimming | |

Obtaining Measures of Dispersion Using SPSS | |

A Final Worked Example | |

Seeing Statistics | |

Summary | |

Exercises | |

The Normal Distribution | |

The Normal Distribution | |

The Standard Normal Distribution | |

Setting Probable Limits on an Observations | |

Measures Related to z | |

Seeing Statistics | |

Summary | |

Exercises | |

Basic Concepts of Probability | |

Probability | |

Basic Terminology and Rules | |

The Application of Probability to Controversial Issues | |

Writing Up the Results | |

Discrete versus Continuous Variables | |

Probability Distributions for Discrete Variables | |

Probability Distributions for Continuous Variables | |

Summary | |

Exercises | |

Sampling Distributions and Hypothesis Testing | |

Two Simple Examples Involving Course Evaluations and Rude Motorists | |

Sampling Distributions | |

Hypothesis Testing | |

The Null Hypothesis | |

Test Statistics and Their Sampling Distributions | |

Using the Normal Distribution to Test Hypotheses | |

Type I and Type II Errors | |

One- and Two-Tailed Tests | |

Seeing Statistics | |

A Final Worked Example | |

Back to Course Evaluations and Rude Motorists | |

Summary | |

Exercises | |

Correlation | |

Scatter Diagrams | |

The Relationship Between Pace of Life and Heart Disease | |

The Covariance | |

The Pearson Product-Moment Correlation Coefficient (r) | |

Correlations with Ranked Data | |

Factors that Affect the Correlation | |

Beware Extreme Observations | |

Correlation and Causation | |

If Something Looks Too Good to be True, Perhaps it Is | |

Testing the Significance of a Correlation Coefficient | |

Intercorrelation Matrices | |

Other Correlation Coefficients | |

Using SPSS to Obtain Correlation Coefficients | |

Seeing Statistics | |

A Final Worked Example | |

Summary | |

Exercises | |

Regression | |

The Relationship Between Stress and Health | |

The Basic Data | |

The Regression Line | |

The Accuracy of Prediction | |

The Influence of Extreme Values | |

Hypothesis Testing in Regression | |

Computer Solutions using SPSS | |

Seeing Statistics | |

Summary | |

Exercises | |

Multiple Regression | |

Overview | |

A Different Data Set | |

Residuals | |

The Visual Representation of Multiple Regression | |

Hypothesis Testing | |

Refining the Regression Equation | |

A Second Example: Height and Weight | |

A Third Example: Psychological Symptoms in Cancer Patients | |

Summary | |

Exercises | |

Hypothesis Testing Applied to Means: One Sample | |

Sampling Distribution of the Mean | |

Testing Hypotheses about Means When ?? is Known | |

Testing a Sample Mean When ?? is Unknown (The One-Sample t) | |

Factors that Affect the Magnitude of t and the Decision about H0 | |

A Second Example: the Moon Illusion | |

How Large is Our Effect? | |

Confidence Limits on the Mean | |

Using SPSS to Run One-Sample t tests | |

A Final Worked Example | |

Seeing Statistics | |

Summary | |

Exercises | |

Hypothesis Tests Applied to Means: Two Related Samples | |

Related Samples | |

Student's t Applied to Difference Scores | |

A Second Example: the Moon Illusion Again | |

Advantages and Disadvantages of Using Related Samples | |

How Large an Effect Have We Found? | |

Confidence Limits on Changes | |

Using SPSS for t Tests on Related Samples | |

Writing Up the Results | |

Summary | |

Exercises | |

Hypothesis Tests Applied to Means: Two Independent Samples | |

Distribution of Differences Between Means | |

Heterogeneity of Variance | |

Nonnormality of Distributions | |

A Second Example with Two Independent Samples | |

Effect Sizes Again | |

Confidence Limits on ??1 ?V ??2 | |

Writing Up the Results | |

Use of Computer Programs for Analysis of Two Independent Sample Means | |

A Final Worked Example | |

Seeing Statistics | |

Summary | |

Exercises | |

Power | |

The Basic Concept | |

Factors that Affect the Power of a Test Effect Size | |

Power Calculations for the One-Sample t Test Power Calculations for Differences Between Two Independent Means | |

Power Calculations for the t Test for Related Samples | |

Power Considerations in Terms of Sample Size | |

You Don't Have to Do it by Hand | |

Seeing Statistics | |

Summary | |

Exercises | |

One-Way Analysis of Variance | |

The General Approach | |

The Logic of the Analysis of Variance | |

Calculations for the Analysis of Variances | |

Unequal Sample Sizes | |

Multiple Comparison Procedures | |

Violations of Assumptions | |

The Size of the Effects | |

Writing Up the Results | |

The Use of SPSS for a One-Way Analysis of Variance | |

A Final Worked Example | |

Seeing Statistics | |

Summary | |

Exercises | |

Factorial Analysis of Variance Factorial Designs | |

The Extension of the Eysenck Study | |

Interactions | |

Simple Effects | |

Measures of Association and Effect Size | |

Reporting the Results | |

Unequal Sample Sizes | |

A Second Example: Maternal Adaptation Revisited | |

Using SPSS for Factorial Analysis of Variance | |

Seeing Statistics | |

Summary | |

Exercises | |

Repeated-Measures Analysis of Variance | |

An Example: Depression as a Response to an Earthquake | |

Multiple Comparisons | |

Effect Size | |

Assumptions involved in Repeated-Measures Designs | |

Advantages and Disadvantages of Repeated-Measures Designs | |

Using SPSS to Analyze Data in a Repeated-Measures Design | |

Writing Up the Results | |

A Final Worked Example | |

Summary | |

Exercises | |

Chi-Square | |

One Classification Variable: the Chi-Square Goodness of Fit Test | |

Two Classification Variables: Analysis of Contingency Tables | |

Possible Improvements on Standard Chi-Square | |

Chi-Square for Larger Contingency Tables | |

The Problem of Small Expected Frequencies | |

The Use of Chi-Square as a Test of Proportions | |

Nonindependent Observations | |

SPSS Analysis of Contingency Tables | |

Measures of Effect Size | |

A Final Worked Example | |

Writing Up the Results | |

Seeing Statistics | |

Summary | |

Exercises | |

Nonparametric and Distribution-Free Statistical Tests | |

The Mann-Whitney Test Wilcoxon's Matched-Pairs Signed-Ranks Test | |

Kruskal-Wallis One-Way Analysis of Variance | |

Friedman's Rank Test for k Correlated Samples | |

Measures of Effect Size | |

Writing Up the Results | |

Summary | |

Exercises | |

Choosing the Appropriate Analysis | |

Exercises and Examples | |

Arithmetic Review | |

Symbols and Notation | |

Basic Statistical Formulae | |

Dataset | |

Statistical Tables | |

Glossary | |

References | |

Answers to Selected Exercises | |

Index | |

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