# Interpreting and Using Statistics in Psychological Research

First Edition

- Andrew N. Christopher - Albion College, USA

Additional resources:

**Other Titles in:**

Educational Research | Quantitative/Statistical Research | Research Methods in Psychology

August 2016 | 584 pages | SAGE Publications, Inc

This practical, conceptual introduction to statistical analysis by award-winning teacher Andrew N. Christopher uses published research with inherently interesting social sciences content to help students make clear connections between statistics and real life. Using a friendly, easy-to-understand presentation, Christopher walks students through the hand calculations of key statistical tools and provides step-by-step instructions on how to run the appropriate analyses for each type of statistic in SPSS and how to interpret the output. With the premise that a conceptual grasp of statistical techniques is critical for students to truly understand why they are doing what they are doing, the author avoids overly formulaic jargon and instead focuses on when and how to use statistical techniques appropriately.

Preface

Acknowledgments

About the Author

Chapter 1- Why Do I Have to Learn Statistics? The Value of Statistical Thinking in Life

Statistical Thinking and Everyday Life |

Failing to Use Information About Probability |

Availability heuristic |

Representativeness heuristic |

Misunderstanding Connections Between Events |

Illusory correlations |

Gambler’s fallacy |

Goals of Research |

Goal: To Describe |

Goal: To Predict |

Goal: To Explain |

Goal: To Apply |

Statistical Thinking: Some Basic Concepts |

Parameters Versus Statistics |

Descriptive Statistics Versus Inferential Statistics |

Sampling Error |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 2- Basics of Quantitative Research: Variables, Scales of Measurement, and an Introduction to the Statistical Package for the Social Sciences (SPSS)

The Study |

Variables |

Operational Definitions |

Measurement Reliability and Validity |

Scales of Measurement: How We Measure Variables |

Nominal Data |

Ordinal Data |

Interval and Ratio (Scale) Data |

Discrete Versus Continuous Variables |

The Basics of SPSS |

Variable View |

Data View |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 3- Describing Data With Frequency Distributions and Visual Displays

The Study |

Frequency Distributions |

Frequency Distribution Tables |

Frequency Distribution Graphs |

Common Visual Displays of Data in Research |

Bar Graphs |

Scatterplots |

Line Graphs |

Using SPSS to Make Visual Displays of Data |

Making a Bar Graph |

Making a Scatterplot |

Making a Line Graph |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 4- Making Sense of Data: Measures of Central Tendency and Variability

Measures of Central Tendency |

Three Measures of Central Tendency |

Mean |

Median |

Mode |

Reporting the measures of central tendency in research |

Choosing a Measure of Central Tendency |

Consideration 1: Outliers in the data |

Consideration 2: Skewed data distributions |

Consideration 3: A variable’s scale of measurement |

Consideration 4: Open-ended response ranges |

Measures of Central Tendency and SPSS |

Measures of Variability |

What Is Variability? Why Should We Care About Variability? |

Three Measures of Variability |

Range |

Variance |

Standard deviation |

Reporting variability in research |

Measures of Variability and SPSS |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 5- Determining “High” and “Low” Scores: The Normal Curve, z Scores, and Probability

Types of Distributions |

Normal Distributions |

Skewed Distributions |

Standardized Scores (z Scores) |

z Scores, the Normal Distribution, and Percentile Ranks |

Locating Scores Under the Normal Distribution |

Percentile Ranks |

z Scores and SPSS |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 6- Drawing Conclusions From Data: Descriptive Statistics, Inferential Statistics, and Hypothesis Testing

Basics of Null Hypothesis Testing |

Null Hypotheses and Research Hypotheses |

Alpha Level and the Region of Null Hypothesis Rejection |

Gathering Data and Testing the Null Hypothesis |

Making a Decision About the Null Hypothesis |

Type I Errors, Type II Errors, and Uncertainty in Hypothesis Testing |

The z Test |

A Real-World Example of the z Test |

Ingredients for the z Test |

Using the z Test for a Directional (One-Tailed) Hypothesis |

Using the z Test for a Nondirectional (Two-Tailed) Hypothesis |

One-Sample t Test |

A Real-Word Example of the One-Sample t Test |

Ingredients for the One-Sample t Test |

Using the One-Sample t Test for a Directional (One-Tailed) Hypothesis |

Using the One-Sample t Test for a Nondirectional (Two-Tailed) Hypothesis |

One-Sample t Test and SPSS |

Statistical Power and Hypothesis Testing |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 7- Comparing Two Group Means: The Independent Samples t Test

Conceptual Understanding of the Statistical Tool |

The Study |

The Tool |

Ingredients |

Hypothesis from Kasser and Sheldon (2000) |

Interpreting the Tool |

Assumptions of the tool |

Testing the null hypothesis |

Extending our null hypothesis test |

Using Your New Statistical Tool |

Hand-Calculating the Independent Samples t Test |

Step 1: State hypotheses |

Step 2: Calculate the mean for each of the two groups |

Step 3: Calculate the standard error of the difference between the means |

Step 4: Calculate the t test statistic |

Step 5: Determine degrees of freedom (dfs) |

Step 6: Locate the critical value |

Step 7: Make a decision about the null hypothesis |

Step 8: Calculate an effect size |

Step 9: Determine the confidence interval |

Independent Samples t Test and SPSS |

Establishing your spreadsheet |

Running your analyses |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 8- Comparing Two Repeated Group Means: The Paired Samples t Test

Conceptual Understanding of the Tool |

The Study |

The Tool |

Ingredients |

Hypothesis from Stirling et al. (2014) |

Interpreting the Tool |

Testing the null hypothesis |

Extending our null hypothesis test |

Assumptions of the tool |

Using Your New Statistical Tool |

Hand-Calculating the Paired Samples t Test |

Step 1: State hypotheses |

Step 2: Calculate the mean difference score |

Step 3: Calculate the standard error of the difference scores |

Step 4: Calculate the t test statistic |

Step 5: Determine degrees of freedom (dfs) |

Step 6: Locate the critical value |

Step 7: Make a decision about the null hypothesis |

Step 8: Calculate an effect size |

Step 9: Determine the confidence interval |

Paired Samples t Test and SPSS |

Establishing your spreadsheet |

Running your analyses |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 9- Comparing Three or More Group Means: The One-Way, Between-Subjects Analysis of Variance (ANOVA)

Conceptual Understanding of the Tool |

The Study |

The Tool |

Ingredients |

Assumptions of the tool |

Hypothesis from Eskine (2012) |

Interpreting the Tool |

Testing the null hypothesis |

Extending our null hypothesis test |

Going beyond the F ratio: Post hoc tests |

Using Your New Statistical Tool |

Hand-Calculating the One-Way, Between-Subjects ANOVA |

Step 1: State hypotheses |

Step 2: Calculate the mean for each group |

Step 3: Calculate the sums of squares (SSs) |

Total Sums of Squares (SStotal) |

Within-Groups Sums of Squares (SSwithin-groups) |

Between-Groups Sums of Squares (SSbetween-groups) |

Step 4: Determine degrees of freedom (dfs) |

Total Degrees of Freedom (dftotal) |

Within-Groups Degrees of Freedom (dfwithin-groups) |

Between-Groups Degrees of Freedom (dfbetween-groups) |

Step 5: Calculate the mean squares (MSs) |

Step 6: Calculate your F ratio test statistic |

Step 7: Locate the critical value |

Step 8: Make a decision about the null hypothesis |

Step 9: Calculate an effect size |

Step 10: Perform post hoc tests |

One-Way Between-Subjects ANOVA and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 10- Comparing Three or More Repeated Group Means: The One-Way, Repeated-Measures Analysis of Variance (ANOVA)

Conceptual Understanding of the Tool |

The Study |

The Tool |

Between-subjects versus repeated-measures ANOVAs |

Assumptions of the tool |

Hypothesis from Bernard et al. (2014) |

Interpreting the Tool |

Testing the null hypothesis |

Extending our null hypothesis test |

Going beyond the F ratio: Post hoc tests |

Using Your New Statistical Tool |

Hand-Calculating the One-Way, Repeated-Measures ANOVA |

Step 1: State the hypothesis |

Step 2: Calculate the mean for each group |

Step 3: Calculate the sums of squares (SSs) |

Total Sums of Squares (SStotal) |

Between Sums of Squares (SSbetween) |

Error Sums of Squares (SSerror) |

Step 4: Determine degrees of freedom (dfs) |

Total Degrees of Freedom (dftotal) |

Between Degrees of Freedom (dfbetween) |

Error Degrees of Freedom (dferror) |

Step 5: Calculate the mean squares (MSs) |

Step 6: Calculate your F ratio test statistic |

Step 7: Locate the critical value |

Step 8: Make a decision about the null hypothesis |

Step 9: Calculate an effect size |

Step 10: Perform post hoc tests |

One-Way, Repeated-Measures ANOVA and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 11- Analyzing Two or More Influences on Behavior: Factorial Designs for Two Between-Subjects Factors

Conceptual Understanding of the Tool |

The Study |

The Tool |

Factorial notation |

Main effects and interactions |

Hypothesis from Troisi and Gabriel (2011) |

Interpreting the Tool |

Testing the null hypothesis |

Extending the null hypothesis tests |

Dissecting a statistically significant interaction |

Using Your New Statistical Tool |

Hand-Calculating the Two-Way, Between-Subjects ANOVA |

Step 1: State the hypotheses |

Step 2: Calculate the mean for each group and the marginal means |

Step 3: Calculate the sums of squares (SSs) |

Total Sums of Squares (SStotal) |

Within-Groups Sums of Squares (SSwithin-groups) |

Between-Groups Sums of Squares (SSbetween-groups) |

Step 4: Determine degrees of freedom (dfs) |

Total Degrees of Freedom (dftotal) |

Within-Groups Degrees of Freedom (dfwithin-groups) |

Between-Groups Degrees of Freedom (dfbetween-groups) |

Step 5: Calculate the mean squares (MSs) |

Step 6: Calculate your F ratio test statistics |

Step 7: Locate the critical values |

Step 8: Make a decision about each null hypothesis |

Step 9: Calculate the effect sizes |

Step 10: Perform follow-up tests |

Two-Way, Between-Subjects ANOVA and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Dissecting interactions in SPSS |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 12- Determining Patterns in Data: Correlations

Conceptual Understanding of the Tool |

The Study |

The Tool |

Types (directions) of correlations |

Strength of correlations |

Assumptions of the Pearson correlation |

Uses for correlations |

Use 1: Studying naturally occurring relationships |

Use 2: Basis for predictions |

Use 3: Establishing measurement reliability and validity |

Hypotheses from Clayton et al. (2013) |

Interpreting the Tool |

Testing the null hypothesis |

Cautions in interpreting correlations |

Caution 1: Don’t confuse type (direction) and strength of a correlation |

Caution 2: Range restriction |

Caution 3: “Person-who” thinking |

Caution 4: Curvilinear relationships |

Caution 5: Spurious correlations |

Using Your New Statistical Tool |

Hand-Calculating the Person Correlation Coefficient (r) |

Step 1: State hypotheses |

Step 2: For both variables, find each participant’s deviation score and then multiply them together |

Step 3: Sum the products in step 2 |

Step 4: Calculate the sums of squares for both variables |

Step 5: Multiply the two sums of squares and then take the square root |

Step 6: Calculate the correlation coefficient (r) test statistic |

Step 7: Locate the critical value |

Step 8: Make a decision about the null hypothesis |

The Pearson Correlation (r) and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 13- Predicting the Future: Univariate and Multiple Regression

Univariate Regression |

Ingredients |

Hand-Calculating a Univariate Regression |

Step 1: Calculate the slope of the line (b) |

Step 2: Calculate the y-intercept (a) |

Step 3: Make predictions |

Univariate Regression and SPSS |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Multiple Regression |

Understanding Multiple Regression in Research |

Multiple Regression and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 14- When We Have Exceptions to the Rules: Nonparametric Tests

Chi-Square (x2) Tests |

Chi-Square (x2) Goodness-of-Fit Test |

Hand-calculating the ?2 goodness-of-fit test |

Step 1: State hypotheses |

Step 2: Determine degrees of freedom (dfs) |

Step 3: Calculate the x2 test statistic |

Step 4: Find the critical value and make a decision about the null hypothesis |

x2 goodness-of-fit test and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chi-Square (x2) Test of Independence |

Hand-calculating the x2 test of independence |

Step 1: State hypotheses |

Step 2: Determine degrees of freedom (dfs) |

Step 3: Calculate expected frequencies |

Step 4: Calculate the x2 test statistic |

Step 5: Find the critical value and make a decision about the null hypothesis |

Step 6: Calculate an effect size |

x2 test for independence and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Spearman Rank-Order Correlation Coefficient |

Hand-Calculating the Spearman Rank-Order Correlation |

Step 1: State the hypothesis |

Step 2: Calculate the difference (D) score between each pair of rankings |

Step 3: Square and sum the difference scores in step 2 |

Step 4: Calculate the Spearman correlation coefficient (rs) test statistic |

Step 5: Locate the critical value and make a decision about the null hypothesis |

Spearman’s Rank-Order Correlation and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Mann-Whitney U Test |

Hand-Calculating the Mann-Whitney U Test |

Step 1: State hypotheses |

Step 2: Calculate the ranks for categories being compared |

Step 3: Sum the ranks for each category |

Step 4: Find the U for each group |

Step 5: Locate the critical value and make a decision about the null hypothesis |

Mann-Whitney U Test and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Chapter 15- Bringing It All Together: Using Your Statistical Toolkit

Deciding on the Appropriate Tool: Six Examples |

Study 1: “Waiting for Merlot: Anticipatory Consumption of Experiential and Material Purchases |

Study 2: “Evaluations of Sexy Women in Low- and High-Status Jobs” |

Study 3: “Evil Genius? How Dishonesty Can Lead to Greater Creativity” |

Study 4: “Differential Effects of a Body Image Exposure Session on Smoking Urge Between Physically Active and Sedentary Female Smokers” |

Study 5: “Texting While Stressed: Implications for Students’ Burnout, Sleep, and Well-Being” |

Study 6: “How Handedness Direction and Consistency Relate to Declarative Memory Task Performance” |

Using Your Toolkit to Identify Appropriate Statistical Tools |

Study 7: “Borderline Personality Disorder: Attitudinal Change Following Training” |

Study 8: “Effects of Gender and Type of Praise on Task Performance Among Undergraduates” |

Study 9: “Please Respond ASAP: Workplace Telepressure and Employee Recovery” |

Answers to Studies 7, 8, and 9 |

Appendices: Statistical Tables

Glossary

References

Index

### Supplements

Student Study Site

**Use the Student Study Site to get the most out of your course! **Our

**Student Study Site**at

**study.sagepub.com/Christopher**is completely open-access and offers a wide range of additional features!

- Mobile-friendly
**web quizzes**allow for independent assessment of progress made in learning course material.

Instructor Resource Site

**Calling all instructors! **It’s easy to log on to SAGE’s password-protected Instructor Teaching Site at

**study.sagepub.com/Christopher**for complete and protected access to all text-specific Instructor Resources for

**Andrew Christopher’s**

**. Simply provide your institutional information for verification and within 72 hours you’ll be able to use your login information for any SAGE title!**

*Interpreting and Using Statistics in Psychological*Research

Password-protected **Instructor Resources** include the following:

- A
**Microsoft® Word®****test bank**, is available containing multiple choice, true/false, short answer, and essay questions for each chapter. The test bank provides you with a diverse range of pre-written options as well as the opportunity for editing any question and/or inserting your own personalized questions to effectively assess students’ progress and understanding. - Editable, chapter-specific Microsoft®
**PowerPoint® slides**offer you complete flexibility in easily creating a multimedia presentation for your course. Highlight essential content and features..