Interpreting and Using Statistics in Psychological Research

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Andrew N. Christopher. Interpreting and Using Statistics in Psychological Research

Interpreting and Using Statistics in Psychological Research

Brief Contents

Detailed Contents

Preface

Guiding philosophy of this book

Content organization

Helpful features

Suggestions welcomed!

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

Learning Check

Misunderstanding Connections Between Events

Illusory correlations

Gambler’s fallacy

Learning Check

Goals of Research

Goal: To Describe

Goal: To Predict

Goal: To Explain

Goal: To Apply

Learning Check

Statistical Thinking: Some Basic Concepts

Parameters Versus Statistics

Descriptive Statistics Versus Inferential Statistics

Sampling Error

Learning Check

Notes

Chapter Application Questions

Answers

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

Learning Check

Variables

Operational Definitions

Measurement Reliability and Validity

Learning Check

Scales of Measurement: How We Measure Variables

Nominal Data

Ordinal Data

Interval and Ratio (Scale) Data

Discrete Versus Continuous Variables

Learning Check

The Basics of SPSS

Variable View

Data View

Notes

Chapter Application Questions

Answers

Questions for Class Discussion

Chapter 3 Describing Data With Frequency Distributions and Visual Displays

The Study

Frequency Distributions

Frequency Distribution Tables

Frequency Distribution Graphs

Learning Check

Common Visual Displays of Data in Research

Bar Graphs

Scatterplots

Line Graphs

Learning Check

Using SPSS to Make Visual Displays of Data

Making a Bar Graph

Making a Scatterplot

Making a Line Graph

Learning Check

Notes

Chapter Application Questions

Answers

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

Learning Check

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

Learning Check

Measures of Central Tendency and SPSS

Learning Check

Measures of Variability

What Is Variability? Why Should We Care About Variability?

Three Measures of Variability

Range

Variance

Standard deviation

Reporting variability in research

Learning Check

Measures of Variability and SPSS

Learning Check

Notes

Chapter Application Questions

Answers

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

Learning Check

Standardized Scores (z Scores)

Learning Check

z Scores, the Normal Distribution, and Percentile Ranks

Locating Scores Under the Normal Distribution

Percentile Ranks

Learning Check

z Scores and SPSS

Notes

Chapter Application Questions

Answers

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

Learning Check

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

Learning Check

The z Test. A Real-World Example of the z Test

Ingredients for the z Test

Learning Check

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

Learning Check

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

Learning Check

One-Sample t Test

A Real-World Example of the One-Sample t Test

Ingredients for the One-Sample t Test

Learning Check

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

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

Learning Check

One-Sample t Test and SPSS

Statistical Power and Hypothesis Testing

Notes

Chapter Application Questions

Answers

Questions for Class Discussion

Chapter 7 Comparing Two Group Means The Independent Samples t Test

Conceptual Understanding of the Statistical Tool. The Study

Learning Check

The Tool

Ingredients

Hypothesis from Kasser and Sheldon (2000)

Learning Check

Interpreting the Tool

Assumptions of the tool

Testing the null hypothesis

Extending our null hypothesis test

Learning Check

Answers

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

Learning Check

Problem #1

Questions to Answer:

Answers

Problem #2

Answers

Independent Samples t Test and SPSS

Establishing your spreadsheet

Running your analyses

What am I looking at? Interpreting your SPSS output

Learning Check

Questions to Answer

Answers

Chapter Application Questions

Answers

Questions for Class Discussion

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

Conceptual Understanding of the Tool. The Study

Learning Check

The Tool

Ingredients

Hypothesis from Stirling et al. (2014)

Learning Check

Interpreting the Tool

Testing the null hypothesis

Extending our null hypothesis test

Assumptions of the tool

Learning Check

Answers

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

Learning Check

Questions to Answer:

Answers

Paired Samples t Test and SPSS

Establishing your spreadsheet

Running your analyses

What am I looking at? Interpreting your SPSS output

Learning Check

Answers

Chapter Application Questions

Answers

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

Learning Check

The Tool

Ingredients

Assumptions of the tool

Hypotheses from Eskine (2012)

Learning Check

Interpreting the Tool

Testing the null hypothesis

Extending our null hypothesis test

Going beyond the F ratio: Post hoc tests

Learning Check

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

Learning Check. Problem #1

Problem #2

Questions to Answer:

Answers

Problem #3

Questions to Answer:

One-Way, Between-Subjects ANOVA and SPSS

Establishing your spreadsheet

Running your analysis

What am I looking at? Interpreting your SPSS output

Learning Check

Answers

Notes

Chapter Application Questions

Answers

Questions for Class Discussion

Questions to Answer

Answers

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

Learning Check

The Tool

Between-subjects versus repeated-measures ANOVAs

Assumptions of the tool

Hypothesis from Bernard et al. (2014)

Learning Check

Interpreting the Tool

Testing the null hypothesis

Extending our null hypothesis test

Going beyond the F ratio: Post hoc tests

Learning Check

Use this presentation to answer the following questions:

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)

Remove “participant individual differences” from within-group sums of squares

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

Learning Check

Problem #1. Use this ANOVA summary table to answer the questions that follow it:

Problem #2

Questions to Answer:

One-Way, Repeated-Measures ANOVA and SPSS

Establishing your spreadsheet

Running your analysis

What am I looking at? Interpreting your SPSS output

Learning Check

Questions:

Answers

Chapter application questions

Answers

Questions to Answer

Answers

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

Learning Check

The Tool

Factorial notation

Main effects and interactions

Hypotheses for Troisi and Gabriel (2011)

Learning Check

Interpreting the Tool

Testing the null hypothesis

Extending the null hypothesis tests

Dissecting a statistically significant interaction

Learning Check

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)

Calculate overall SSbetween-groups

Calculate SSiron

Calculate SSVitaminC

Calculate SSinteraction

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

Learning Check. Problem #1

Problem #2

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

Learning Check

Questions to Answer

Answers

Chapter application questions

Answers

Questions for Class Discussion

Chapter 12 Determining Patterns in Data Correlations

Conceptual Understanding of the Tool. The Study

Learning Check

The Tool

Types (directions) of correlations

Strength of correlations

Assumptions of the Pearson correlation

Uses for correlations

Use 1: Study naturally occurring relationships

Use 2: Basis for predictions

Use #3: Establishing measurement reliability and validity

Hypotheses from Clayton et al. (2013)

Learning Check

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

Learning Check

Using Your New Statistical Tool

Hand-Calculating the Pearson 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

Learning Check

Answer the following questions:

The Pearson Correlation (r) and SPSS

Establishing your spreadsheet

Running your analysis

What am I looking at? Interpreting your SPSS output

Learning Check

Answer the following questions:

Notes

Chapter Application Questions

Answers

Questions for Class Discussion

Addendum to Chapter 12. Obtaining a Cronbach’s Alpha Using SPSS

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

Learning Check

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

Learning Check

Notes

Chapter Application Questions

Answers

Questions for Class Discussion

Chapter 14 When We Have Exceptions to the Rules Nonparametric Tests

Chi-Square (χ2) Tests

Chi-Square (χ2) Goodness-of-Fit Test

Hand-calculating the χ2 goodness-of-fit test

Step 1: State hypotheses

Step 2: Determine degrees of freedom (dfs)

Step 3: Calculate the χ2 test statistic

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

χ2 goodness-of-fit test and SPSS

Establishing your spreadsheet

Running your analysis

What am I looking at? Interpreting your SPSS output

Learning Check

Questions to Answer:

Chi-Square (χ2) Test of Independence

Hand-calculating the χ2 test of independence

Step 1: State hypotheses

Step 2: Determine degrees of freedom (dfs)

Step 3: Calculate expected frequencies

Step 4: Calculate the χ2 test statistic

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

Step 6: Calculate an effect size

χ2 test for independence and SPSS

Establishing your spreadsheet

Running your analysis

What am I looking at? Interpreting your SPSS output

Learning Check

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 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

Learning Check

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

Learning Check

Note

Chapter Application Questions

Answer the following questions:

Answers

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

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”

Notes

Appendix A Statistical Tables

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

Appendix G

Appendix H

Glossary

References

Index

Отрывок из книги

In almost any class at my college, there is a natural gap between the teacher’s enthusiasm for the subject matter and the students’ level of enthusiasm for that same material. This makes sense. The teacher has made a career of that subject matter, whereas students are still learning to appreciate it. Perhaps in no class within psychology is this enthusiasm gap wider than it is in statistics classes. This is unfortunate, as statistics are useful not only for interpreting and conducting research but also in navigating many of life’s everyday situations. I make no qualms about my love for statistics. They can be, once understood, powerful tools not only in research but also in many life situations more generally. Most of my students come into this class with dread and apprehension about what’s to come. Most of these same students leave the class with reactions such as “It wasn’t that bad,” and some even admit “It was pretty interesting.” Indeed, I want all students to see statistics as at least “pretty interesting,” and I am hoping this book can help you not only learn statistics but also see the practical value they hold.

Teachers in the social sciences are fortunate to have inherently interesting material to discuss with students. However, the research process used to systematically investigate our subject matter is of lesser interest to many students. I can understand why. To paraphrase from a conversation with a colleague at another college, when learning about various statistics, students get lost in a myriad of symbols, numbers, and formulas, and when they finish calculating a statistic, they often have no idea what it means or how to use it. Indeed, to many students, statistics courses tend to be an evil necessity. Therefore, this book attempts to use the inherently interesting content of the discipline as the basis for teaching the statistical techniques we use to learn about the subject matter. In a sense, this book starts its discussions of statistical tools with what people often find interesting and then discusses the statistical tools needed to discern such information.

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In Chapters 12 and 13, we will learn statistical tools that quantify the strength of the relationship between two scale variables displayed in a scatterplot. For now, understand that there are three types of relationships between scale variables that a scatterplot can reveal. First, there is a linear relationship; that is, the relationship can be displayed with a straight line. The relationship between role overload and burnout in Wendt’s (2013) research is an example of a linear relationship because the general pattern of data points flows from the lower left to the upper right (what is called a “positive” linear relationship, which we touched on quickly in Chapter 1 and will discuss in detail in Chapter 12). Another example of a linear relationship would be the relationship between sleep quality and depression (Davidson, Babson, Bonn-Miller, Soutter, & Vannoy, 2013). You can see an example of this linear relationship in Figure 3.8. Here, the data points flow from the upper left corner to the lower right corner (what is called a “negative” linear relationship).

Figure 3.7 Using a Scatterplot to Display a Positive Linear Relationship Between Role Overload and Burnout in Wendt’s (2013) Research

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