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# Interpreting and Using Statistics in Psychological Research

First Edition

- Andrew N. Christopher - Albion College, USA

Additional resources:

September 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

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