Cover
Preface
1. Goals of the Text
2. Organization and Flexibility
3. Student Aids in the Text
Part 1: Introduction
1. 1 Basic Concepts in Research
  1. 1.1 The Scientific Method
  2. 1.2 The Goals of the Researcher
  3. 1.3 Types of Variables
  4. 1.4 Controlling Extraneous Variables
  5. 1.5 Validity Issues
  6. 1.6 Causality and Correlation
  7. 1.7 The Role of Statistical Analysis and the Organization of the Textbook
  8. Summary
  9. Key Terms
  10. Questions and Exercises
Part 2: Descriptive Statistics
1. 2 Scales of Measurement and Data Display
  1. 2.1 Scales of Measurement
  2. 2.2 Discrete Variables, Continuous Variables, and the Real Limits of Numbers
  3. 2.3 Using Tables to Organize Data
  4. 2.4 Using Graphs to Display Data
  5. 2.5 The Shape of Things to Come
  6. 2.6 Introduction to Microsoft Excel and SPSS
  7. Summary
  8. Key Terms
  9. Questions and Exercises
2. 3 Measures of Central Tendency
  1. 3.1 Describing a Distribution of Scores
  2. 3.2 Parameters and Statistics
  3. 3.3 The Rounding Rule
  4. 3.4 The Mean
  5. 3.5 The Median
  6. 3.6 The Mode
  7. 3.7 How the Shape of Distributions Affects Measures of Central Tendency
  8. 3.8 When to Use the Mean, Median, and Mode
  9. 3.9 Experimental Research and the Mean: A Glimpse of Things to Come
  10. Summary
  11. Using Microsoft Excel^® and SPSS^® to Find Measures of Centrality
  12. Key Terms
  13. Questions and Exercises
3. 4 Measures of Variability
  1. 4.1 The Importance of Measures of Variability
  2. 4.2 Range
  3. 4.3 Mean Deviation
  4. 4.4 The Variance
  5. 4.5 The Standard Deviation
  6. 4.6 Simple Transformations and Their Effect on the Mean and Variance
  7. 4.7 Deciding Which Measure of Variability to Use
  8. Summary
  9. Using Microsoft Excel^® and SPSS^® to Find Measures of Variability
  10. Key Terms
  11. Questions and Exercises
4. 5 The Normal Curve and Transformations
  1. 5.1 Percentile Rank
  2. 5.2 The Normal Distributions
  3. 5.3 Standard Scores (z Scores)
  4. Summary
  5. Using Microsoft Excel^® and SPSS^® to Find z Scores
  6. Key Formulas
  7. Key Terms
  8. Questions and Exercises
Part 3: Inferential Statistics: Theoretical Basis
1. 6 Basic Concepts of Probability
  1. 6.1 Theoretical Support for Inferential Statistics
  2. 6.2 The Taming of Chance
  3. 6.3 What Is Probability?
  4. 6.4 Sampling with and Without Replacement
  5. 6.5 A Priori and A Posteriori Approaches to Probability
  6. 6.6 The Addition Rule
  7. 6.7 The Multiplication Rule
  8. 6.8 Conditional Probabilities
  9. 6.9 Bayes’ Theorem
  10. Summary
  11. Key Formulas
  12. Key Terms
  13. Questions and Exercises
2. 7 Hypothesis Testing and Sampling Distributions
  1. 7.1 Inferential Statistics
  2. 7.2 Hypothesis Testing
  3. 7.3 Sampling Distributions
  4. 7.4 Estimating the Features of Sampling Distributions
  5. Summary
  6. Key Formulas
  7. Key Terms
  8. Questions and Exercises
Part 4: Inferential Statistics: z Test, t Tests, and Power Analysis
1. 8 Testing a Single Mean: The Single‐Sample z and t Tests
  1. 8.1 The Research Context
  2. 8.2 Using the Sampling Distribution of Means for the Single‐Sample z Test
  3. 8.3 Type I and Type II Errors
  4. 8.4 Is a Significant Finding “Significant?”
  5. 8.5 The Statistical Test for the Mean of a Population When σ Is Unknown: The t Distributions
  6. 8.6 Assumptions of the Single‐Sample z and t Tests
  7. 8.7 Interval Estimation of the Population Mean
  8. 8.8 How to Present Formally the Findings from a Single‐Sample t Test
  9. Summary
  10. Using Microsoft Excel^® and SPSS^® to Run Single‐Sample t Tests
  11. Key Formulas
  12. Key terms
  13. Questions and Exercises
2. 9 Testing the Difference Between Two Means: The Independent‐Samples t Test
  1. 9.1 The Research Context
  2. 9.2 The Independent‐Samples t Test
  3. 9.3 The Appropriateness of Unidirectional Tests
  4. 9.4 Assumptions of the Independent‐Samples t Test
  5. 9.5 Interval Estimation of the Population Mean Difference
  6. 9.6 How to Present Formally the Conclusions for an Independent‐Samples t Test
  7. Summary
  8. Using Microsoft Excel^® and SPSS^® to Run an Independent‐Samples t Test
  9. Key Formulas
  10. Key Terms
  11. Questions and Exercises
3. 10 Testing the Difference Between Two Means: The Dependent‐Samples t Test
  1. 10.1 The Research Context
  2. 10.2 The Sampling Distribution for the Dependent‐Samples t Test
  3. 10.3 The t Distribution for Dependent Samples
  4. 10.4 Comparing the Independent‐ and Dependent‐Samples t Tests
  5. 10.5 The One‐Tailed t Test Revisited
  6. 10.6 Assumptions of the Dependent‐Samples t Test
  7. 10.7 Interval Estimation of the Population Mean Difference
  8. 10.8 How to Present Formally the Conclusions for a Dependent‐Samples t Test
  9. Summary
  10. Using Microsoft Excel^® and SPSS^® to Run a Dependent‐Samples t Test
  11. Key Terms
  12. Questions and Exercises
4. 11 Power Analysis and Hypothesis Testing
  1. 11.1 Decision‐Making While Hypothesis Testing
  2. 11.2 Why Study Power?
  3. 11.3 The Five Factors that Influence Power
  4. 11.4 Decision Criteria that Influence Power
  5. 11.5 Using the Power Table
  6. 11.6 Determining Effect Size: The Achilles Heel of the Power Analysis
  7. 11.7 Determining Sample Size for a Single‐Sample Test
  8. 11.8 Failing to Reject the Null Hypothesis: Can a Power Analysis Help?
  9. Summary
  10. Key Formulas
  11. Key Term
  12. Questions and Exercises
Part 4: Review The z Test, t Tests, and Power Analysis
Part 5: Inferential Statistics: Analyses of Variance
1. 12 One‐Way Analysis of Variance
  1. 12.1 The Research Context
  2. 12.2 The Conceptual Basis of ANOVA: Sources of Variation
  3. 12.3 The Assumptions of the One‐Way ANOVA
  4. 12.4 Hypotheses and Error Terms for the One‐Way ANOVA
  5. 12.5 Computing the F Ratio in a One‐Way ANOVA
  6. 12.6 Testing Null Hypotheses
  7. 12.7 The One‐Way ANOVA Summary Table
  8. 12.8 An Example of an ANOVA with Unequal Numbers of Participants
  9. 12.9 Measuring Effect Size for a One‐Way ANOVA
  10. 12.10 Locating the Source(s) of Significance
  11. 12.11 How to Present Formally the Conclusions for a One‐Way ANOVA
  12. Summary
  13. Using Microsoft Excel^® and SPSS^® to Run a One‐Way ANOVA
  14. Key Formulas
  15. Key Terms
  16. Questions and Exercises
2. 13 Two‐Way Analysis of Variance
  1. 13.1 The Research Context
  2. 13.2 The Logic of the Two‐Way ANOVA
  3. 13.3 Definitional and Computational Formulas for the Two‐Way ANOVA
  4. 13.4 Using the F Ratios to Test Null Hypotheses
  5. 13.5 Assumptions of the Two‐Way ANOVA
  6. 13.6 Measuring Effect Sizes for a Two‐Way ANOVA
  7. 13.7 Multiple Comparisons
  8. 13.8 Interpreting the Factors in a Two‐Way ANOVA
  9. 13.9 How to Present Formally the Conclusions for a Two‐Way ANOVA
  10. Summary
  11. Using Microsoft Excel^® and SPSS^® to Run a Two‐Way ANOVA
  12. Key Formulas
  13. Key Terms
  14. Questions and Exercises
  15. Computer Work
3. 14 Repeated‐Measures Analysis of Variance
  1. 14.1 The Research Context
  2. 14.2 The Logic of the Repeated‐Measures ANOVA
  3. 14.3 The Formulas for the Repeated‐Measures ANOVA
  4. 14.4 Using the F Ratio to Test the Null Hypothesis
  5. 14.5 Interpreting the Findings
  6. 14.6 The ANOVA Summary Table
  7. 14.7 Assumptions of the Repeated‐Measures ANOVA
  8. 14.8 Measuring Effect Size for Repeated‐Measures ANOVA
  9. 14.9 Locating the Source(s) of Statistical Evidence
  10. 14.10 How to Present Formally the Conclusions for a Repeated‐Measures ANOVA
  11. Summary
  12. Using Microsoft Excel^® and SPSS^® to Run a Repeated‐Measures ANOVA
  13. Key Formulas
  14. Key Terms
  15. Questions and Exercises
Part 5: Review Analyses of Variance
Part 6: Inferential Statistics: Bivariate Data Analyses
1. 15 Linear Correlation
  1. 15.1 The Research Context
  2. 15.2 The Correlation Coefficient and Scatter Diagrams
  3. 15.3 The Coefficient of Determination, r
  4. 15.4 Using the Pearson r for Hypothesis Testing
  5. 15.5 Factors That Can Create Misleading Correlation Coefficients
  6. 15.6 How to Present Formally the Conclusions of a Pearson r
  7. Summary
  8. Using Microsoft Excel^® and SPSS^® to Calculate Pearson r
  9. Key Formulas
  10. Key Terms
  11. Questions and Exercises
2. 16 Linear Regression
  1. 16.1 The Research Context
  2. 16.2 Overview of Regression
  3. 16.3 Establishing the Regression Line
  4. 16.4 Putting It All Together: A Worked Problem
  5. 16.5 The Coefficient of Determination in the Context of Prediction
  6. 16.6 The Pitfalls of Linear Regression
  7. 16.7 How to Present Formally the Conclusions of a Linear Regression Analysis
  8. Summary
  9. Using Microsoft Excel^® and SPSS^® to Create a Linear Regression Line
  10. SPSS
  11. Key Formulas
  12. Addendum
  13. Key Terms
  14. Questions and Exercises
Part 6: Review Linear Correlation and Linear Regression
Part 7: Inferential Statistics: Nonparametric Tests
1. 17 The Chi‐Square Test
  1. 17.1 The Research Context
  2. 17.2 The Chi‐Square Test for One‐Way Designs: The Goodness‐of‐Fit Test
  3. 17.3 The Chi‐Square Distribution and Degrees of Freedom
  4. 17.4 Two‐Way Designs: The Chi‐Square Test for Independence
  5. 17.5 The Chi‐Square Test for a 2 × 2 Contingency Table
  6. 17.6 A Measure of Effect Size for Chi‐Square Tests
  7. 17.7 Which Cells are Major Contributors to a Significant Chi‐Square Test?
  8. 17.8 Using the Chi‐Square Test with Quantitative Variables
  9. 17.9 Assumptions of the Chi‐Square Test
  10. 17.10 How to Present Formally the Conclusions for a Chi‐Square Test
  11. Summary
  12. Using Microsoft Excel^® and SPSS^® to Calculate a Chi‐Square
  13. SPSS: Chi‐Square Goodness‐of‐fit Test
  14. SPSS: Chi‐Square Test for Independence
  15. Data Analysis
  16. Key Formulas
  17. Key Terms
  18. Questions and Exercises
2. 18 Other Nonparametric Tests
  1. 18.1 The Research Context
  2. 18.2 The Use of Ranked Data in Research
  3. 18.3 The Spearman Rank Correlation Coefficient
  4. 18.4 The Point‐Biserial Correlation Coefficient
  5. 18.5 The Mann–Whitney U Test
  6. 18.6 The Wilcoxon Signed‐Ranks Test
  7. 18.7 Using Nonparametric Tests
  8. 18.8 How to Present Formally the Conclusions for Various Nonparametric Tests
  9. Summary
  10. Using Microsoft Excel^® and SPSS^® to Calculate Various Nonparametrics
  11. Key Formulas
  12. Key Terms
  13. Questions and Exercises
Part 7: Review Nonparametric Tests
Appendix A: Statistical Tables
Appendix B: Answers to Questions and Exercises
Appendix C: Basic Data Entry for Microsoft^{^®} Excel and SPSS^{^®}
References
Glossary
List of Selected Formulas
List of Symbols
Index
End User License Agreement

List of Tables

Chapter 01
1. Table 1.1 Diagram A depicts “therapist” confounded with “treatment.” Diagram B depicts a redesign in which therapist effects are spread equally across treatment conditions. Diagram C depicts a redesign in which the therapist is held constant.
2. Table 1.2 Some common participant variables.
Chapter 02
1. Table 2.1 The midpoint, upper, and lower real limits for average temperatures and amount of rainfall for several cities in the month of March.
2. Table 2.2 Unorganized raw data.
3. Table 2.3 The simple frequency distribution constructed from the unorganized data of Table 2.2.
4. Table 2.4 A grouped frequency distribution based on the raw data from Table 2.2.
5. Table 2.5 A cumulative frequency distribution based on the grouped frequency distribution in Table 2.4.
Chapter 03
1. Table 3.1 Deviation scores always sum to zero.
2. Table 3.2 Calculating the mean from a frequency distribution.
3. Table 3.3 A distribution with two modes: 40 and 34.
Chapter 04
1. Table 4.1 Several equivalent expressions of the population and sample variances.
2. Table 4.2 Several equivalent expressions of the population and sample standard deviations.
3. Table 4.3 The effect on the mean and variance when the scores of the distribution are transformed by the four basic arithmetic operations.
Chapter 07
1. Table 7.1 Important symbols of sampling distributions and population estimates.
Chapter 08
1. Table 8.1 A comparison of the z score formula used to transform raw scores with the z statistic used to transform a sampling distribution of means.
2. Table 8.2 The decision grid depicting the four possible outcomes of hypothesis testing.
Chapter 09
1. Table 9.1 A summary comparison of the transformation formulas for a z score, z statistic, single‐sample t statistic, and independent‐samples t statistic.
2. Table 9.2 Computing t_obt for an independent‐samples t test.
Chapter 10
1. Table 10.1 A worked problem using the dependent‐samples t test.
2. Table 10.2 An independent‐samples t test on the raw data of Table 10.1.
Chapter 11
1. Table 11.1 The four outcomes when rejecting or failing to reject a true or false null hypothesis.
Chapter 12
1. Table 12.1 Between‐group variation.
2. Table 12.2 Hypothetical raw data and summary statistics for a study with three groups.
3. Table 12.3 An ANOVA summary table.
4. Table 12.4 An ANOVA with unequal numbers of participants.
5. Table 12.5 Protected t tests following a significant ANOVA.
Chapter 13
1. Table 13.1 Two separate between‐group designs, each with one independent variable.
2. Table 13.2 A 2 × 2 factorial design with a significant interaction and no significant main effects.
3. Table 13.3 A 2 × 2 factorial design with one main effect (Factor B) and no interaction.
4. Table 13.4 A 2 × 2 factorial design with one main effect (Factor A) and no interaction.
5. Table 13.5 A 2 × 2 factorial design with one main effect (Factor A) as well as an interaction.
6. Table 13.6 The degrees of freedom and their computation.
7. Table 13.7 The 2 × 2 factorial design of the worked problem, including cell notations.
8. Table 13.8 The raw data for the worked problem.
9. Table 13.9 Summary statistics for the raw data of Table 13.8.
10. Table 13.10 The ANOVA summary table based on the analysis of the data in Table 13.8.
11. Table 13.13 A 2 × 3 factorial design.
12. Table 13.14 The sample sizes, cell, and marginal means for a hypothetical therapy study.
13. Table 13.15 The ANOVA summary table based on the data in Table 13.14.
14. Table 13.11 Mean number of shocks delivered to the confederate.
15. Table 13.12 The ANOVA summary table.
Chapter 14
1. Table 14.1 A within‐participants design: 20 Participants are exposed to each treatment condition.
2. Table 14.2 The degrees of freedom for a repeated‐measures ANOVA.
3. Table 14.3 The repeated‐measures design for the hypothetical worked problem.
4. Table 14.4 Raw data for the worked problem.
5. Table 14.5 General form of the summary table for a repeated‐measures ANOVA.
6. Table 14.6 The ANOVA summary table for the hypothetical study.
Chapter 15
1. Table 15.1 Hypothetical data depicting peer ratings of aggression (X) and observed aggression (Y).
2. Table 15.2 Computing the population correlation with the z score formula.
3. Table 15.3 Some shared and unshared abilities between the “block design” and “object assembly” tasks of the WISC‐R.^a^,^b
4. Table 15.4 The relationship between r and r ².
5. Table 15.5 Correlations between political prejudice and antismoking attitudes.
Chapter 17
1. Table 17.1 A portion of the table of critical values for the chi‐square distribution.
2. Table 17.2 Observed frequencies for a worked problem.
3. Table 17.3 Observed, expected, and marginal frequencies for a worked problem.
4. Table 17.4 Computing χ².
5. Table 17.5 The standardized residuals for each category of the hypothetical study on schizophrenia and birth complications (BC).^a
6. Table 17.6 A 3 × 4 contingency table.^a
Chapter 18
1. Table 18.1 Converting continuous measures to ranks.
2. Table 18.2 Using the Spearman rank formula to compute the correlation between dominance and popularity.
3. Table 18.3 Using the Spearman rank formula to correlate rankings of two judges.
4. Table 18.4 Calculating the point‐biserial correlation coefficient between sex and fear of commitment.
Appendix A: Statistical Tables
1. Table A.1 z Table.
2. Table A.2 t Table.
3. Table A.3 Power table (finding power).
4. Table A.4 Power table (finding delta).
5. Table A.5 F table.
6. Table A.6 The critical values for studentized range statistic (q), α = .05.
7. Table A.7 Pearson r table.
8. Table A.8 Chi‐square table.
9. Table A.9 Spearman r_s table.
10. Table A.10 Mann–Whitney U table, critical values for a one‐tailed test at α = .01 (roman type) and α = .005 (boldface type) and for a two‐tailed test at α =.02 (roman type) and α = .01 (boldface type).^a
11. Table A.11 Mann–Whitney U table, critical values for a one‐tailed test at α = .05 (roman type) and α = .025 (boldface type) and for a two‐tailed test at α = .10 (roman type) and α = .05 (boldface type).
12. Table A.12 Wilcoxon signed‐ranks table.^a

List of Illustrations

Chapter 01
1. Figure 1.1 “Negative thinking” and “depression” are correlated, but which one causes the other? It is also possible that a third variable, “loss of control,” causes both “negative thinking” and “depression.”
Chapter 02
1. Figure 2.1 The upper and lower limits of a score of 13. (a) The unit of measurement is 1. The real limits are 13 + 0.5 = 13.5 and 13 − 0.5 = 12.5. (b) The unit of measurement is 0.1. The real limits are 13 + 0.05 = 13.05 and 13 − 0.05 = 12.95.
2. Figure 2.2 (a) The axes of a group without negative numbers. (b) A graph where the axes intersect at their midpoints, which allows for the inclusion of negative numbers on each axis.
3. Figure 2.3 A frequency polygon of the data in Table 2.4. Points are plotted above each interval’s midpoint.
4. Figure 2.4 The X and Y axes are broken between 0 and the lowest scores of each axis.
5. Figure 2.5 A frequency polygon superimposed onto a histogram based on the data in Table 2.4.
6. Figure 2.6 The number of undergraduates majoring in psychology (A), sociology (B), history (C), biology (D), and business (E).
7. Figure 2.7 Data from “Confidence in Institutions: Trends in Americans’ Attitudes toward Government, Media, and Business, 2016” presented in graphical form.
8. Figure 2.8 A graph that shows the relative effects of two training methods on performance. The lines on the graph indicate that there is little difference between the two methods. Note the scaling of the Y axis; it appears to start at zero.
9. Figure 2.9 The data points of Figure 2.7 are redrawn to create the impression of a vast difference between the two training methods. Altering the numbers on the Y axis, especially without signifying that it has been truncated by including a broken line, can give a misleading picture of the results of the study.
10. Figure 2.10 One type of bell‐shaped curve is the normal curve. Note that it is symmetrical and most of the scores are found in the middle of the distribution.
11. Figure 2.11 A positively skewed distribution. Here, most of the scores are found in the lower end of the distribution, and the elongated tail is pointing toward larger positive numbers.
12. Figure 2.12 A negatively skewed distribution. Here, most of the scores are found in the upper end of the distribution, and the elongated tail is pointing toward smaller or negative numbers.
13. Figure 2.13 A leptokurtic distribution. Scores are concentrated heavily around the middle of the distribution with little dispersion among the scores.
14. Figure 2.14 A platykurtic distribution. Scores are dispersed widely, and the shape of the curve is relatively broad.
15. Figure 2.15 A table and graph generated using Microsoft Excel.
16. Figure 2.16 A histogram generated using the Chart Builder function in SPSS. The data comes from Table 2.2.
Chapter 03
1. Figure 3.1 A visual representation of how to find a median when there are identical scores in the middle of the distribution.
2. Figure 3.2 Three distributions with varying degrees of kurtosis but with the same mean, median, and mode.
3. Figure 3.3 A symmetrical, bimodal distribution. The mean and median are the same.
4. Figure 3.4 (a) The mean is to the left of the median in a negatively skewed distribution. (b) The mean is to the right of the median in a positively skewed distribution.
5. Figure 3.5 Graphical presentation of the results of the Balague‐Dahlberg study on heart rate control.
Chapter 04
1. Figure 4.1 Two distributions with different variabilities yet having the same mean, median, and mode.
2. Figure 4.2 The interquartile range (IQR) spans the width of the middle 50% of the distribution.
3. Figure 4.3 The variability of a sample of scores will tend to be less than the variability of the population from which the scores are taken. So that the variance of a sample is an unbiased estimate of the population variance, a correction factor (n – 1) is used in the denominator of the formula for the variance of a sample.
4. Figure 4.4 The 68‐95‐99.7 rule describes approximate areas of a normal curve that are respectively within plus and minus one, two, and three standard deviations of the mean.
Chapter 05
1. Figure 5.1 Three normal distributions that differ in their M’s and s’s.
2. Figure 5.2 Approximately two‐thirds of the scores of a normal distribution fall between z scores of ±1.
3. Figure 5.3 The percentage of scores that lie between various points of a normal distribution. This figure represents a more precise representation of the 68‐95‐99.7 rule presented in Chapter 4.
4. Figure 5.4 The probability that a randomly selected score will fall in the shaded area is 0.1517 or 15.17%.
5. Figure 5.5 The shaded area includes 34.13% of the scores.
6. Figure 5.6 Just over 68% of scores fall within ±1 z score.
7. Figure 5.7 The shaded area contains 28.62% of the scores.
8. Figure 5.8 The shaded areas contain a total of 5% of the scores.
9. Figure 5.9 Approximately 90% of the scores fall between z scores of ±1.645.
10. Figure 5.10 What are the cutoffs that bracket the middle 60% of scores in the distribution?
11. Figure 5.11 In finding the percentile rank of 15, the shaded area is the percentage of scores that fall below a raw score of 15.
12. Figure 5.12 The shaded area defines the interquartile range.
Chapter 06
1. Figure 6.1 A probability distribution representing a single roll of a pair of six‐sided dice.
Chapter 07
1. Figure 7.1 Several sampling distributions constructed with different sample sizes. As the sample size increases, the standard error, σ_M, reflected in the width of the distribution, correspondingly decreases.
2. Figure 7.2 The sampling distribution in (a) has a smaller standard error than the sampling distribution in (b). The amount of sampling error is greater as σ_M increases.
Chapter 08
1. Figure 8.1 The sampling distribution on the left is from a population in which μ = 100. The sampling distribution on the right is from a population in which μ = 104; this represents the true state of affairs. A sample mean of 105 falls in the tail of the left distribution, but closer to the middle of the distribution on the right.
2. Figure 8.2 In this sampling distribution μ = 100 and σ_M = 1.67. A sample mean of 105 is 2.99 standard error units above the mean.
3. Figure 8.3 The acceptance and rejection regions for alpha levels of .10, .05, and .01.
4. Figure 8.4 Distributions of the t distribution as the degrees of freedom change. As the sample size decreases, the tails of the distribution elongate. Note that the critical values that define the rejection region become more extreme as the sample size decreases.
5. Figure 8.5 A worked example of using Microsoft Excel to calculate a single‐sample t test value.
6. Figure 8.6 An example of entered data for a single‐sample t test in SPSS.
7. Figure 8.7 A worked example using SPSS to calculate a single‐sample t test.
Chapter 09
1. Figure 9.1 An independent‐samples t test uses two samples. Do the samples come from the same or different populations?
2. Figure 9.2 The sampling distribution of differences has the same mean as the difference between the means of the sampling distributions of the two populations.
3. Figure 9.3 The rejection region of a t distribution for a one‐tailed and two‐tailed test, α = .05.
4. Figure 9.4 A worked example of using Microsoft Excel to calculate an independent‐samples t test value.
5. Figure 9.5 An example of entered data for an independent‐samples t test in SPSS.
6. Figure 9.6 A worked example using SPSS to calculate an independent‐samples t test.
Chapter 10
1. Figure 10.1 In (b), the mean of the sampling distribution of differences, , equals the difference between population means, μ_X − μ_Y, found in (a). In (c), the t statistic transforms the sampling distribution to a t distribution with a mean of 0.
2. Figure 10.2 A worked example of using Microsoft Excel to calculate a dependent‐samples t test value.
3. Figure 10.3 An example of entered data for a dependent‐samples t test in SPSS.
4. Figure 10.4 A worked example using SPSS to calculate a dependent‐samples t test.
Chapter 11
1. Figure 11.1 Sampling distributions of means. (a) Under H₀ : μ = 500. (b) Under H₁ : μ = 525.
Chapter 12
1. Figure 12.1 The ANOVA partitions the sources of variation in an experiment into between‐group variation and within‐group variation.
2. Figure 12.2 Sources of variance when the null hypothesis is correct and incorrect.
3. Figure 12.3 When the H₀ is true, the sample means are drawn from identical populations, which, in effect, is the same as saying “drawn from one population.” Here we would expect the sample means to show little variation.
4. Figure 12.4 When the H₀ is false, at least one sample is drawn from a population that is different from the rest.
5. Figure 12.5 Two F distribution for df_BG = 3 and df_W = 20, and df_BG = 7 and df_W = 7.
6. Figure 12.6 A worked example using Microsoft Excel to calculate a one‐way ANOVA.
7. Figure 12.7 An example of entered data for a one‐way ANOVA in SPSS.
8. Figure 12.8 An output table from worked example using SPSS to calculate a one‐way ANOVA.
Chapter 13
1. Figure 13.1 A graph of the group means in Table 13.2. There is an interaction but no main effects.
2. Figure 13.2 A graph of the means in Table 13.3. There is one main effect but no interaction.
3. Figure 13.3 Group means from Table 13.3 are graphed. There is a main effect for Mood During Recall. However, by placing Mood During Recall on the X axis, the main effect is more difficult to identify. Figure 13.2 is a more useful display of the main effect presented in Table 13.3.
4. Figure 13.4 The graph of the means in Table 13.4. There is a main effect for Factor A but no interaction.
5. Figure 13.5 The graph of the means from Table 13.5. There is a main effect for Factor A and an interaction.
6. Figure 13.6 Partitioning the total variation in the two‐way ANOVA.
7. Figure 13.7 Partitioning the degrees of freedom in the two‐way ANOVA.
8. Figure 13.8 A graph of the cell means from Table 13.9.
9. Figure 13.9 A worked example using Microsoft Excel to calculate a two‐way ANOVA.
10. Figure 13.10 An example of entered data for a two‐way ANOVA in SPSS.
11. Figure 13.11 An output table from a worked example using SPSS to calculate a two‐way ANOVA.
Chapter 14
1. Figure 14.1 Partitioning the total variation in the repeated‐measures ANOVA.
2. Figure 14.2 Partitioning the degrees of freedom in the repeated‐measures ANOVA.
3. Figure 14.3 An example of an encoded data set in preparation for running a repeated‐measures ANOVA in Excel.
4. Figure 14.4 A worked example using Microsoft Excel to calculate a repeated‐measures ANOVA.
5. Figure 14.5 An example of entered data for a repeated‐measures ANOVA in SPSS.
6. Figure 14.6 An output table from a worked example using SPSS to calculate a repeated‐measures ANOVA.
Chapter 15
1. Figure 15.1 The scatter plot of the data from Table 15.1.
2. Figure 15.2 Several scatter diagrams that depict the magnitude and direction of the correlation. (a) is a strong positive correlation; (b) is a strong negative correlation; (c) is a weak positive correlation; and (d) reflects no correlation.
3. Figure 15.3 A plot of a curvilinear relationship between X and Y. As arousal increases, performance improves until arousal becomes too high, and then performance declines.
4. Figure 15.4 The shaded overlapping areas depict shared variance. As r increases so does r².
5. Figure 15.5 The true strength of association between X and Y is underestimated when the range of scores is restricted.
6. Figure 15.6 Some nonlinear relations between X and Y.
7. Figure 15.7 Using extreme groups increases the magnitude of the correlation between X and Y. The oval surrounding scatter plot (a) is narrower than the one surrounding scatterplot (b).
8. Figure 15.8 A worked example using Microsoft Excel to calculate a Pearson r.
9. Figure 15.9 An example of entered data for a Pearson r calculation in SPSS.
10. Figure 15.10 An output table from a worked example using SPSS to calculate a Pearson r.
Chapter 16
1. Figure 16.1 Several straight lines drawn through a scatter plot. The regression equation establishes which line, of a potentially infinite number of lines, is the best one to predict a Y score given an X score.
2. Figure 16.2 Using the regression line to predict Y given X = 4.
3. Figure 16.3 The straight lines with different slopes. (a) Slope of 0.5; (b) slope of 0; (c) slope of –1.
4. Figure 16.4 An error is the deviation of an actual Y from the predicted Y (Y_p).
5. Figure 16.5 (a) The scatter plot has been fitted with a regression line in (b). The line is drawn so that Σe² is minimized.
6. Figure 16.6 Drawing the regression line using two points: (4, 6.15) and (8, 9.87).
7. Figure 16.7 When r = 0, the slope of the regression line is zero (b = 0). The regression line will intersect the Y axis at M_Y.
8. Figure 16.8 Normally distributed conditional distributions of four values of X.
9. Figure 16.9 Ninety‐five percent of the actual Y scores fall between Y_p ± 1.96 s_e.
10. Figure 16.10 The scatter plot and regression line for the data on marital satisfaction.
11. Figure 16.11 A linear relationship may be impossible to detect if either X or Y has a restricted range of scores.
12. Figure 16.12 Even though the majority of scores suggest no relationship exists between X and Y, the extreme score in the upper right can create the impression of a linear relationship between X and Y.
13. Figure 16.13 Conditional distributions with progressively larger standard deviations as the value of X increases. This is a violation of homoscedasticity.
14. Figure 16.14 A worked example of a regression analysis using Microsoft Excel.
15. Figure 16.15 An example of entered data for a regression analysis in SPSS.
16. Figure 16.16 Output tables from a worked example using SPSS to run a regression analysis.
Chapter 17
1. Figure 17.1 Chi‐square distributions for degrees of freedom of 1, 5, and 8.
2. Figure 17.2 Each bar reflects the number of people given one of the three diagnoses. The pattern of bars in (a) is different from the pattern of bars in (b). This indicates that the distribution of various diagnoses depends on the presence or absence of a history of birth complications. Viewed together, these graphs reflect a relationship between diagnostic category and birth complications, with schizophrenics showing a greater frequency of birth complications.
3. Figure 17.3 Unlike Figure 17.2, the relative occurrence of different diagnoses is similar in (a) and (b). This reflects the fact that birth complications and diagnostic category are independent, that is, unrelated.
4. Figure 17.4 A worked example of a chi‐square test for independence analysis using Microsoft Excel.
5. Figure 17.5 An example of entered data for a chi‐square goodness‐of‐fit test is SPSS.
6. Figure 17.6 Output tables from a worked example using SPSS to run a chi‐square goodness‐of‐fit test.
7. Figure 17.7 An example of entered data for a chi‐square test for independence is SPSS.
8. Figure 17.8 Output tables from a worked example using SPSS to run a chi‐square test for independence.
Chapter 18
1. Figure 18.1 Observe how the nonlinear scatter plot in (a) becomes linear when the continuous measures have been changed to ranks in (b).
2. Figure 18.2 (a) More ranks of Condition A are shown at the lower end of the scale, and more ranks from Condition B are at the higher end of the scale. This indicates the presence of a treatment effect. (b) The ranks of Conditions A and B fail to show a systematic grouping in either end of the scale. When there is no treatment effect, the ranks of Conditions A and B are intermixed and evenly dispersed across the span of the ranks.
3. Figure 18.3 An example of entered data for a Spearman and point‐biserial correlation using SPSS.
4. Figure 18.4 Output tables from worked examples using SPSS to run a Spearman and point‐biserial correlation.
5. Figure 18.5 An example of entered data for a Mann–Whitney U test using SPSS.
6. Figure 18.6 Output tables from a worked example using SPSS to run a Mann–Whitney U test.
7. Figure 18.7 An example of entered data for a Wilcoxon signed‐ranks test using SPSS.
8. Figure 18.8 Output tables from a worked example using SPSS to run a Wilcoxon signed‐ranks test.

Preface

This textbook is an outgrowth of our combined 40+ years worth of experience teaching undergraduate statistics for social and behavioral science students, an experience that has impressed us with the dread students face when entering the course and the frustration they voice in trying to understand statistics. The dread is most likely a result of the unimaginative manner in which mathematics is taught in the American grade school system. Unfortunately, there is nothing a statistics instructor can do about that. However, there is something the instructor of an undergraduate statistics course can (and must) do to combat this frustration. To be sure, most students may not find a statistics course as engaging as a course in social psychology or child development, but it need not rival the forced reading of the unending pages of terms and conditions associated with approving a new software program!

This book has been written with the typical student in mind – one who not only dislikes math but also has no confidence in their ability to “deal with numbers.” Consequently, even the student with only a little background in algebra will be able to understand the computational flow of the formulas. A knowledge of algebraic derivations and proofs is unnecessary for mastering the material in this text.

Goals of the Text

The primary goal of this book is to teach students the conceptual foundations of statistical analyses, particularly inferential statistics. Where applicable, the conceptual foundation of statistical tests is explained in the context of standardized scores. Throughout the chapters on hypothesis testing, the surface mechanics of computing a test statistic are always related to the underlying sampling distribution of relevance. In this way, students learn why the formula for a test statistic looks as it does, and they gain an appreciation of the statistical meaning of each analysis.

Emphasis on the conceptual underpinnings of hypothesis testing distinguishes this textbook from those that offer a “cookbook” approach. In addition, this text places heavy emphasis on the research context of the statistical analysis under discussion. As a result, students will feel “connected” to the research activities of social and behavioral scientists and come to view formulas as tools to answer questions about human behavior.

Nonetheless, the arithmetic operations involved in arriving at problem solutions are not sacrificed. Indeed, another goal of this book is to teach students how to “work the formulas.” Learning to “crunch the numbers” is accomplished by presenting definable, clearly specified steps in working through statistical problems. Despite the existence of numerous statistical software packages that can quickly and accurately arrive at the solution to problems, we believe that the initial introduction to a statistical tool should utilize a hand calculation. This number‐crunching process provides the student with a deeper understanding of the inner workings of statistical formulas. Once familiarity is achieved by crunching through small sample versions of the mathematics of statistical tools, then the introduction of a computer software program becomes a welcome timesaving aid, and not a method of obscuring what is going on. For this reason, at the end of most chapters, brief tutorials are presented, showing the user how to use Microsoft^® Excel and SPSS^® to compute various descriptive and inferential statistical values.

Organization and Flexibility

The text has 18 chapters organized into seven parts: (1) “Introduction,” (2) “Descriptive Statistics,” (3) “Inferential Statistics: Theoretical Basis,” (4) “Inferential Statistics: z Test, t Tests, and Power Analysis,” (5) “Inferential Statistics: Analysis of Variance,” (6) “Inferential Statistics: Bivariate Data Analysis,” and (7) “Inferential Statistics: Nonparametric Tests.” The breadth of coverage of topic areas makes this book suitable for a semester course, a two‐quarter course, or a one‐quarter course. If students have had exposure to research design, Chapter 1 may be skipped or used as a brief summary of research concepts.

Because earlier chapters build the conceptual foundation for later chapters, there is only a modest amount of leeway in assigning chapters out of sequence. Nonetheless, the chapters covering chi‐square and other nonparametric tests may be assigned before the chapter on one‐way ANOVA. The chapters covering two‐way and repeated‐measures ANOVA can be omitted without hampering the students’ understanding of subsequent chapters. The chapters covering linear correlation and regression treat these data analytic procedures in the context of inferential statistics. Consequently, it is not recommended that they be presented immediately after the section on descriptive statistics. The chapter on probability can be left out if there is limited time or a desired lack of emphasis on the theoretical underpinnings of inferential statistical tests. Finally, the chapter on power may be omitted without sacrificing the students’ understanding of hypothesis testing. The concept of power is defined simply whenever it is mentioned in chapters covering hypothesis testing.

Student Aids in the Text

Because most students approach statistics with considerable foreboding, we have included several pedagogical features in the text to enhance learning and maintain motivation:

The application of formulas is illustrated in step‐by‐step computational procedures so that students can master the sequential process of arriving at the correct answer to sample problems.
Boxes that highlight the topic under discussion using published and unpublished research are presented in each chapter. The material is selected for its interest value to students.
One series of boxes addresses, head‐on, a major issue in the social and behavioral sciences, the so‐called replication crisis. These boxes bring students into this larger discussion, help them understand the underlying issues, and empower them to think critically about their own and others’ research.
Spotlights present biographical sketches of some of the luminaries in the field of statistics. Interesting aspects of the person and their times are provided to bring the material to life.
A list of selected formulas can be found in the back of the text for easy reference.
Recognizing that many instructors want their students to be able to communicate the outcomes of statistical analyses in written form, most chapters contain a section informing the students how to present statistical findings in sentence form.
Each chapter ends with an extended summary of the chapter (where applicable), brief tutorials for how to use Microsoft^® Excel and SPSS^® to generate statistical values associated with that chapter, a presentation of the key formulas, and numerous questions and exercises for concept checks and practice. Many of the questions and exercises are based on published research findings of high interest to students, so that students not only receive practice in data analyses but also increase their knowledge of the content of psychology.
A glossary of terms is provided at the end of the text.
A list of symbols is provided in the back matter.

Appendix A contains helpful tables for determining various critical values needed for determining probability and testing null hypotheses. (Although the tables are incomplete, they will provide the appropriate values for almost all of the exercises. However, students may need to reference tables online to find the critical values needed to answer a few questions.)

It is our experience that students overwhelmingly prefer that all the answers to work problems be provided, and so they are, in Appendix B. In addition, for computation problems, the answers are provided along with the interim steps, thereby allowing students to locate the source of potential errors in the use of formulas. Most of the chapters also include short data sets that can be used with any statistical software program. The answers to these problems are also provided in Appendix B.

Appendix C presents brief instructions for basic data entry procedures for Microsoft^® Excel and SPSS^®. This resource further supports student’s ability to use these software products for statistical calculation purposes.

Statistical Applications for the Behavioral and Social Sciences

Preface

Goals of the Text

Organization and Flexibility

Student Aids in the Text

Acknowledgments

About the Companion Website

Part 1