Elementary Statistics in Social Research

Cover
Title Page
Copyright Page
Brief Contents
Contents
Preface
Acknowledgments
1 Why the Social Researcher Uses Statistics
	1.1 The Nature of Social Research
		1.1.1 The Experiment
		1.1.2 The Survey
		1.1.3 Content Analysis
		1.1.4 Participant Observation
		1.1.5 Secondary Analysis
		1.1.6 Meta-Analysis
	1.2 Why Test Hypotheses?
		1.2.1 Contrary to Popular Belief
	1.3 The Stages of Social Research
	1.4 Using Series of Numbers to Do Social Research
		1.4.1 The Nominal Level
		1.4.2 The Ordinal Level
		1.4.3 The Interval/Ratio Level
			The Difference Between Ratio and Interval Level
		1.4.4 Different Ways to Measure the Same Variable
		1.4.5 Treating Some Ordinal Variables as Interval
		1.4.6 Further Measurement Issues
	1.5 The Functions of Statistics
		1.5.1 Description
			Graphs and the Arithmetic Averages
		1.5.2 Decision Making
			Generalizing from Samples to Populations
			Generalizing from Samples to Larger Populations
		1.5.3 An Important Note about Rounding
		Summary: Why the Social Researcher Uses Statistics
		Homework 1.1: Practice Why the Social Researcher Uses Statistics
		Homework 1.2: General Social Survey Practice
2 Organizing the Data
	2.1 Frequency Distributions of Nominal Data
	2.2 Comparing Distributions
	2.3 Proportions and Percentages
	2.4 Ratios and Rates
		2.4.1 Rates
			Rate of change
	2.5 Simple Frequency Distributions of Ordinal and Interval Data
	2.6 Grouped Frequency Distributions of Interval Data
		2.6.1 Class Limits
		2.6.2 The Midpoint
		2.6.3 Guidelines for Constructing Class Intervals
	2.7 Cumulative Distributions
		2.7.1 Cumulative Percentage
	2.8 Percentiles
	2.9 Dealing with Decimal Data
	2.10 More on Class Limits
		2.10.1 Two Approaches for Setting Class Limits
	2.11 Flexible Class Intervals
	2.12 Cross-Tabulations
		2.12.1 A Frequency Distribution of Two Variables Taken Simultaneously
		2.12.2 Percentages
			Row Percents
			Column Percents
		2.12.3 Choosing among Total, Row, and Column Percent
	2.13 Graphic Presentations
		2.13.1 Pie Charts
		2.13.2 Bar Graphs and Histograms
			The Difference Between Bar Graphs and Histograms
			Graphing Volumes and Rates
		2.13.3 Frequency Polygons
		2.13.4 The Shape of a Frequency Distribution
		2.13.5 Line Charts
		2.13.6 Maps
		Summary: Organizing the Data
		Homework 2.1: Practice Organizing the Data
		Homework 2.2: General Social Survey Practice
3 Measures of Central Tendency
	3.1 The Mode
	3.2 The Median
	3.3 The Mean
	3.4 Deviation from the Mean
	3.5 The Weighted Mean
	3.6 Taking One Step at a Time
		Step-by-Step Illustration: Mode, Median, and Mean
	3.7 Obtaining the Mode, Median, and Mean from a Simple Frequency Distribution
	3.8 Comparing the Mode, Median, and Mean
		3.8.1 Level of Measurement
		3.8.2 Shape of the Distribution
			Skewed Distributions
			Bimodal Distributions
		3.8.3 Research Objective
		Summary: Measures of Central Tendency
		Homework 3.1: Practice Measures of Central Tendency
		Homework 3.2: General Social Survey
4 Measures of Variability
	4.1 The Range
	4.2 The Inter-Quartile Range
		4.2.1 Using Formulas to Calculate the IQR
	4.3 The Variance and the Standard Deviation
		Step-by-Step Illustration: Standard Deviation
	4.4 The Raw-Score Formula for Variance and Standard Deviation
		Step-by-Step Illustration: Variance and Standard Deviation Using Raw Scores
	4.5 Obtaining the Variance and Standard Deviation from a Simple Frequency Distribution
		Step-by-Step Illustration: Variance and Standard Deviation of a Simple Frequency Distribution
	4.6 The Meaning of the Standard Deviation
		4.6.1 Measuring the Base Line in Units of Standard Deviation
		4.6.2 Standard Deviation and the Normal Distribution
	4.7 Coefficient of Variation
	4.8 Comparing Measures of Variability
	4.9 Visualizing Distributions
	4.10 Obtaining the Mean and Standard Deviation from a Grouped Frequency Distribution
		Summary: Measures of Variability
		Homework 4.1: Practice Measures of Variability
		Homework 4.2: General Social Survey Practice
5 Probability and the Normal Curve
	Theoretical Probability
	Empirical Probability
	5.1 Rules of Probability
		5.1.1 The Converse Rule of Probability
		5.1.2 The Addition Rule
		5.1.3 The Multiplication Rule
	5.2 Probability Distributions
		5.2.1 Constructing a Probability Distribution for Equally Likely Events
		5.2.2 Constructing a Probability Distribution for Not Equally Likely Events
		5.2.3 The Difference between Probability Distributions and Frequency Distributions
		5.2.4 Mean and Standard Deviation of a Probability Distribution
	5.3 The Normal Curve as a Probability Distribution
		5.3.1 Characteristics of the Normal Curve
		5.3.2 The Model and the Reality of the Normal Curve
			Departures from Normality
	5.4 The Area under the Normal Curve
		5.4.1 Clarifying the Standard Deviation
		5.4.2 Using Table A
	5.5 Standard Scores and the Normal Curve
		5.5.1 Obtaining a z-Score
	5.6 Finding Probability under the Normal Curve
		Step-by-Step Illustration: Finding the Probability under the Normal Curve
		5.6.1 The Percent Area at or Beyond a Particular Raw Score
		5.6.2 Finding Scores from Probability Based on the Normal Curve
		Step-by-Step Illustration: Finding Scores from Probability Based on the Normal Curve
		Summary: Probability and the Normal Curve
		Homework 5.1: Practice Probability and the Normal Curve
		Homework 5.2: General Social Survey Practice
6 Samples and Populations
	6.1 Errors in the Conduct of Research
	6.2 Sampling Methods
		6.2.1 Types of Nonrandom Samples
		6.2.2 Random Samples
		6.2.3 Systematic Sampling
		6.2.4 Stratified Random Sampling
		6.2.5 Cluster Sampling
	6.3 Sampling Error
	6.4 Sampling Distribution of Means
		6.4.1 Characteristics of a Sampling Distribution of Means
			The Diminishing Variability of a S ampling Distribution
		6.4.2 The Sampling Distribution of Means as a Normal Curve
			Moving from Raw Scores to Sample Means
			Finding the Probability of Obtaining Any Sample Mean
	6.5 Standard Error of the Mean
		6.5.1 The Distinction Between Standard Deviation and Standard Error
	6.6 Confidence Intervals
		6.6.1 The 95% Confidence Interval
		Step-by-Step Illustration: Finding a 95% Confidence Interval Using z
		6.6.2 The 99% Confidence Interval
		Step-by-Step Illustration: Finding a 99% Confidence Interval Using z
	6.7 The t Distribution
		6.7.1 Choosing the Appropriate Denominator
			The Unbiased Estimate of the Standard Error of the Mean
		6.7.2 Finding the t Value
		Step-by-Step Illustration: Constructing a Confidence Interval Using t (small sample case)
		Step-by-Step Illustration: Constructing a Confidence Interval Using t (large sample case)
	6.8 Estimating Proportions
		Step-by-Step Illustration: Confidence Interval for Proportions
		Summary: Samples and Populations
		Homework 6.1: Practice Samples and Populations
		Homework 6.2: General Social Survey Practice
7 Testing Differences between Means
	7.1 Testing the Difference between Sample and Population Means
	7.2 Testing the Difference between Two Sample Means
	7.3 The Null Hypothesis: No Difference between Means
	7.4 The Research Hypothesis: A Difference between Means
	7.5 Sampling Distribution of Differences between Means
		7.5.1 The Frequency Distribution of a Large Number of Differences between Means
			Key Properties of a Sampling Distribution of Differences between Means
	7.6 Testing Hypotheses with the Distribution of Differences between Means
		7.6.1 Using One Pair of Samples to Draw Inferences
	7.7 Levels of Significance
		7.7.1 Type I and Type II Errors
		7.7.2 Choosing a Level of Significance
		7.7.3 What Is the Difference between P and  z?
	7.8 Standard Error of the Difference between Means
	7.9 Testing the Difference between Means
		7.9.1 Testing the Null Hypothesis
		Step-by-Step Illustration: Test of Difference between Means
		7.9.2 Adjustment for Unequal Variances
	7.10 Comparing Dependent Samples
		7.10.1 A Before-After Comparison
		Step-by-Step Illustration: Test of Difference between Means for Same Sample Measured Twice
		7.10.2 Matched Pairs
		Step-by-Step Illustration: Test of Difference between Means for Matched Samples
	7.11 Two-Sample Test of Proportions
		Step-by-Step Illustration: Test of Difference between Proportions
	7.12 One-Tailed Tests
		7.12.1 The Differences between One- and Two-Tailed Tests
		Step-by-Step Illustration: One-Tailed Test of Means for Same Sample Measured Twice
		7.12.2 Modifying Any Test to a Two-Tailed Test
		Step-by-Step Illustration: Applying One-Tailed Test to Independent Groups
	7.13 Effect Size
		Step-by-Step Illustration: Calculating Cohen's d
	7.14 Requirements for Testing the Difference between Means
		Summary: Testing Differences between Means
		Homework 7.1: Practice Testing Differences between Means
		Homework 7.2: General Social Survey Practice
8 Analysis of Variance
	8.1 The Logic of Analysis of Variance
	8.2 The Sum of Squares
		8.2.1 A Research Illustration
			Calculating the Total Sum of Squares
			Calculating the Within-Groups Sum of Squares
			Calculating the Between-Groups Sum of Squares
		8.2.2 Computing Sums of Squares
	8.3 Mean Square
	8.4 The F Ratio
		8.4.1 Two Contrasting Examples of ANOVA
			Sums of Squares, Mean Squares, and the F Ratio
		Step-by-Step Illustration: Analysis of Variance
	8.5 A Multiple Comparison of Means
		8.5.1 Using Tukey's HSD
		Step-by-Step Illustration: HSD for Analysis of Variance
	8.6 Two-Way Analysis of Variance
		8.6.1 The Influence of Two Factors in the Same Experiment
		8.6.2 Dividing the Total Sum of Squares
			An Illustration of Two-Way ANOVA
			Calculating the Sums of Squares
		Step-by-Step Illustration: Two-Way Analysis of Variance
	8.7 Requirements for Using the F Ratio
		Summary: Analysis of Variance
		Homework 8.1: Practice Analysis of Variance
		Homework 8.2: General Social Survey Practice
9 Nonparametric Tests of Significance
	9.1 One-Way Chi-Square Test
		9.1.1 The Chi-Square Statistic
			Finding the Chi-Square Value
		Step-by-Step Illustration: One-Way Chi-Square
	9.2 Two-Way Chi-Square Test
		9.2.1 Computing the Two-Way Chi-Square
			Setting Up Cross -Tabulations
			Applying the Chi-Square Formula
		9.2.2 Finding the Expected Frequencies
			Obtaining Chi-Square for a Cross-Tabulation
		Step-by-Step Illustration: Two-Way Chi-Square Test of Significance
		9.2.3 Comparing Several Groups
		Step-by-Step Illustration: Comparing Several Groups
		9.2.4 Correcting for Small Expected Frequencies
			Yates’s Correction
		9.2.5 Requirements for the Use of Two-Way Chi-Square
	9.3 The Median Test
		Step-by-Step Illustration: Median Test
		9.3.1 Requirements for the Use of the Median Test
	9.4 Mann-Whitney U Test
		Calculations for the Mann-Whitney U Test
		Step-by-Step Illustration: Mann-Whitney U Test
	9.5 Kruskal-Wallis Test
		Step-by-Step: Kruskal-Wallis Test
		Summary: Nonparametric Tests of Significance
		Homework 9.1: Practice Nonparametric Tests of Significance
		Homework 9.2: General Social Survey Practice
10 Correlation
	10.1 Strength of Correlation
	10.2 Direction of Correlation
	10.3 Curvilinear Correlation
	10.4 The Correlation Coefficient
	10.5 Pearson’s Correlation Coefficient
		10.5.1 A Computational Formula for Pearson’s r
		10.5.2 Testing the Significance of Pearson’s r
		10.5.3 A Simplified Method for Testing the Significance of r
		Step-by-Step Illustration: Obtaining Pearson’s Correlation Coefficient
		10.5.4 Requirements for the Use of Pearson’s r Correlation Coefficient
	10.6 The Importance of Scatter Plots
		Inspecting Scatter Plots for Outliers
	10.7 Partial Correlation
		10.7.1 Control Variables with Three or More Categories
			Simple Versus Partial Correlation
			The Partial Correlation Coefficient and Spurious Relationships
		10.7.2 Testing the Significance of a Partial Correlation
		Summary: Correlation
		Homework 10.1: Practice Correlation
		Homework 10.2: General Social Survey Practice
11 Regression Analysis
	11.1 The Regression Model
		11.1.1 A Graphical Representation of the Data
		11.1.2 Determining the Equation of the Regression Line
		11.1.3 Plotting the Regression Line
		11.1.4 Requirements for Regression
	11.2 Interpreting the Regression Line
		Projecting the Impact of the Independent Variable
	11.3 Prediction Errors
		11.3.1 The Regression Sum of Squares
		11.3.2 Calculating the Sums of Squares
		11.3.3 The Least Squares Criterion
	11.4 Regression and Pearson's Correlation
	11.5 Regression and Analysis of Variance
		11.5.1 An Analysis of Variance Summary Table
		Step-by-Step Illustration: Regression Analysis
	11.6 Multiple Regression
		11.6.1 The Multiple Linear Regression Model
		11.6.2 The Multiple Coefficient of Determination
		11.6.3 Dummy Variables
		11.6.4 Interpreting SPSS Output
			Finding the F Ratio
		11.6.5 Interaction Terms
		11.6.6 Multicollinearity
	11.7 Logistic Regression
		11.7.1 Using Odds to Interpret Logistic Regression Results
		11.7.2 The Logistic Regression Model
		11.7.3 Determining Statistical Significance
		Summary: Regression Analysis
		Homework 11.1: Practice Regression Analysis
		Homework 11.2: General Social Survey Practice
12 Nonparametric Measures of Correlation
	12.1 Spearman's Rank-Order Correlation Coefficient
		12.1.1 Dealing with Tied Ranks
		12.1.2 Testing the Significance of the Rank-Order Correlation Coefficient
			Testing Significance for Sample Sizes Greater than 30
		Step-by-Step Illustration: Spearman's Rank-Order Correlation Coefficient
		12.1.3 Requirements for Using the Rank-Order Correlation Coefficient
	12.2 Goodman's and Kruskal's Gamma
		Step-by-Step Illustration: Goodman's and Kruskal's Gamma
		12.2.1 Testing the Significance of Gamma
		12.2.2 Requirements for Using Gamma
	12.3 Correlation Coefficient for Nominal Data Arranged in a 2 x 2 Table
		12.3.1 Testing the Significance of Phi
		12.3.2 Requirements for Using the Phi Coefficient
	12.4 Correlation Coefficients for Nominal Data in Larger than 2 X 2 Tables
		12.4.1 Testing the Significance of the Contingency Coefficient
		12.4.2 An Alternative to the Contingency Coefficient
		12.4.3 Requirements for Using the Contingency Coefficient or Cramér's V
	12.5 Elaboration
		12.5.1 Spurious Relationships
		Summary: Nonparametric Measures of Correlation
		Homework 12.1: Practice Nonparametric Measures of Correlation
		Homework 12.2: General Social Survey Practice
13 Choosing Statistical Procedures for Research Problems
	13.1 Research Situations
	13.2 Student Behavior
		13.2.1 Situation 1
			Solution: Student Behavior Situation 1
		13.2.2 Situation 2
			Solution: Student Behavior Situation 2
		13.2.3 Situation 3
			Solution: Student Behavior Situation 3
	13.3 Social Behaviour
		13.3.1 Research Situation 1
			Solution: Social Behavior Situation 1
		13.3.2 Situation 2
			Solution: Social Behavior Situation 2
		13.3.3 Situation 3
			Solution: Social Behavior Situation 3
		13.3.4 Situation 4
			Solution: Social Behavior Situation 4
	13.4 Educational Evaluation
		13.4.1 Situation 1
			Solution: Educational Evaluation Situation 1
		13.4.2 Situation 2
			Solution: Educational Evaluation Situation 2
		13.4.3 Situation 3
			Solution: Educational Evaluation Situation 3
			13.4.4: Situation 4
			Solution: Educational Evaluation Situation 4
	13.5 Physical and Mental Health
		13.5.1 Situation 1
			Solution: Physical and Mental Health Situation 1
		13.5.2 Situation 2
			Solution: Physical and Mental Health Situation 2
		13.5.3 Situation 3
			Solution: Physical and Mental Health Situation 3
		13.5.4 Situation 4
			Solution: Physical and Mental Health Situation 4
	13.6 Financial Status
		13.6.1 Situation 1
			Solution: Financial Status Situation 1
		13.6.2 Situation 2
			Solution: Financial Status Situation 2
		13.6.3 Situation 3
			Solution: Financial Status Situation 3
	13.7 Audience Preferences
		13.7.1 Situation 1
			Solution: Audience Preferences Situation 1
		13.7.2 Situation 2
			Solution: Audience Preferences Situation 2
		13.7.3 Situation 3
			Solution: Audience Preferences Situation 3
	13.8 Additional Questions
		13.8.1 Practice Set 1
			Situation 1
			Situation 2
		13.8.2 Practice Set 2
			Situation 3
			Situation 4
		13.8.3 Practice Set 3
			Situation 5
			Situation 6
		13.8.4 Practice Set 4
			Situation 7
			Situation 8
		13.8.5 Practice Set 5
			Situation 9
			Situation 10
		13.8.6 Practice Set 6
			Situation 11
			Situation 12
		13.8.7 Practice Set 7
			Situation 13
			Situation 14
Appendix A The Social Research Process In Practice
Appendix B Using SPSS and the General Social Survey
Appendix C Tables
Appendix D List of Formulas
Appendix E A Review of Some Fundamentals of Mathematics
Glossary
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Answers to Homework Problems
Credits
Index
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