Elementary Statistics in Social Research: The Essentials Book

	Preface	xi
1	Why the Social Researcher Uses Statistics	1
	The Nature of Social Research	1
	Why Test Hypotheses?	2
	The Stages of Social Research	4
	Using Series of Numbers To Do Social Research	4
	The Functions of Statistics	9
	Summary	13
	Questions and Problems	14
	Looking at the Larger Picture: A Student Survey	16
Part 1	Description	19
2	Organizing the Data	21
	Frequency Distributions of Nominal Data	21
	Comparing Distributions	22
	Proportions and Percentages	23
	Simple Frequency Distributions of Ordinal and Interval Data	24
	Grouped Frequency Distributions of Interval Data	25
	Cumulative Distributions	27
	Dealing with Decimal Data	29
	Flexible Class Intervals	31
	Cross-Tabulations	33
	Graphic Presentations	39
	Summary	45
	Questions and Problems	45
3	Measures of Central Tendency	53
	The Mode	53
	The Median	54
	The Mean	55
	Taking One Step at a Time	57
	Step-By-Step Illustration: Mode, Median, and Mean	57
	Comparing the Mode, Median, and Mean	58
	Summary	62
	Questions and Problems	63
4	Measures of Variability	67
	The Range	68
	The Variance and the Standard Deviation	69
	Step-By-Step Illustration: Standard Deviation	70
	The Raw-Score Formula for Variance and Standard Deviation	71
	Step-By-Step Illustration: Variance and Standard Deviation Using Raw Scores	72
	The Meaning of the Standard Deviation	73
	Comparing Measures of Variability	76
	Summary	77
	Questions and Problems	77
	Looking at the Larger Picture: Describing Data	80
Part 2	From Description to Decision Making	85
5	Probability and the Normal Curve	87
	Probability	88
	Probability Distributions	88
	The Normal Curve as a Probability Distribution	92
	Characteristics of the Normal Curve	92
	The Model and the Reality of the Normal Curve	93
	The Area under the Normal Curve	94
	Standard Scores and the Normal Curve	100
	Finding Probability under the Normal Curve	104
	Step-By-Step Illustration: Probability under the Normal Curve	104
	Summary	108
	Questions and Problems	109
6	Samples and Populations	112
	Random Sampling	113
	Sampling Error	114
	Sampling Distribution of Means	115
	Standard Error of the Mean	122
	Confidence Intervals	123
	The t Distribution	126
	Step-By-Step Illustration: Confidence Interval Using t	131
	Estimating Proportions	134
	Step-By-Step Illustration: Confidence Interval for Proportions	135
	Summary	136
	Questions and Problems	136
	Looking at the Larger Picture: Generalizing from Samples to Populations	140
Part 3	Decision Making	143
7	Testing Differences between Means	145
	The Null Hypothesis: No Difference between Means	147
	The Research Hypothesis: A Difference between Means	148
	Sampling Distribution of Differences between Means	148
	Testing Hypotheses with the Distribution of Differences between Means	152
	Levels of Significance	155
	Standard Error of the Difference between Means	160
	Testing the Difference between Means	161
	Step-by-Step Illustration: Test of Difference between Means	162
	Comparing the Same Sample Measured Twice	165
	Step-by-Step Illustration: Test of Difference between Means for Same Sample Measured Twice	166
	Two-Sample Test of Proportions	168
	Step-by-Step Illustration: Test of Difference between Proportions	169
	Requirements for Testing the Difference between Means	171
	Summary	172
	Questions and Problems	172
8	Analysis of Variance	183
	The Logic of Analysis of Variance	184
	The Sum of Squares	186
	Mean Square	192
	The F Ratio	193
	Step-by-Step Illustration: Analysis of Variance	196
	Requirements for Using the F Ratio	200
	Summary	200
	Questions and Problems	201
9	Nonparametric Tests of Significance	207
	The Chi-Square Test	208
	Step-by-Step Illustration: Chi-Square Test of Significance	213
	Step-by-Step Illustration: Chi-Square Test for Several Groups	217
	The Median Test	224
	Step-by-Step Illustration: Median Test	224
	Summary	226
	Questions and Problems	227
	Looking at the Larger Picture: Testing Differences	234
Part 4	From Decision Making to Association	237
10	Correlation	239
	Strength of Correlation	239
	Direction of Correlation	240
	Curvilinear Correlation	241
	The Correlation Coefficient	241
	Pearson's Correlation Coefficient	243
	A Simplified Method for Testing the Significance of r	249
	Step-by-Step Illustration: Pearson's Correlation Coefficient	249
	Summary	251
	Questions and Problems	252
11	Regression Analysis	258
	The Regression Model	259
	Interpreting the Regression Line	264
	Regression and Pearson's Correlation	266
	Step-by-Step Illustration: Regression Analysis	267
	Summary	268
	Questions and Problems	269
12	Nonparametric Measures of Correlation	275
	Spearman's Rank-Order Correlation Coefficient	275
	Step-by-Step Illustration: Spearman's Rank-Order Correlation Coefficient	279
	Goodman's and Kruskal's Gamma	283
	Step-by-Step Illustration: Goodman's and Kruskal's Gamma	284
	Correlation Coefficient for Nominal Data Arranged in a 2 x 2 Table	288
	Correlation Coefficients for Nominal Data in Larger than 2 x 2 Tables	290
	Summary	293
	Questions and Problems	293
	Looking at the Larger Picture: Measuring Association	300
Part 5	Applying Statistics	303
13	Applying Statistical Procedures to Research Problems	305
	Research Situations	309
	Research Solutions	321
	Appendixes	329
Appendix A	A Review of Some Fundamentals of Mathematics	330
	Working with Decimals	330
	Dealing with Negative Numbers	332
	The Summation Sign	333
Appendix B	Tables	335
Appendix C	List of Formulas	347
	Answers to Selected Problems	351
	Index	357