Essential Statistics, Fourth Edition

by Rees; D.G.

• ISBN13: 9781584880073
• ISBN10: 1584880074
• Edition: 4th
• Format: Nonspecific Binding
• Copyright: 2000-12-26
• Publisher: Chapman & Hall/

Summary

An introductory text for students taking a first course in statistics-in fields as diverse as engineering, business, chemistry, and biology-Essential Statistics: Fourth Edition thoroughly updates and enhances the hugely successful third edition. It presents new information on modern statistical techniques such as Analysis of Variance (ANOVA), and software such as MINITAB for WINDOWS.

Table of Contents

Preface	xiii
Preface to the Third Edition	xv
Preface to the Second Edition	xvii
Preface to the First Edition	xix
Acknowledgements	xxi
What is Statistics?	1	(8)
Statistics as a Science	1	(3)
Types of Statistical Data	4	(5)
Statistics and Types of Statistical Data	6	(3)
Some Statistical Notation	9	(6)
Introduction	9	(1)
Σ	9	(2)
Factorials	11	(1)
xy	11	(1)
ex	12	(1)
Decimal Places and Significant Figures	12	(3)
Some Statistical Notation	13	(2)
Summarizing Data by Tables and by Graphical Methods	15	(16)
Introduction	15	(1)
Tables and Graphs for One Continuous Variable	15	(4)
Using Minitab for Windows to Draw Graphs	19	(2)
Tables and Graphs for One Discrete Variable	21	(1)
Tables and Graphs for One Categorical Variable	22	(1)
Tables and Graphs for Two-Variable Data	23	(3)
Summary	26	(5)
Summarizing Data by Tables and by Graphical Methods	26	(5)
Summarizing Data by Numerical Measures	31	(16)
Introduction	31	(1)
Averages	31	(1)
Sample Mean (x)	32	(1)
Sample Median	33	(1)
Sample Mode	34	(1)
When to Use the Mean, Median, and Mode	35	(2)
Measures of Variation	37	(1)
Sample Standard Deviation (s)	38	(2)
Sample Inter-Quartile Range	40	(1)
When to Use Standard Deviation and Inter-Quartile Range	41	(1)
Box and Whisker Plots	41	(1)
Other Measures of Variation	42	(1)
A Measure of Skewness	42	(1)
Summary	43	(4)
Summarizing Data by Numerical Measures	44	(3)
Probability	47	(20)
Introduction	47	(1)
Basic Ideas of Probability	48	(1)
The a priori Definition of Probability for Equally Likely Outcomes	49	(1)
The Relative Frequency Definition of Probability, Based on Experimental Data	50	(1)
The Range of Possible Values for a Probability Value	51	(1)
Probability, Percentage, Proportion, and Odds	52	(1)
Subjective Probability	52	(1)
Probabilities Involving More Than One Event	52	(1)
Multiplication Law (The `and' Law)	53	(2)
Addition Law (The `or' Law)	55	(1)
Mutually Exclusive and Exhaustive Events	56	(1)
Complementary Events and the Calculation of P (at Least 1...)	57	(1)
Probability Trees	58	(1)
Venn Diagrams and Rees Diagrams	59	(1)
Summary	60	(7)
Probability	61	(6)
Discrete Probability Distributions	67	(20)
Introduction	67	(1)
Bernoulli Distribution	68	(1)
Binomial Distribution	68	(1)
Calculating Binomial Probabilities: An Example	69	(1)
Binomial Probabilities Using Tables and Minitab for Windows	70	(3)
Mean and Standard Deviation of the Binomial Distribution	73	(1)
Simulation of Binomial Distributions, Using Minitab for Windows	74	(1)
Poisson Distribution, an Introduction	75	(1)
Some Examples of Poisson Variables	75	(1)
The General Poisson Distribution	75	(1)
Calculating Poisson Probabilities, an Example	76	(1)
Mean and Standard Deviation of the Poisson Distribution	77	(1)
Poisson Probabilities Using Tables and Minitab for Windows	77	(3)
Simulation of Poisson Distribution Using Minitab for Windows	80	(1)
Poisson Approximation to the Binomial Distribution	80	(1)
Summary	81	(6)
The Bernoulli, Binomial, and Poisson Distributions	81	(6)
Continuous Probability Distributions	87	(14)
Introduction	87	(2)
The Normal Distribution	89	(1)
An Example of a Normal Distribution	90	(3)
Normal Probabilities Using Minitab for Windows	93	(1)
Simulation of the Normal Distribution Using Minitab for Windows	94	(1)
Rectangular Distribution	95	(1)
The Normal Approximation to the Binomial Distribution	96	(1)
Summary	97	(4)
The Normal and Rectangular Distributions	98	(3)
Samples and Populations	101	(14)
Introduction	101	(1)
Reasons for Sampling	102	(1)
Sampling Methods	102	(2)
Sample Size	104	(2)
Sampling Distribution of the Sample Mean	106	(2)
Simulation of the Sampling Distribution of the Sample Mean Using Minitab	108	(1)
Summary	109	(6)
Samples and Populations	110	(5)
Confidence Interval Estimation	115	(24)
Introduction	115	(1)
95% Confidence Intervals	116	(1)
Calculating a 95% Confidence Interval for the Mean, μ, of a Population: Large Sample Size	117	(3)
Calculating a 95% Confidence Interval for the Mean, μ, of a Population: Small Sample Size	120	(3)
The t Distribution	123	(1)
The Choice of Sample Size When Estimating the Mean of a Population	124	(1)
Degrees of Freedom	125	(1)
95% Confidence Interval for a Binomial Probability	126	(1)
The Choice of Sample Size When Estimating a Binomial Probability	127	(1)
95% Confidence Interval for the Mean of a Population of Differences: `Paired' Samples Data, and Including Minitab	128	(2)
95% Confidence Interval for the Difference in the Means of Two Populations, `Unpaired' Samples Data, and Including Minitab	130	(4)
Summary	134	(5)
Confidence Interval Estimation	134	(5)
Hypothesis Testing	139	(22)
Introduction	139	(1)
What is a Hypothesis?	140	(1)
Which is the Null Hypothesis and Which is the Alternative Hypothesis?	141	(1)
What is a Significance Level?	141	(1)
What is a Test Statistic, and How do We Calculate It?	142	(1)
How do We Find the Tabulated Test Statistic?	143	(1)
How do We Compare the Calculated and the Tabulated Test Statistics?	143	(1)
What is Our Conclusion, and What Assumptions Have We Made?	144	(1)
Using p Values Instead of Tables	144	(1)
Hypothesis Test for the Mean, μ, of a Population	145	(1)
Two Examples of Tests with One-Sided Alternative Hypotheses	146	(1)
Hypothesis Test for a Binomial Probability	147	(2)
Hypothesis Test for the Mean of a Population of Differences, `Paired' Samples Data	149	(1)
Hypothesis Test for the Difference between the Means of Two Populations, `Unpaired' Samples Data	150	(2)
Hypothesis Test for the Equality of the Variances of Two Normally Distributed Populations	152	(1)
The Effect of Choosing Significance Levels Other Than 5%	153	(1)
What if the Assumptions of a Hypothesis Test are not Valid?	153	(1)
The Connection between Confidence Interval Estimation and Hypothesis Testing	154	(1)
Summary	154	(7)
Hypothesis Testing Including t, z, and F Tests	155	(6)
Nonparametric Hypothesis Tests	161	(18)
Introduction	161	(1)
Sign Test for the Median of a Population	161	(3)
Sign Test for the Median of a Population of Differences, `Paired' Samples Data	164	(1)
Sign Test for Large Sample Sizes (n > 10)	165	(1)
Sign Test Using Minitab for Windows	166	(1)
Wilcoxon Signed Rank Test for the Median of a Population of Differences, `Paired' Samples Data	167	(2)
Wilcoxon Signed Rank Test for Large Sample Sizes (n > 25)	169	(1)
Wilcoxon Signed Rank Test Using Minitab for Windows	170	(1)
Mann-Whitney U Test for the Difference between the Medians of Two Populations, `Unpaired' Samples Data	171	(2)
Mann-Whitney U Test for Large Sample Sizes (n1 or n2 > 20)	173	(1)
Mann-Whitney U Test Using Minitab	174	(1)
Summary	175	(4)
Sign Test, Wilcoxon Signed Rank Test, Mann-Whitney U Test	176	(3)
An Introduction to the Analysis of Variance (ANOVA)	179	(16)
Introduction	179	(1)
An ANOVA Example	179	(5)
The Connection between the Unpaired Samples t Test and the F Test in ANOVA	184	(1)
ANOVA to Compare Four Means, an Example	185	(3)
A Posterior Test if H0 is Rejected in ANOVA	188	(2)
ANOVA to Compare Means, Using Minitab for Windows	190	(2)
Summary	192	(3)
ANOVA	192	(3)
Association of Categorical Variables	195	(16)
Introduction	195	(1)
Contingency Tables	195	(1)
x2 Test of Independence, 2 x 2 Contingency Table Data	196	(3)
x2 Test of Independence, 3 x 3 Table	199	(2)
x2 Test of Independence, Using Minitab for Windows	201	(1)
Fisher Exact Test	202	(3)
x2 Trend Test	205	(1)
Summary	206	(5)
Association of Categorical Variables	207	(4)
Correlation of Quantitative Variables	211	(20)
Introduction	211	(1)
Pearson's Correlation Coefficient	212	(3)
Hypothesis Test for Pearson's Population Correlation Coefficient, p	215	(1)
The Interpretation of Significant and Nonsignificant Correlation Coefficients	216	(3)
Spearman's Rank Correlation Coefficient	219	(2)
Hypothesis Test for Spearman's Rank Correlation Coefficient	221	(1)
Spearman's Coefficient in the Case of Ties	221	(2)
Correlation Coefficients Using Minitab for Windows	223	(1)
Summary	224	(7)
Correlation of Quantitative Variables	225	(6)
Regression Analysis, An Introduction	231	(20)
Introduction	231	(1)
Determining the Regression Equation, an Example	232	(2)
Plotting the Regression Line on the Scatter Diagram	234	(1)
Predicting Values of y	235	(1)
Residuals	236	(1)
ANOVA in Regression Analysis	236	(4)
More Inferences in Regression Analysis	240	(1)
Regression Analysis Using Minitab for Windows	241	(4)
Summary	245	(6)
Regression Analysis	246	(5)
Goodness-of-Fit Tests	251	(14)
Introduction	251	(1)
Goodness-of-Fit for a Simple Proportion Distribution	251	(3)
Goodness-of-Fit for a Binomial Distribution	254	(2)
Goodness-of-Fit for a Poisson Distribution	256	(2)
The Shapiro-Wilk Test For Normality	258	(2)
Summary	260	(5)
Goodness-of-Fit Tests	260	(5)
Appendix A Statistical Formulae	265	(10)
Appendix B Solutions to Worksheets	275	(38)
Appendix C Statistical Tables	313	(34)
Appendix D Glossary of Symbols	347	(4)
Appendix E Introduction to Minitab for Windows	351	(4)
Index	355