Biostatistical Analysis

by Zar, Jerrold H.

• ISBN13: 9780130815422
• ISBN10: 013081542X
• Edition: 4th
• Format: Hardcover
• Copyright: 2010-01-01
• Publisher: Pearson College Div

Summary

The latest edition of this best-selling biostatistics book is both comprehensive and easy to read.It provides a broad and practical overview of the statistical analysis methods used by researchers to collect, summarize, analyze, and draw conclusions from biological research data. TheFourth Editioncan serve as either an introduction to the discipline for beginning studentsora comprehensive procedural reference for today's practitioners.

Table of Contents

PREFACE	x
1 INTRODUCTION	1	(15)
1.1 Types of Biological Data	2	(3)
1.2 Accuracy and Significant Figures	5	(1)
1.3 Frequency Distributions	6	(7)
1.4 Cumulative Frequency Distributions	13	(3)
2 POPULATIONS AND SAMPLES	16	(4)
2.1 Populations	16	(1)
2.2 Samples from Populations	17	(1)
2.3 Random Sampling	17	(1)
2.4 Parameters and Statistics	18	(2)
3 MEASURES OF CENTRAL TENDENCY	20	(12)
3.1 The Arithmetic Mean	20	(3)
3.2 The Median	23	(3)
3.3 Other Quantiles	26	(1)
3.4 The Mode	27	(1)
3.5 Other Measures of Central Tendency	28	(1)
3.6 The Effect of Coding Data	29	(2)
Exercises	31	(1)
4 MEASURES OF DISPERSION AND VARIABILITY	32	(16)
4.1 The Range	32	(2)
4.2 Dispersion Measured with Quantiles	34	(1)
4.3 The Mean Deviation	34	(1)
4.4 The Variance	35	(4)
4.5 The Standard Deviation	39	(1)
4.6 The Coefficient of Variation	40	(1)
4.7 Indices of Diversity	40	(4)
4.8 The Effect of Coding Data	44	(3)
Exercises	47	(1)
5 PROBABILITIES	48	(17)
5.1 Counting Possible Outcomes	49	(1)
5.2 Permutations	50	(4)
5.3 Combinations	54	(2)
5.4 Sets	56	(2)
5.5 Probability of an Event	58	(1)
5.6 Adding Probabilities	59	(2)
5.7 Multiplying Probabilities	61	(2)
Exercises	63	(2)
6 THE NORMAL DISTRIBUTION	65	(26)
6.1 Symmetry and Kurtosis	67	(5)
6.2 Proportions of a Normal Distribution	72	(4)
6.3 The Distribution of Means	76	(3)
6.4 Introduction to Statistical Hypothesis Testing	79	(7)
6.5 Assessing Departures from Normality	86	(3)
Exercises	89	(2)
7 ONE-SAMPLE HYPOTHESES	91	(31)
7.1 Two-Tailed Hypotheses Concerning the Mean	91	(5)
7.2 One-Tailed Hypotheses Concerning the Mean	96	(2)
7.3 Confidence Limits for the Population Mean	98	(2)
7.4 Reporting Variability about the Mean	100	(5)
7.5 Sample Size and Estimation of the Population Mean	105	(1)
7.6 Power and Sample Size in Tests Concerning the Mean	105	(3)
7.7 Sampling Finite Populations	108	(2)
7.8 Confidence Limits for the Population Median	110	(1)
7.9 Hypotheses Concerning the Median	110	(1)
7.10 Confidence Limits for the Population Variance	110	(2)
7.11 Hypotheses Concerning the Variance	112	(1)
7.12 Power and Sample Size in Tests Concerning the Variance	113	(1)
7.13 Hypotheses Concerning the Coefficient of Variation	114	(1)
7.14 Hypotheses Concerning Symmetry and Kurtosis	115	(5)
Exercises	120	(2)
8 TWO-SAMPLE HYPOTHESES	122	(39)
8.1 Testing for Difference between Two Means	122	(7)
8.2 Confidence Limits for Population Means	129	(2)
8.3 Sample Size and Estimation of the Difference between Two Population Means	131	(1)
8.4 Power and Sample Size in Tests for Difference between Two Means	132	(4)
8.5 Testing for Difference between Two Variances	136	(3)
8.6 Confidence Interval for the Population Variance Ratio	139	(1)
8.7 Sample Size and Power in Tests for Difference between Two Variances	140	(1)
8.8 Testing for Difference between Two Coefficients of Variation	141	(4)
8.9 Nonparametric Statistical Methods	145	(1)
8.10 Two-Sample Rank Testing	146	(9)
8.11 Testing for Difference between Two Medians	155	(1)
8.12 The Effect of Coding	155	(1)
8.13 Two-Sample Testing of Nominal-Scale Data	156	(1)
8.14 Testing for Difference between Two Diversity Indices	156	(3)
Exercises	159	(2)
9 PAIRED-SAMPLE HYPOTHESES	161	(16)
9.1 Testing Mean Difference	161	(3)
9.2 Confidence Limits for the Population Mean Difference	164	(1)
9.3 Power and Sample Size in Paired-Sample Testing of Means	164	(1)
9.4 Testing for the Difference between Variances from Two Correlated Populations	164	(1)
9.5 Paired-Sample Testing by Ranks	165	(4)
9.6 Confidence Limits for the Population Median Difference	169	(1)
9.7 Paired-Sample Testing of Nominal-Scale Data	169	(6)
Exercises	175	(2)
10 MULTISAMPLE HYPOTHESES: THE ANALYSIS OF VARIANCE	177	(31)
10.1 Single-Factor Analysis of Variance	178	(11)
10.2 Confidence Limits for Population Means	189	(1)
10.3 Power and Sample Size in Analysis of Variance	189	(6)
10.4 Nonparametric Analysis of Variance	195	(5)
10.5 Testing for Difference among Several Medians	200	(2)
10.6 Homogeneity of Variances	202	(2)
10.7 Homogeneity of Coefficients of Variation	204	(2)
10.8 The Effect of Coding	206	(1)
10.9 Multisample Testing for Nominal-Scale Data	206	(1)
Exercises	206	(2)
11 MULTIPLE COMPARISONS	208	(23)
11.1 The Tukey Test	210	(4)
11.2 The Newman-Keuls Test	214	(1)
11.3 Confidence Intervals Following Multiple Comparisons	215	(2)
11.4 Comparisons of a Control Mean to Each Other Group Mean	217	(2)
11.5 Scheffe's Multiple Contrasts	219	(4)
11.6 Nonparametric Multiple Comparisons	223	(3)
11.7 Nonparametric Multiple Contrasts	226	(1)
11.8 Multiple Comparisons among Medians	226	(2)
11.9 Multiple Comparisons among Variances	228	(2)
Exercises	230	(1)
12 TWO-FACTOR ANALYSIS OF VARIANCE	231	(42)
12.1 Two-Factor Analysis of Variance with Equal Replication	232	(13)
12.2 Two-Factor Analysis of Variance with Unequal Replication	245	(3)
12.3 Two-Factor Analysis of Variance without Replication	248	(2)
12.4 The Randomized Block Experimental Design	250	(5)
12.5 Repeated-Measures Experimental Designs	255	(5)
12.6 Multiple Comparisons and Confidence Intervals in Two-Factor Analysis of Variance	260	(1)
12.7 Power and Sample Size in Two-Factor Analysis of Variance	261	(2)
12.8 Nonparametric Randomized Block or Repeated-Measures Analysis of Variance	263	(4)
12.9 Multiple Comparisons for Nonparametric Randomized Block or Repeated-Measures Analysis of Variance	267	(1)
12.10 Dichotomous Nominal-Scale Data in Randomized Blocks or from Repeated Measures	268	(2)
12.11 Multiple Comparisons with Dichotomous Randomized Block or Repeated-Measures Data	270	(1)
12.12 Introduction to Analysis of Covariance	270	(1)
Exercises	271	(2)
13 DATA TRANSFORMATIONS	273	(9)
13.1 The Logarithmic Transformation	275	(1)
13.2 The Square Root Transformation	275	(3)
13.3 The Arcsine Transformation	278	(2)
13.4 Other Transformations	280	(1)
Exercises	280	(2)
14 MULTIWAY FACTORIAL ANALYSIS OF VARIANCE	282	(21)
14.1 Three-Factor Analysis of Variance	283	(3)
14.2 The Latin Square Experimental Design	286	(1)
14.3 Higher-Order Factorial Analysis of Variance	287	(1)
14.4 Blocked and Repeated-Measures Experimental Designs	288	(10)
14.5 Factorial Analysis of Variance with Unequal Replication	298	(1)
14.6 Multiple Comparisons and Confidence Intervals in Multiway Analysis of Variance	299	(1)
14.7 Power and Sample Size in Multiway Analysis of Variance	300	(1)
Exercises	300	(3)
15 NESTED (HIERARCHICAL) ANALYSIS OF VARIANCE	303	(9)
15.1 Nesting within One Main Factor	305	(3)
15.2 Nesting in Factorial Experiments	308	(2)
15.3 Multiple Comparisons and Confidence Intervals	310	(1)
15.4 Power and Sample Size in Nested Analysis of Variance	311	(1)
Exercises	311	(1)
16 MULTIVARIATE ANALYSIS OF VARIANCE	312	(12)
16.1 The Multivariate Normal Distribution	313	(3)
16.2 Multivariate Analysis of Variance Hypothesis Testing	316	(6)
16.3 Further Analysis	322	(1)
16.4 Other Experimental Designs	322	(1)
Exercises	323	(1)
17 SIMPLE LINEAR REGRESSION	324	(36)
17.1 Regression vs. Correlation	324	(2)
17.2 The Simple Linear Regression Equation	326	(7)
17.3 Testing the Significance of a Regression	333	(4)
17.4 Confidence Intervals in Regression	337	(5)
17.5 Inverse Prediction	342	(2)
17.6 Interpretations of Regression Functions	344	(1)
17.7 Regression with Replication and Testing for Linearity	345	(5)
17.8 Power and Sample Size in Regression	350	(1)
17.9 Regression through the Origin	351	(2)
17.10 Data Transformations in Regression	353	(4)
17.11 The Effect of Coding	357	(1)
Exercises	358	(2)
18 COMPARING SIMPLE LINEAR REGRESSION EQUATIONS	360	(17)
18.1 Comparing Two Slopes	360	(4)
18.2 Comparing Two Elevations	364	(4)
18.3 Comparing Points on Two Regression Lines	368	(1)
18.4 Comparing more than Two Slopes	369	(3)
18.5 Comparing more than Two Elevations	372	(1)
18.6 Multiple Comparisons among Slopes	372	(1)
18.7 Multiple Comparisons among Elevations	373	(1)
18.8 Multiple Comparisons of Points among Regression Lines	374	(1)
18.9 An Overall Test for Coincidental Regressions	375	(1)
Exercises	375	(2)
19 SIMPLE LINEAR CORRELATION	377	(36)
19.1 The Correlation Coefficient	377	(4)
19.2 Hypotheses about the Correlation Coefficient	381	(2)
19.3 Confidence Intervals for the Population Correlation Coefficient	383	(2)
19.4 Power and Sample Size in Correlation	385	(1)
19.5 Comparing Two Correlation Coefficients	386	(2)
19.6 Power and Sample Size in Comparing Two Correlation Coefficients	388	(2)
19.7 Comparing more than Two Correlation Coefficients	390	(2)
19.8 Multiple Comparisons among Correlation Coefficients	392	(3)
19.9 Rank Correlation	395	(3)
19.10 Weighted Rank Correlation	398	(3)
19.11 Correlation for Dichotomous Nominal-Scale Data	401	(3)
19.12 Intraclass Correlation	404	(3)
19.13 Concordance Correlation	407	(3)
19.14 The Effect of Coding	410	(1)
Exercises	410	(3)
20 MULTIPLE REGRESSION AND CORRELATION	413	(39)
20.1 Intermediate Computational Steps	414	(5)
20.2 The Multiple Regression Equation	419	(3)
20.3 Analysis of Variance of Multiple Regression or Correlation	422	(2)
20.4 Hypotheses Concerning Partial Regression Coefficients	424	(2)
20.5 Standardized Partial Regression Coefficients	426	(1)
20.6 Partial Correlation	426	(2)
20.7 Round-off Error and Coding Data	428	(1)
20.8 Selection of Independent Variables	429	(4)
20.9 Predicting Y Values	433	(3)
20.10 Testing Difference between Two Partial Regression Coefficients	436	(1)
20.11 "Dummy" Variables	436	(1)
20.12 Interaction of Independent Variables	437	(1)
20.13 Comparing Multiple Regression Equations	437	(3)
20.14 Multiple Regression through the Origin	440	(1)
20.15 Nonlinear Regression	440	(2)
20.16 Descriptive vs. Predictive Models	442	(1)
20.17 Concordance: Rank Correlation among Several Variables	443	(7)
Exercises	450	(2)
21 POLYNOMIAL REGRESSION	452	(9)
21.1 Polynomial Curve Fitting	452	(5)
21.2 Round-off Error and Coding Data	457	(1)
21.3 Quadratic Regression	457	(2)
Exercises	459	(2)
22 TESTING FOR GOODNESS OF FIT	461	(25)
22.1 Chi-Square Goodness of Fit	462	(2)
22.2 Chi-Square Goodness of Fit for More than Two Categories	464	(2)
22.3 Subdividing Chi-Square Analyses	466	(2)
22.4 Chi-Square Correction for Continuity	468	(2)
22.5 Bias in Chi-Square Calculations	470	(1)
22.6 Heterogeneity Chi-Square	471	(2)
22.7 The Log-Likehood Ratio	473	(2)
22.8 Kolmogorov-Smirnov Goodness of Fit for Discrete Data	475	(3)
22.9 Kolmogorov-Smirnov Goodness of Fit for Continuous Data	478	(3)
22.10 Sample Size Required for Kolmogorov-Smirnov Goodness of Fit for Continuous Data	481	(2)
Exercises	483	(3)
23 CONTINGENCY TABLES	486	(30)
23.1 Chi-Square Analysis of Contingency Tables	488	(2)
23.2 Graphing Contingency Table Data	490	(1)
23.3 The 2 x 2 Contingency Table	491	(9)
23.4 Heterogeneity Testing of 2 x 2 Tables	500	(2)
23.5 Subdividing Contingency Tables	502	(2)
23.6 Bias in Chi-Square Contingency Table Analyses	504	(1)
23.7 The Log-Likehood Ratio for Contingency Tables	505	(1)
23.8 Three-Dimensional Contingency Tables	506	(6)
23.9 Log-Linear Models for Multidimensional Contingency Tables	512	(2)
Exercises	514	(2)
24 MORE ON DICHOTOMOUS VARIABLES	516	(55)
24.1 Binomial Probabilities	517	(6)
24.2 The Hypergeometric Distribution	523	(1)
24.3 Sampling a Binomial Population	524	(3)
24.4 Confidence Limits for Population Proportions	527	(3)
24.5 Goodness of Fit for the Binomial Distribution	530	(3)
24.6 The Binomial Test	533	(5)
24.7 The Sign Test	538	(1)
24.8 Power of the Binomial and Sign Tests	539	(3)
24.9 Confidence Interval for the Population Median	542	(1)
24.10 The Fisher Exact Test	543	(2)
24.11 Comparing Two Proportions	555	(3)
24.12 Power and Sample Size in Comparing Two Proportions	558	(4)
24.13 Comparing more than Two Proportions	562	(1)
24.14 Multiple Comparisons for Proportions	563	(2)
24.15 Trends among Proportions	565	(3)
Exercises	568	(3)
25 TESTING FOR RANDOMNESS	571	(21)
25.1 Poisson Probabilities	571	(3)
25.2 Confidence Limits for the Poisson Parameter	574	(1)
25.3 Goodness of Fit of the Poisson Distribution	575	(3)
25.4 The Binomial Test Revisited	578	(4)
25.5 Comparing Two Poisson Counts	582	(1)
25.6 Serial Randomness of Nominal-Scale Categories	583	(3)
25.7 Serial Randomness of Measurements: Parametric Testing	586	(1)
25.8 Serial Randomness of Measurements: Nonparametric Testing	587	(3)
Exercises	590	(2)
26 CIRCULAR DISTRIBUTIONS: DESCRIPTIVE STATISTICS	592	(24)
26.1 Data on a Circular Scale	592	(3)
26.2 Graphical Presentation of Circular Data	595	(2)
26.3 Sines and Cosines of Circular Data	597	(2)
26.4 The Mean Angle	599	(3)
26.5 Angular Dispersion	602	(3)
26.6 The Median and Modal Angles	605	(1)
26.7 Confidence Limits for the Population Mean and Median Angles	605	(2)
26.8 Diametrically Bimodal Distributions	607	(1)
26.9 Second-Order Analysis: The Mean of Mean Angles	608	(3)
26.10 Confidence Limits for the Second-Order Mean Angle	611	(3)
Exercises	614	(2)
27 CIRCULAR DISTRIBUTIONS: HYPOTHESIS TESTING	616
27.1 Testing Significance of the Mean Angle Unimodal Distributions	616	(5)
27.2 Testing Significance of the Median Angle: Omnibus Test	621	(3)
27.3 Testing Significance of the Median Angle: Binomial Test	624	(1)
27.4 Testing Symmetry around the Median Angle	624	(1)
27.5 Two-Sample and Multisample Testing of Mean Angles	625	(5)
27.6 Nonparametric Two-Sample and Multisample Testing of Angles	630	(5)
27.7 Two-Sample and Multisample Testing of Median Angles	635	(1)
27.8 Two-Sample and Multisample Testing of Angular Distances	635	(2)
27.9 Two-Sample and Multisample Testing of Angular Dispersion	637	(1)
27.10 Parametric One-Sample Second-Order Analysis of Angles	638	(1)
27.11 Nonparametric One-Sample Second-Order Analysis of Angles	639	(2)
27.12 Parametric Two-Sample Second-Order Analysis of Angles	641	(2)
27.13 Nonparametric Two-Sample Second-Order Analysis of Angles	643	(2)
27.14 Parametric Paired-Sample Testing with Angles	645	(2)
27.15 Nonparametric Paired-Sample Testing with Angles	647	(2)
27.16 Parametric Angular Correlation and Regression	649	(4)
27.17 Nonparametric Angular Correlation	653	(1)
27.18 Goodness of Fit Testing for Circular Distributions	654	(4)
27.19 Serial Randomness of Nominal-Scale Categories on a Circle	658	(2)
Exercises	660
APPENDIX A ANALYSIS OF VARIANCE HYPOTHESIS TESTING	App1	(10)
A.1 Determination of Appropriate F's and Degrees of Freedom	App1	(4)
A.2 Two-Factor Analysis of Variance	App5	(1)
A.3 Three-Factor Analysis of Variance	App6	(1)
A.4 Nested Analysis of Variance	App7	(1)
A.5 Split-Plot and Mixed Within-Subjects Analysis of Variance	App8	(3)
APPENDIX B STATISTICAL TABLES AND GRAPHS	App11
Table B.1 Critical Values of Chi-Square Distribution	App12	(5)
Table B.2 Proportions of the Normal Curve (One-Tailed)	App17	(2)
Table B.3 Critical Values of the t Distribution	App19	(2)
Table B.4 Critical Values of the F Distribution	App21	(37)
Table B.5 Critical Values of the q Distribution	App58	(16)
Table B.6 Critical Values of q' for the One-Tailed Dunnett's Test	App74	(2)
Table B.7 Critical Values of q' for the Two-Tailed Dunnett's Test	App76	(1)
Table B.8 Critical Values of d(max) for the Kolmogorov-Smirnov Goodness of Fit Test for Discrete or Grouped Data	App77	(6)
Table B.9 Critical Values of D for the Kolmogorov-Smirnov Goodness of Fit Test for Continuous Distributions	App83	(4)
Table B.10 Critical Values of D(Delta) for the Delta-Corrected Kolmogorov-Smirnov Goodness of Fit Test for Continuous Distribution	App87	(2)
Table B.11 Critical Values of the Mann-Whitney U Distribution	App89	(12)
Table B.12 Critical Values of the Wilcoxon T Distribution	App101	(3)
Table B.13 Critical Values of the Kruskal-Wallis H Distribution	App104	(2)
Table B.14 Critical Values of the Friedman X(2)(r) Distribution	App106	(1)
Table B.15 Critical Values of Q for Nonparametric Multiple Comparison Testing	App107	(1)
Table B.16 Critical Values of Q' for Nonparametric Multiple Comparison Testing with a Control	App108	(1)
Table B.17 Critical Values of the Correlation Coefficient, r	App109	(2)
Table B.18 Fisher's z Transformation for Correlation Coefficients, r	App111	(2)
Table B.19 Correlation Coefficients, r, Corresponding to Fisher's z Transformation	App113	(3)
Table B.20 Critical Values of the Spearman Rank Correlation Coefficient, r(s)	App116	(2)
Table B.21 Critical Values of the Top-Down Correlation Coefficient, r(T)	App118	(1)
Table B.22 Critical Values of the Symmetry Measure, g(1)	App119	(2)
Table B.23 Critical Values of the Kurtosis Measure, g(2)	App121	(3)
Table B.24 The Arcsine Transformation, p'	App124	(3)
Table B.25 Proportions, p, Corresponding to Arcsine Transformations, p'	App127	(2)
Table B.26a Binomial Coefficients, (n)C(X)	App129	(3)
Table B.26b Proportions of the Binomial Distribution for p = q = 0.5	App132	(1)
Table B.27 Critical Values of C for the Sign Test or for the Binomial Test with p = 0.5	App133	(10)
Table B.28 Critical Values for Fisher's Exact Test	App143	(28)
Table B.29 Critical Values for Runs Test	App171	(9)
Table B.30 Critical Values of C for the Mean Square Successive Difference Test	App180	(2)
Table B.31 Critical Values for the Runs Up and Down Test	App182	(2)
Table B.32 Angular Deviation, s, As a Function of Vector Length, r	App184	(2)
Table B.33 Circular Standard Deviation, s(0), As a Function of Vector Length, r	App186	(2)
Table B.34 Critical Values of Rayleigh's z	App188	(2)
Table B.35 Critical Values of u for the V Test of Circular Uniformity	App190	(1)
Table B.36 Critical Values of m for the Hodges-Ajne Test	App191	(2)
Table B.37 Correction Factor, K, for the Watson and Williams Test	App193	(2)
Table B.38 Critical Values of Watson's U(2)	App195	(3)
Table B.39 Critical Values of R' for the Moore Test of Circular Uniformity	App198	(1)
Table B.40 Common Logarithms of Factorials	App199	(2)
Table B.41 Ten Thousand Random Digits	App201	(4)
Figure B.1 Power and Sample Size in Analysis of Variance	App205
ANSWERS TO EXERCISES	Ans1
LITERATURE CITED	L1
INDEX	I1