Biostatistics and microbiology : a survival manual / Daryl S. Paulson.

Format:

Book

Author/Creator:

Paulson, Daryl S., 1947-

Language:

English

Subjects (All):

Microbiology--Statistical methods.

Microbiology.

Biometry.

Statistics.

Physical Description:

ix, 216 pages : illustrations ; 24 cm

Place of Publication:

New York, NY : Springer, [2008]

Summary:

Biostatistics and Microbiology: A Survival Manual enables the reader to access and apply statistical methods that generally frustrate and intimidate the uninitiated. Statistics, like chemistry, microbiology, woodworking, or sewing, requires that the individual put some time into learning the concepts and methods. This book presents a step-by-step manner that eliminates the greatest obstacle to the learner, which is applying the many processes that comprise a statistical method. The author counters the fear of statistical methods by describing early in the book a step-by-step procedure to perform a statistical method "a process that we will term 'the six-step procedure'." All of the testing will be performed adhering to six well-defined steps, which will greatly simplify the statistical process. Each step in the sequence must be completed before moving on to the next step. In the context of microbiology, statistics can be extremely useful in making interpretations and decisions concerning collected data. Statistics, then, is a way of formally communicating the interpretation of clinical or experimental data and is particularly important when a treatment result is not clearly differentiable from another treatment.

Contents:

1 BioStatistics and Microbiology: Introduction 1

1.1 Normal Distribution 2

1.2 Mean 6

1.3 Variance and Standard Deviation 7

1.4 Mode of Sample Data 8

1.5 Median of Sample Data 8

1.6 Using Normal Distribution Tables 8

1.7 Standard Error of the Mean 12

1.8 Confidence Intervals 13

1.9 Hypothesis Testing 14

2 One-Sample Tests 15

2.1 Estimation of a One-Sample Mean 15

2.2 Comparing One Sample Group Mean to a Standard Value 20

2.2.1 Confidence Interval Approach 20

2.2.2 Use of the Student's t Test to Make the Determination of a Sample Mean Different, Less than, or Greater than a Standard Value 24

2.3 Determining Adequate Sample Sizes for One-Sample Statistical Tests 28

2.3.1 Quick Sample Size Formula: Sample Set Mean Versus a Standard Value 29

2.4 Detection Level 30

2.5 A More Accurate Method of Sample Size Determination 30

2.6 (Optional) Equivalency Testing 32

2.6.1 Nonsuperiority Test 35

2.6.2 Confidence Interval Approach to Superiority/Inferiority Testing 37

3 Two-Sample Statistical Tests, Normal Distribution 41

3.1 Requirements of all t Tests 42

3.1.1 Two-Sample Independent t Test: Variances are not Assumed Equivalent, [sigma subscript 1 superscript 2 not equal sigma subscript 2 superscript 2] 42

3.1.2 Two-Sample Pooled t Test: Variances are Equivalent, [sigma subscript 1 superscript 2] = [sigma subscript 2 superscript 2] 45

3.1.3 Paired t Test 48

3.1.4 Sample Size Determination 52

3.2 Other Topics 55

3.2.1 Proportions 55

3.2.2 Optional Two-Sample Bioequivalency Testing 57

3.2.3 Two Independent Samples: Sample Variances Assumed Equal 58

3.2.4 Confidence Interval Approach 61

4 Analysis of Variance 63

4.1 The Completely Randomized One-Factor ANOVA 64

4.2 Contrasts 71

4.3 Confidence Intervals 72

4.4 Sample Size Calculation 73

4.5 Randomized Block Design 74

4.6 Pair-wise Contrasts 79

4.7 100 (1 - a) Confidence Intervals 79

4.8 Sample Size Calculation 81

5 Regression and Correlation Analysis 83

5.1 Least Squares Equation 85

5.2 Strategy for Linearizing Data 89

5.3 The Power Scale 90

5.4 Using Regression Analysis 90

5.5 Predicting the Average y from an x Value 91

5.6 Predicting a Specific y Value from an x Value 92

5.7 Correlation 93

5.8 Correlation Coefficient: r 94

5.9 Coefficient of Determination: r[superscript 2] 96

5.10 Predicting an x Value from a y Value 97

5.11 Confidence Interval for a Specific x 99

5.12 Confidence Interval for the Average x Value 100

5.13 D-Value Calculation 100

6 Qualitative Data Analysis 101

6.1 Binomial Distribution 101

6.1.1 Version I: Mean, Variance, and Standard Deviation Estimates for Predicting Outcome Events 101

6.1.2 Version II: Mean, Variance, and Standard Deviation Estimates for Predicting Proportions or Percentages 102

6.2 Confidence Interval Estimation 102

6.2.1 Confidence Intervals on Proportions that are not Extreme (Not Close to 0 or 1): The Yates Adjustment 104

6.2.2 Confidence Intervals on Proportions that are Extreme (Close to 0 or 1) 104

6.3 Comparing Two Samples 105

6.3.1 Proportions: One Sample Compared to a Standard Value 105

6.3.2 Confidence Interval Approach 107

6.4 Comparing Two Sample Proportions 109

6.5 Equivalence Testing: Proportions 112

6.5.1 Equivalence Testing: One Proportion Sample Compared to a Standard 112

6.5.2 Confidence Interval Approach 114

6.5.3 Nonsuperiority 114

6.5.4 Two-Tail Test: Equivalence 115

6.5.5 Confidence Interval 116

6.6 Two-Sample Equivalence: Proportions 116

7 Nonparametric Statistical Methods 121

7.1 Comparing Two Independent Samples: Nominal Scale Data 123

7.1.1 Comparing Two Independent Samples: 2 x 2 Chi Square Test 123

7.1.2 Comparing Two Related Samples: Nominal Scale Data 126

7.1.3 Comparing More than Two Independent Samples: Nominal Scale Data 129

7.1.4 Comparing More than Two Related Samples: Nominal Scale Data 132

7.2 Ordinal Scale Data: Rankable 133

7.2.1 Comparing Two Independent Sample Sets: Ordinal Data 133

7.2.2 Comparing Two Related Sample Sets: Ordinal Data 138

7.2.3 Comparing More than Two Independent Samples: Ordinal or Interval Data 142

7.2.4 Multiple Contrasts 146

7.2.5 Comparing More than Two Related Samples: Ordinal Data 147

7.3 Interval-Ratio Scale Data 152

7.3.1 Comparing Two Independent Samples: Interval-Ratio Data 152

7.3.2 Comparing Two Related or Paired Samples: Interval-Ratio Data 154

7.3.3 Independent Samples, n > 2: Interval-Ratio Data 157

7.3.4 Related Samples, n > 2: Interval-Ratio Data 157

Appendix Tables of Mathematical Values 163

Table A.1 Student's t table (percentage points of the t distribution) 164

Table A.2 Z-table (normal curve areas [entries in the body of the table give the area under the standard normal curve from 0 to z]) 165

Table A.3 Studentized range table 166

Table A.4 F distribution tables 168

Table A.5 Chi square table 173

Table A.6 Quantiles of the Mann-Whitney test statistic 174

Table A.7 Binomial probability distribution 178

Table A.8 Critical values of the Kruskal-Wallis test 207

Table A.9 Friedman ANOVA table 209

Table A.10 Wilcoxon table 211.

Notes:

Includes index.

ISBN:

9780387772813

0387772812

OCLC:

191243196