Statistical analysis in microbiology: statnotes
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken
Wiley-Blackwell
2011
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 166 S. graph. Darst. |
| ISBN: | 9780470559307 |
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| 100 | 1 | |a Armstrong, Richard A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical analysis in microbiology |b statnotes |c Richard A. Armstrong and Anthony C. Hilton |
| 264 | 1 | |a Hoboken |b Wiley-Blackwell |c 2011 | |
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Datensatz im Suchindex
| _version_ | 1804143573318238208 |
|---|---|
| adam_text | Titel: Statistical analysis in microbiology
Autor: Armstrong, Richard A
Jahr: 2011
CONTENTS
Preface
Acknowledgments
Note on Statistical Software
xv
xvii
xix
ARE THE DATA NORMALLY D1STRIBUTED?
1.1 Introduction
1.2 Types of Data and Scores
1.3 Scenario
1.4 Data
1.5 Analysis: Fitting the Normal Distribution
1.5.1 How Is the Analysis Carried Out?
1.5.2 Interpretation
1.6 Conclusion
DESCRIBING THE NORMAL DISTRIBUTION
2.1 Introduction
2.2 Scenario
2.3 Data
2.4 Analysis: Describing the Normal Distribution
2.4.1 Mean and Standard Deviation
2.4.2 Coefficient of Variation
2.4.3 Equation of the Normal Distribution
2.5 Analysis: Is a Single Observation Typical of the Population?
2.5.1 How Is the Analysis Carried Out?
2.5.2 Interpretation
2.6 Analysis: Describing the Variation of Sample Means
2.7 Analysis: How to Fit Confidence Intervals to a Sample Mean
2.8 Conclusion
7
7
8
8
8
8
10
10
11
11
11
12
12
13
3 TESTING THE DIFFERENCE BFTWEEN TWO GROUPS
3.1 Introduction
3.2 Scenario
3.3 Data
15
15
16
16
VI
CONTENTS
3.4 Analysis: The Unpaired t Test 16
3.4.1 How Is the Analysis Carried Out? 16
3.4.2 Interpretation 18
3.5 One-Tail and Two-Tail Tests 18
3.6 Analysis: The Paired t Test 18
3.7 Unpaired versus the Paired Design 19
3.8 Conclusion 19
WHAT IF THE DATA ARE NOT NORMALLY DISTR1BUTED? 21
4.1 Introduction 21
4.2 How to Recognize a Normal Distribution 21
4.3 Nonnormal Distributions 22
4.4 Data Transformation 23
4.5 Scenario 24
4.6 Data 24
4.7 Analysis: Mann-Whitney U test (for Unpaired Data) 24
4.7.1 How Is the Analysis Carried Out? 24
4.7.2 Interpretation 24
4.8 Analysis: Wilcoxon Signed-Rank Test (for Paired Data) 25
4.8.1 How Is the Analysis Carried Out? 25
4.8.2 Interpretation 26
4.9 Comparison of Parametric and Nonparametric Tests 26
4.10 Conclusion 26
CHt-SQUARE CONTtNGENCY TABLES *9
5.1 Introduction 29
5.2 Scenario 30
5.3 Data 30
5.4 Analysis: 2x2 Contingency Table 31
5.4.1 How Is the Analysis Carried Out? 31
5.4.2 Interpretation 3*
5.4.3 Yates Correction 3*
5.5 Analysis: Fisher s 2 x2ExactTest 31
5.6 Analysis: Rows x Columns (Ä x Q Contingency Tables 32
5.7 Conclusion 3^
6 ONE-WAY ANALYSIS OF VARIANCE (ANOVA) 33
6.1 Introduction
6.2 Scenario
6.3 Data
33
34
34
CONTENTS VÜ
6.4 Analysis 35
6.4.1 Logic of ANOVA 35
6.4.2 How Is the Analysis Carried Out? 35
6.4.3 Interpretation 36
6.5 Assumptions of ANOVA 37
6.6 Conclusion 37
7 POST HOC TESTS 39
7.1 Introduction 39
7.2 Scenario 40
7.3 Data 40
7.4 Analysis: Planned Comparisons between the Means 40
7.4.1 Orthogonal Contrasts 40
7.4.2 Interpretation 41
7.5 Analysis: Post Hoc Tests 42
7.5.1 Common Post Hoc Tests 42
7.5.2 Which Test to Use? 43
7.5.3 Interpretation 44
7.6 Conclusion 44
8 IS ONE SET OF DATA MORE VARIABLE THAN ANOTHER? 45
8.1 Introduction 45
8.2 Scenario 46
8.3 Data 46
8.4 Analysis of Two Groups: Variance Ratio Test 46
8.4.1 How Is the Analysis Carried Out? 46
8.4.2 Interpretation 47
8.5 Analysis of Three or More Groups: Bartlett s Test 47
8.5.1 How Is the Analysis Carried Out? 47
8.5.2 Interpretation 48
8.6 Analysis of Three or More Groups: Levene s Test 48
8.6.1 How Is the Analysis Carried Out? 48
8.6.2 Interpretation 48
8.7 Analysis of Three or More Groups: Brown-Forsythe Test 48
8.8 Conclusion 49
9 STATISTICAL POWER AND SAMPLE SIZE 51
9.1 Introduction 51
9.2 Calculate Sample Size for Comparing Two Independent
Treatments 52
9.2.1 Scenario 52
9.2.2 How Is the Analysis Carried Out? 52
VÜi CONTENTS
9.3 Implications of Sample Size Calculations 53
9.4 Calculation of the Power (P) of a Test 53
9.4.1 How Is the Analysis Carried Out? 53
9.4.2 Interpretation 54
9.5 Power and Sample Size in Other Designs 54
9.6 Power and Sample Size in ANOVA 54
9.7 More Complex Experimental Designs 55
9.8 Simple RuIeofThumb 56
9.9 Conclusion 56
10 ONE-WAY ANALYSIS OF VARIANCE (RANDOM
EFFECTS MODEL): THE NESTED OR HIERARCHICAL
DESIGN 57
10.1 Introduction 57
10.2 Scenario 58
10.3 Data 58
10.4 Analysis 58
10.4.1 How Is the Analysis Carried Out? 58
10.4.2 Random-Effects Model 58
10.4.3 Interpretation 60
10.5 Distinguish Random- and Fixed-Effect Factors 61
10.6 Conclusion 61
11 TWO-WAY ANALYSIS OF VARIANCE 63
11.1 Introduction 63
11.2 Scenario 64
11.3 Data 64
11.4 Analysis 64
11.4.1 How Is the Analysis Carried Out? 64
11.4.2 Statistical Model of Two-Way Design 65
11.4.3 Interpretation 65
11.5 Conclusion 66
12 TWO-FACTOR ANALYSIS OF VARIANCE «
12.1 Introduction 67
12.2 Scenario 68
12.3 Data 68
12.4 Analysis . . . ¦
12.4.1 How Is the Analysis Carried Out? ®
12.4.2 Interpretation w
12.5 Conclusion W
CONTENTS IX
13 SPLIT-PLOT ANALYSIS OF VARIANCE 71
13.1 Introduction 71
13.2 Scenario 72
13.3 Data 72
13.4 Analysis 73
13.4.1 How Is the Analysis Carried Out? 73
13.4.2 Interpretation 74
13.5 Conclusion 75
14 REPEATED-MEASURES ANALYSIS OF VARIANCE 77
14.1 Introduction 77
14.2 Scenario 78
14.3 Data 78
14.4 Analysis 78
14.4.1 How Is the Analysis Carried Out? 78
14.4.2 Interpretation 78
14.4.3 Repeated-Measures Design and Post Hoc Tests 80
14.5 Conclusion 80
15 CORRELATION OF TWO VARIABLES 81
15.1 Introduction 81
15.2 Naming Variables 82
15.3 Scenario 82
15.4 Data 83
15.5 Analysis 83
15.5.1 How Is the Analysis Carried Out? 83
15.5.2 Interpretation 83
15.6 Limitations of r 85
15.7 Conclusion 86
16 LIMITS OF AGREEMENT 87
16.1 Introduction 87
16.2 Scenario 88
16.3 Data 88
16.4 Analysis 88
16.4.1 Theory 88
16.4.2 How Is the Analysis Carried Out? 89
16.4.3 Interpretation 90
16.5 Conclusion 90
CONTENTS
17 NONPARAMETRIC CORRELATION COEFFICIENTS 91
17.1 Introduction 91
17.2 Bivariate Normal Distribution 91
17.3 Scenario 92
17.4 Data 92
17.5 Analysis: Spearman s Rank Correlation (p, rs) 93
17.5.1 How Is the Analysis Carried Out? 93
17.5.2 Interpretation 94
17.6 Analysis: Kendall s Rank Correlation (x) 94
17.7 Analysis: Gamma (y) 94
17.8 Conclusion 94
18 FITTING A REGRESSION LINE TO DATA 95
18.1 Introduction 95
18.2 Line of Best Fit 96
18.3 Scenario 97
18.4 Data 98
18.5 Analysis: Fitting the Line 98
18.6 Analysis: Goodness of Fit of the Line to the Points 98
18.6.1 Coefficient of Determination (r2) 98
18.6.2 Analysis of Variance 99
18.6.3 t Test of Slope of Regression Line
100
18.7 Conclusion 10°
19 USING A REGRESSION UNE FOR PREDICTION AND
CAUBRATION 101
19.1 Introduction 1°1
19.2 Types of Prediction Problem 101
19.3 Scenario 102
19.4 Data 102
19.5 Analysis 102
19.5.1 Fitting the Regression Line
19.5.2 Confidence Intervals for a Regression Line
19.5.3 Interpretation l04
19.6 Conclusion 104
20 COMPARISON OF REGRESSION LINES 105
20.1 Introduction J05
20.2 Scenario l05
20.3 Data 106
102
103
CONTENTS
Xi
20.4 Analysis
20.4.1 How Is the Analysis Carried Out?
20.4.2 Interpretation
20.5 Conclusion
106
106
107
108
21 NONLINEAR REGRESSION: FITTING AN EXPONENTIAL
22
CURVE 109
21.1 Introduction 109
21.2 Common Types of Curve 110
21.3 Scenario 111
21.4 Data 111
21.5 Analysis 112
21.5.1 How Is the Analysis Carried Out? 112
21.5.2 Interpretation 112
21.6 Conclusion 112
NONLINEAR REGRESSION: FITTING A GENERAL
POLYNOMIAL-TYPE CURVE 113
22.1 Introduction 113
22.2 Scenario A: Does a Curve Fit Better Than a Straight Line? 114
22.3 Data 114
22.4 Analysis 114
22.4.1 How Is the Analysis Carried Out? 114
22.4.2 Interpretation 115
22.5 Scenario B: Fitting a General Polynomial-Type Curve 115
22.6 Data 116
22.7 Analysis 117
22.7.1 How Is the Analysis Carried Out? 117
22.7.2 Interpretation 117
22.8 Conclusion 118
23 NONUNEAR REGRESSION: FITTING A LOGISTK
GROWTH CURVE
23.1 Introduction
23.2 Scenario
23.3 Data
23.4 Analysis: Nonlinear Estimation Methods
23.4.1 How b the Analysis Carried Out?
23.4.2 Interpretation
23.6 Conclusion
119
119
119
120
120
120
121
122
Xjj CONTENTS
24 NONPARAMETRIC ANALYSIS OF VARIANCE 123
24.1 Introduction 123
24.2 Scenario 123
24.3 Analysis: Kruskal-Wallis Test 124
24.3.1 Data 124
24.3.2 How Is the Analysis Carried Out? 124
24.3.3 Interpretation 125
24.4 Analysis: Friedmann s Test 125
24.4.1 Data 125
24.4.2 How Is the Analysis Carried Out? 126
24.4.3 Interpretation 126
24.5 Conclusion 126
25 MULTIPLE LINEAR REGRESSION 127
25.1 Introduction 127
25.2 Scenario 128
25.3 Data 128
25.4 Analysis 129
25.4.1 Theory 129
25.4.2 Goodness-of-Fit Test of the Points to the Regression
Plane 131
25.4.3 Multiple Correlation Coefficient (R) 131
25.4.4 Regression Coefficients 131
25.4.5 Interpretation 132
25.5 Conclusion 132
26 STEPWISE MULTIPLE REGRESSION 135
26.1 Introduction 135
26.2 Scenario 136
26.3 Data 136
22.4 Analysis by the Step-Up Method 136
26.4.1 How Is the Analysis Carried Out? 136
26.4.2 Interpretation 137
26.4.3 Step-Down Method 137
26.5 Conclusion 138
27 CLASSIFICATION AND DENDROGRAMS 139
27.1 IntroductioB 139
27.2 Scenario 140
27.3 Data 140
CONTENTS
XIII
27.4 Analysis
27.4.1 Theory
27.4.2 How Is the Analysis Carried Out?
27.4.3 Interpretation
27.5 Conclusion
140
140
142
142
144
28 FACTOR ANALYSIS AND PRINCIPAL COMPONENTS ANALYSIS 145
28.1 Introduction 145
28.2 Scenario 146
28.3 Data 146
28.4 Analysis: Theory 147
28.5 Analysis: How Is the Analysis Carried Out? 148
28.5.1 Correlation Matrix 148
28.5.2 Statistical Tests on the Correlation Coefficient Matrix 148
28.5.3 Extraction of Principal Components 149
28.5.4 Stopping Rules 149
28.5.5 Factor Loadings 149
28.5.6 What Do the Extracted Factors Mean? 149
28.5.7 Interpretation 150
28.6 Conclusion 152
References
Appendix 1 Which Test to Use: Table
Appendix 2 Which Test to Use: Key
Appendix 3 Glossary of Statistical Terms and
Their Abbreviations
Appendix 4 Summary of Sample Size Procedures for
Different Statistical Tests
Index of Statistical Tests and Procedures
153
157
159
163
167
169
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| spelling | Armstrong, Richard A. Verfasser aut Statistical analysis in microbiology statnotes Richard A. Armstrong and Anthony C. Hilton Hoboken Wiley-Blackwell 2011 XIII, 166 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Microbiology / Statistical methods Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Mikrobiologie (DE-588)4316357-9 gnd rswk-swf Mikrobiologie (DE-588)4316357-9 s Statistische Analyse (DE-588)4116599-8 s DE-604 Hilton, Anthony C. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020784953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Armstrong, Richard A. Hilton, Anthony C. Statistical analysis in microbiology statnotes Microbiology / Statistical methods Statistische Analyse (DE-588)4116599-8 gnd Mikrobiologie (DE-588)4316357-9 gnd |
| subject_GND | (DE-588)4116599-8 (DE-588)4316357-9 |
| title | Statistical analysis in microbiology statnotes |
| title_auth | Statistical analysis in microbiology statnotes |
| title_exact_search | Statistical analysis in microbiology statnotes |
| title_full | Statistical analysis in microbiology statnotes Richard A. Armstrong and Anthony C. Hilton |
| title_fullStr | Statistical analysis in microbiology statnotes Richard A. Armstrong and Anthony C. Hilton |
| title_full_unstemmed | Statistical analysis in microbiology statnotes Richard A. Armstrong and Anthony C. Hilton |
| title_short | Statistical analysis in microbiology |
| title_sort | statistical analysis in microbiology statnotes |
| title_sub | statnotes |
| topic | Microbiology / Statistical methods Statistische Analyse (DE-588)4116599-8 gnd Mikrobiologie (DE-588)4316357-9 gnd |
| topic_facet | Microbiology / Statistical methods Statistische Analyse Mikrobiologie |
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