Statistics for terrified biologists:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Malden, MA [u.a.]
Blackwell
2008
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 343 S. graph. Darst. |
| ISBN: | 9781405149563 |
Staff View
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| 100 | 1 | |a Emden, Helmut Fritz van |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistics for terrified biologists |c Helmut F. van Emden |
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| adam_text |
Titel: Statistics for terrified biologists
Autor: Van Emden, Helmut F
Jahr: 2008
Contents
Preface xiii
1 How to use this book 1
Introduction 1
The text of the chapters 1
What should you do if you run into trouble? 2
Elephants 3
The numerical examples in the text 3
Boxes 3
Spare-time activities 4
Executive summaries 4
Why go to all that bother? 4
The bibliography 6
2 Introduction 8
What are statistics? 8
Notation 8
Notation for calculating the mean 10
3 Summarizing variation 12
Introduction 12
Different summaries of variation 13
Range 13
Total deviation 13
Mean deviation 1 3
Variance 14
Whyn-1? 16
Why the squared deviations? 17
The standard deviation 18
The next chapter 20
Spare-time activities 20
vi Contents
4 When are sums of squares NOT sums of squares? 21
Introduction 21
Calculating machines offer a quicker method of calculating
sums of squares 21
Added squares 21
The correction factor 22
Avoid being confused by the term "sum of squares" 22
Summary of the calculator method of calculating down to
standard deviation 2 3
Spare-time activities 24
5 The normal distribution 25
Introduction 2 5
Frequency distributions 2 5
The normal distribution 26
What per cent is a standard deviation worth? 2 7
Are the percentages always the same as these? 29
Other similar scales in everyday life 30
The standard deviation as an estimate of the frequency
of a number occurring in a sample 31
From per cent to probability 31
Executive summary 1 -- The standard deviation 3 3
6 The relevance of the normal distribution to
biological data 3 S
To recap 3 5
Is our observed distribution normal? 36
Checking for normality 3 7
What can we do about a distribution that clearly is not normal? 3 8
Transformation 3 8
Grouping samples 40
Doing nothing! 40
How many samples are needed? 40
Factors affecting how many samples we should take 41
Calculating how many samples are needed 41
7 Further calculations from the normal distribution 42
Introduction 42
Is "A" bigger than "B"? 42
The yardstick for deciding 43
Derivation of the standard error of a difference between
two means 4 5
Step 1 - from variance of single data to variance of means 45
Contents vii
Step 2 - from variance of single data to "variance of
differences" 48
Step 3 - the combination of Steps 1 and 2 ; the standard
error of difference between means (s.e.d.m.) 49
Recap of the calculation of s.e.d.m. from the variance
calculated from the individual values 51
The importance oí the standard error of differences between
means 52
Summary of this chapter 52
Executive summary 2 - Standard error of a difference
between two means 56
Spare-time activities 5 7
8 Thei-test 58
Introduction 58
The principle of the i-test 5 8
The t-test in statistical terms 59
Why i? 60
Tables of the t-distribution 61
The standard £-test 64
The procedure 64
The actual i-test 69
i-test for means associated with unequal variances 69
The s.e.d.m. when variances are unequal 70
A worked example of the t-test for means associated
with unequal variances 73
The paired t-test 75
Pair when possible 78
Executive summary 3 - The i-test 80
Spare-time activities 82
9 One tail or two? 83
Introduction 8 3
Why is the analysis of variance F-test one-tailed? 83
The two-tailed F-test 84
How many tails has the t-test? 86
The final conclusion on number of tails 8 7
10 Analysis of variance - What is it? How does it work? 88
Introduction 88
Sums of squares in the analysis of variance 89
Some "made-up" variation to analyze by Anova 89
The sum of squares table 91
viii Contents
Using Anova to sort out the variation in Table C
Phase 1
Phase 2
SqADS - an important acronym
Back to the sum of squares table
How well does the analysis reflect the input?
End Phase
Degrees of freedom in Anova
The completion of the End Phase
The variance ratio
The relationship between "t" and "F"
Constraints on the analysis of variance
Adequate size of experiment
Equality of variance between treatments
Testing the homogeneity of variance
The element of chance: randomization
Comparison between treatment means in the analysis of
variance
The least significant difference
A caveat about using the LSD
Executive summary 4 - The principle of the analysis of variance
11 Experimental designs for analysis of variance
Introduction
Fully randomized
Data for analysis of a fully randomized experiment
Prelims
Phase 1
Phase 2
End Phase
Randomized blocks
Data for analysis of a randomized block experiment
Prelims
Phase 1
Phase 2
End Phase
Incomplete blocks
Latin square
Data for the analysis of a Latin square
Prelims
Phase 1
Phase 2
91
91
92
93
96
96
97
97
99
100
101
103
103
103
104
104
107
108
110
111
115
115
116
117
117
118
118
120
121
123
123
125
126
127
127
130
131
132
134
134
Contents ix
End Phase 135
Further comments on the Latin square design 136
Split plot 137
Executive summary 5 - Analysis of a randomized block
experiment 139
Spare-time activities 141
12 Introduction to factorial experiments 143
What is a factorial experiment? 143
Interaction 145
If there is no interaction 145
What if there is interaction? 147
How about a biological example? 148
Measuring any interaction between factors is often the
main/only purpose of an experiment 148
How does a factorial experiment change the form of the
analysis of variance? 150
Degrees of freedom for interactions 150
The similarity between the "residual" in Phase 2 and
the "interaction" in Phase 3 151
Sums of squares for interactions 152
13 2-Factor factorial experiments 154
Introduction 154
An example of a 2-factor experiment 154
Analysis of the 2-factor experiment 155
Prelims 155
Phase 1 156
Phase 2 156
End Phase (of Phase 2) 157
Phase 3 158
End Phase (of Phase 3) 162
Two important things to remember about factorials before
tackling the next chapter 163
Analysis of factorial experiments with unequal replication 163
Executive summary 6 - Analysis of a 2-factor randomized
block experiment 166
Spare-time activity 169
14 Factorial experiments with more than two factors 170
Introduction 170
Different "orders" of interaction 171
x Contents
Example of a 4-factor experiment 172
Prelims 173
Phase 1 175
Phase 2 175
Phase 3 176
To the End Phase 183
Addendum - Additional working of sums of squares calculations 186
Spare-time activity 192
15 Factorial experiments with split plots 194
Introduction 194
Deriving the split plot design from the randomized block design 195
Degrees of freedom in a split plot analysis 198
Main plots 198
Sub-plots 198
Numerical example of a split plot experiment and its analysis 201
Calculating the sums of squares 202
End Phase 205
Comparison of split plot and randomized block experiment 206
Uses of split plot designs 209
Spare-time activity 211
16 The t-test in the analysis of variance 213
Introduction 213
Brief recap of relevant earlier sections of this book 214
Least significant difference test 215
Multiple range tests 216
Operating the multiple range test 217
Testing differences between means 222
Suggested "rules" for testing differences between means 222
Presentation of the results of tests of differences between means 223
The results of the experiments analyzed by analysis of
variance in Chapters 11-15 225
Spare-time activities 236
17 Linear regression and correlation 238
Introduction 238
Cause and effect 239
Other traps waiting for you to fall into 239
Extrapolating beyond the range of your data 239
Is a straight line appropriate? 239
The distribution of variability 244
Contents xi
Regression
Independent and dependent variables
The regression coefficient (b)
Calculating the regression coefficient (b)
The regression equation
A worked example on some real data
The data (Box 17.2)
Calculating the regression coefficient (b) - i.e.
the slope of the regression line
Calculating the intercept (a)
Drawing the regression line
Testing the significance of the slope (b) of the regression
How well do the points fit the line? - the coefficient of
determination (r2
)
Correlation
Derivation of the correlation coefficient (r)
An example of correlation
Is there a correlation line?
Extensions of regression analysis
Nonlinear regression
Multiple linear regression
Multiple nonlinear regression
Analysis of covariance
Executive summary 7 - Linear regression
Spare-time activities
18 Chi-square tests
Introduction
When and where not to use x2
The problem of low frequencies
Yates' correction for continuity
The x2
test for "goodness of fit"
The case of more than two classes
X2
with heterogeneity
Heterogeneity x2
analysis with "covariance"
Association (or contingency) x2
2 x 2 contingency table
Fisher's exact test for a 2 x 2 table
Larger contingency tables
Interpretation of contingency tables
Spare-time activities
244
245
247
248
253
255
255
256
257
257
258
262
263
263
264
266
266
269
270
272
272
274
276
277
277
278
279
279
280
282
284
286
289
289
291
292
293
294
xii Contents
19 Nonparametric methods (what are they?)
Disclaimer
Introduction
Advantages and disadvantages of the two approaches
Where nonparametric methods score
Where parametric methods score
Some ways data are organized for nonparametric tests
The sign test
The Kruskal--Wallis analysis of ranks
Kendall's rank correlation coefficient
The main nonparametric methods that are available
Appendix 1 How many replicates
Appendix 2 Statistical tables
Appendix 3 Solutions to "Spare-time activities"
Appendix 4 Bibliography
Index
296
296
296
298
298
299
300
300
301
302
303
306
314
321
337
339 |
| adam_txt |
Titel: Statistics for terrified biologists
Autor: Van Emden, Helmut F
Jahr: 2008
Contents
Preface xiii
1 How to use this book 1
Introduction 1
The text of the chapters 1
What should you do if you run into trouble? 2
Elephants 3
The numerical examples in the text 3
Boxes 3
Spare-time activities 4
Executive summaries 4
Why go to all that bother? 4
The bibliography 6
2 Introduction 8
What are statistics? 8
Notation 8
Notation for calculating the mean 10
3 Summarizing variation 12
Introduction 12
Different summaries of variation 13
Range 13
Total deviation 13
Mean deviation 1 3
Variance 14
Whyn-1? 16
Why the squared deviations? 17
The standard deviation 18
The next chapter 20
Spare-time activities 20
vi Contents
4 When are sums of squares NOT sums of squares? 21
Introduction 21
Calculating machines offer a quicker method of calculating
sums of squares 21
Added squares 21
The correction factor 22
Avoid being confused by the term "sum of squares" 22
Summary of the calculator method of calculating down to
standard deviation 2 3
Spare-time activities 24
5 The normal distribution 25
Introduction 2 5
Frequency distributions 2 5
The normal distribution 26
What per cent is a standard deviation worth? 2 7
Are the percentages always the same as these? 29
Other similar scales in everyday life 30
The standard deviation as an estimate of the frequency
of a number occurring in a sample 31
From per cent to probability 31
Executive summary 1 -- The standard deviation 3 3
6 The relevance of the normal distribution to
biological data 3 S
To recap 3 5
Is our observed distribution normal? 36
Checking for normality 3 7
What can we do about a distribution that clearly is not normal? 3 8
Transformation 3 8
Grouping samples 40
Doing nothing! 40
How many samples are needed? 40
Factors affecting how many samples we should take 41
Calculating how many samples are needed 41
7 Further calculations from the normal distribution 42
Introduction 42
Is "A" bigger than "B"? 42
The yardstick for deciding 43
Derivation of the standard error of a difference between
two means 4 5
Step 1 - from variance of single data to variance of means 45
Contents vii
Step 2 - from variance of single data to "variance of
differences" 48
Step 3 - the combination of Steps 1 and 2 ; the standard
error of difference between means (s.e.d.m.) 49
Recap of the calculation of s.e.d.m. from the variance
calculated from the individual values 51
The importance oí the standard error of differences between
means 52
Summary of this chapter 52
Executive summary 2 - Standard error of a difference
between two means 56
Spare-time activities 5 7
8 Thei-test 58
Introduction 58
The principle of the i-test 5 8
The t-test in statistical terms 59
Why i? 60
Tables of the t-distribution 61
The standard £-test 64
The procedure 64
The actual i-test 69
i-test for means associated with unequal variances 69
The s.e.d.m. when variances are unequal 70
A worked example of the t-test for means associated
with unequal variances 73
The paired t-test 75
Pair when possible 78
Executive summary 3 - The i-test 80
Spare-time activities 82
9 One tail or two? 83
Introduction 8 3
Why is the analysis of variance F-test one-tailed? 83
The two-tailed F-test 84
How many tails has the t-test? 86
The final conclusion on number of tails 8 7
10 Analysis of variance - What is it? How does it work? 88
Introduction 88
Sums of squares in the analysis of variance 89
Some "made-up" variation to analyze by Anova 89
The sum of squares table 91
viii Contents
Using Anova to sort out the variation in Table C
Phase 1
Phase 2
SqADS - an important acronym
Back to the sum of squares table
How well does the analysis reflect the input?
End Phase
Degrees of freedom in Anova
The completion of the End Phase
The variance ratio
The relationship between "t" and "F"
Constraints on the analysis of variance
Adequate size of experiment
Equality of variance between treatments
Testing the homogeneity of variance
The element of chance: randomization
Comparison between treatment means in the analysis of
variance
The least significant difference
A caveat about using the LSD
Executive summary 4 - The principle of the analysis of variance
11 Experimental designs for analysis of variance
Introduction
Fully randomized
Data for analysis of a fully randomized experiment
Prelims
Phase 1
Phase 2
End Phase
Randomized blocks
Data for analysis of a randomized block experiment
Prelims
Phase 1
Phase 2
End Phase
Incomplete blocks
Latin square
Data for the analysis of a Latin square
Prelims
Phase 1
Phase 2
91
91
92
93
96
96
97
97
99
100
101
103
103
103
104
104
107
108
110
111
115
115
116
117
117
118
118
120
121
123
123
125
126
127
127
130
131
132
134
134
Contents ix
End Phase 135
Further comments on the Latin square design 136
Split plot 137
Executive summary 5 - Analysis of a randomized block
experiment 139
Spare-time activities 141
12 Introduction to factorial experiments 143
What is a factorial experiment? 143
Interaction 145
If there is no interaction 145
What if there is interaction? 147
How about a biological example? 148
Measuring any interaction between factors is often the
main/only purpose of an experiment 148
How does a factorial experiment change the form of the
analysis of variance? 150
Degrees of freedom for interactions 150
The similarity between the "residual" in Phase 2 and
the "interaction" in Phase 3 151
Sums of squares for interactions 152
13 2-Factor factorial experiments 154
Introduction 154
An example of a 2-factor experiment 154
Analysis of the 2-factor experiment 155
Prelims 155
Phase 1 156
Phase 2 156
End Phase (of Phase 2) 157
Phase 3 158
End Phase (of Phase 3) 162
Two important things to remember about factorials before
tackling the next chapter 163
Analysis of factorial experiments with unequal replication 163
Executive summary 6 - Analysis of a 2-factor randomized
block experiment 166
Spare-time activity 169
14 Factorial experiments with more than two factors 170
Introduction 170
Different "orders" of interaction 171
x Contents
Example of a 4-factor experiment 172
Prelims 173
Phase 1 175
Phase 2 175
Phase 3 176
To the End Phase 183
Addendum - Additional working of sums of squares calculations 186
Spare-time activity 192
15 Factorial experiments with split plots 194
Introduction 194
Deriving the split plot design from the randomized block design 195
Degrees of freedom in a split plot analysis 198
Main plots 198
Sub-plots 198
Numerical example of a split plot experiment and its analysis 201
Calculating the sums of squares 202
End Phase 205
Comparison of split plot and randomized block experiment 206
Uses of split plot designs 209
Spare-time activity 211
16 The t-test in the analysis of variance 213
Introduction 213
Brief recap of relevant earlier sections of this book 214
Least significant difference test 215
Multiple range tests 216
Operating the multiple range test 217
Testing differences between means 222
Suggested "rules" for testing differences between means 222
Presentation of the results of tests of differences between means 223
The results of the experiments analyzed by analysis of
variance in Chapters 11-15 225
Spare-time activities 236
17 Linear regression and correlation 238
Introduction 238
Cause and effect 239
Other traps waiting for you to fall into 239
Extrapolating beyond the range of your data 239
Is a straight line appropriate? 239
The distribution of variability 244
Contents xi
Regression
Independent and dependent variables
The regression coefficient (b)
Calculating the regression coefficient (b)
The regression equation
A worked example on some real data
The data (Box 17.2)
Calculating the regression coefficient (b) - i.e.
the slope of the regression line
Calculating the intercept (a)
Drawing the regression line
Testing the significance of the slope (b) of the regression
How well do the points fit the line? - the coefficient of
determination (r2
)
Correlation
Derivation of the correlation coefficient (r)
An example of correlation
Is there a correlation line?
Extensions of regression analysis
Nonlinear regression
Multiple linear regression
Multiple nonlinear regression
Analysis of covariance
Executive summary 7 - Linear regression
Spare-time activities
18 Chi-square tests
Introduction
When and where not to use x2
The problem of low frequencies
Yates' correction for continuity
The x2
test for "goodness of fit"
The case of more than two classes
X2
with heterogeneity
Heterogeneity x2
analysis with "covariance"
Association (or contingency) x2
2 x 2 contingency table
Fisher's exact test for a 2 x 2 table
Larger contingency tables
Interpretation of contingency tables
Spare-time activities
244
245
247
248
253
255
255
256
257
257
258
262
263
263
264
266
266
269
270
272
272
274
276
277
277
278
279
279
280
282
284
286
289
289
291
292
293
294
xii Contents
19 Nonparametric methods (what are they?)
Disclaimer
Introduction
Advantages and disadvantages of the two approaches
Where nonparametric methods score
Where parametric methods score
Some ways data are organized for nonparametric tests
The sign test
The Kruskal--Wallis analysis of ranks
Kendall's rank correlation coefficient
The main nonparametric methods that are available
Appendix 1 How many replicates
Appendix 2 Statistical tables
Appendix 3 Solutions to "Spare-time activities"
Appendix 4 Bibliography
Index
296
296
296
298
298
299
300
300
301
302
303
306
314
321
337
339 |
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| discipline_str_mv | Biologie Agrarwissenschaft Mathematik |
| edition | 1. publ. |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV023231981 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:20:13Z |
| indexdate | 2024-07-20T07:52:49Z |
| institution | BVB |
| isbn | 9781405149563 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016417685 |
| oclc_num | 253917675 |
| open_access_boolean | |
| owner | DE-M49 DE-BY-TUM DE-29T DE-19 DE-BY-UBM DE-20 DE-11 DE-188 DE-B16 DE-703 DE-355 DE-BY-UBR |
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| physical | XV, 343 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Blackwell |
| record_format | marc |
| spelling | Emden, Helmut Fritz van Verfasser aut Statistics for terrified biologists Helmut F. van Emden 1. publ. Malden, MA [u.a.] Blackwell 2008 XV, 343 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Biometry Textbooks Biostatistik (DE-588)4729990-3 gnd rswk-swf Biologie (DE-588)4006851-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Biologie (DE-588)4006851-1 s Statistik (DE-588)4056995-0 s DE-604 Biostatistik (DE-588)4729990-3 s b DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016417685&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Emden, Helmut Fritz van Statistics for terrified biologists Biometry Textbooks Biostatistik (DE-588)4729990-3 gnd Biologie (DE-588)4006851-1 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4729990-3 (DE-588)4006851-1 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Statistics for terrified biologists |
| title_auth | Statistics for terrified biologists |
| title_exact_search | Statistics for terrified biologists |
| title_exact_search_txtP | Statistics for terrified biologists |
| title_full | Statistics for terrified biologists Helmut F. van Emden |
| title_fullStr | Statistics for terrified biologists Helmut F. van Emden |
| title_full_unstemmed | Statistics for terrified biologists Helmut F. van Emden |
| title_short | Statistics for terrified biologists |
| title_sort | statistics for terrified biologists |
| topic | Biometry Textbooks Biostatistik (DE-588)4729990-3 gnd Biologie (DE-588)4006851-1 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Biometry Textbooks Biostatistik Biologie Statistik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016417685&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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