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ОбложкаMcKillup S. Statistics explained: an introductory guide for life scientists. - 2nd ed. - Cambridge; New York: Cambridge University Press, 2011 (2012). - xiv, 403 p.: ill. - Ref.: p.394-395. - Ind.: p.396-403. - ISBN 978-0-521-18328-4
Шифр: (И/Е-М44) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
   Preface ................................................... xiii

1  Introduction ................................................. 1
   1.1  Why do life scientists need to know about experimental
        design and statistics? .................................. 1
   1.2  What is this book designed to do? ....................... 5
2  Doing science: hypotheses, experiments and disproof .......... 7
   2.1  Introduction ............................................ 7
   2.2  Basic scientific method ................................. 7
   2.3  Making a decision about an hypothesis .................. 11
   2.4  Why can't an hypothesis or theory ever be proven? ...... 11
   2.5  'Negative' outcomes .................................... 12
   2.6  Null and alternate hypotheses .......................... 12
   2.7  Conclusion ............................................. 14
   2.8  Questions .............................................. 14
3  Collecting and displaying data .............................. 15
   3.1  Introduction ........................................... 15
   3.2  Variables, experimental units and types of data ........ 15
   3.3  Displaying data ........................................ 17
   3.4  Displaying ordinal or nominal scale data ............... 23
   3.5  Bivariate data ......................................... 25
   3.6  Multivariate data ...................................... 26
   3.7  Summary and conclusion ................................. 28
4  Introductory concepts of experimental design ................ 29
   4.1  Introduction ........................................... 29
   4.2  Sampling - mensurative experiments ..................... 30
   4.3  Manipulative experiments ............................... 34
   4.4  Sometimes you can only do an unreplicated experiment ... 41
   4.1  Realism ................................................ 42
   4.6  A bit of common sense .................................. 43
   4.7  Designing a 'good' experiment .......................... 44
   4.8  Reporting your results ................................. 45
   4.9  Summary and conclusion ................................. 46
   4.10 Questions .............................................. 46
5  Doing science responsibly and ethically ..................... 48
   5.1  Introduction ........................................... 48
   5.2  Dealing fairly with other people's work ................ 48
   5.3  Doing the experiment ................................... 50
   5.4  Evaluating and reporting results ....................... 52
   5.5  Quality control in science ............................. 53
   5.6  Questions .............................................. 54
6  Probability helps you make a decision about your results .... 56
   6.1  Introduction ........................................... 56
   6.2  Statistical tests and significance levels .............. 57
   6.3  What has this got to do with making a decision about
        your results? .......................................... 60
   6.4  Making the wrong decision .............................. 60
   6.5  Other probability levels ............................... 61
   6.6  How are probability values reported? ................... 62
   6.7  All statistical tests do the same basic thing .......... 63
   6.8  A very simple example - the chi-square test for
        goodness of fit ........................................ 64
   6.9  What if you get a statistic with a probability
        of exactly 0.05? ....................................... 66
   6.10 Statistical significance and biological significance ... 67
   6.11 Summary and conclusion ................................. 69
   6.12 Questions .............................................. 70
7  Probability explained ....................................... 71
   7.1  Introduction ........................................... 71
   7.2  Probability ............................................ 71
   7.3  The addition rule ...................................... 71
   7.4  The multiplication rule for independent events ......... 72
   7.5  Conditional probability ................................ 75
   7.6  Applications of conditional probability ................ 77
8  Using the normal distribution to make statistical
   decisions ................................................... 87
   8.1  Introduction ........................................... 87
   8.2  The normal curve ....................................... 87
   8.3  Two statistics describe a normal distribution .......... 89
   8.4  Samples and populations ................................ 93
   8.5  The distribution of sample means is also normal ........ 95
   8.6  What do you do when you only have data from one
        sample? ................................................ 99
   8.7  Use of the 95% confidence interval in significance
        testing ............................................... 102
   8.8  Distributions that are not normal ..................... 102
   8.9  Other distributions ................................... 103
   8.10 Other statistics that describe a distribution ......... 105
   8.11 Summary and conclusion ................................ 106
   8.12 Questions ............................................. 106
9  Comparing the means of one and two samples of normally
   distributed data ........................................... 108
   9.1  Introduction .......................................... 108
   9.2  The 95% confidence interval and 95% confidence
        limits ................................................ 108
   9.3  Using the Z statistic to compare a sample mean and
        population mean when population statistics are known .. 108
   9.4  Comparing a sample mean to an expected value when
        population statistics are not known ................... 112
   9.5  Comparing the means of two related samples ............ 116
   9.6  Comparing the means of two independent samples ........ 118
   9.7  One-tailed and two-tailed tests ....................... 121
   9.8  Are your data appropriate for a t test? ............... 124
   9.9  Distinguishing between data that should be analysed
        by a paired sample test and a test for two
        independent samples ................................... 125
   9.10 Reporting the results of t tests ...................... 126
   9.11 Conclusion ............................................ 127
   9.12 Questions ............................................. 128
10 Type 1 error and Type 2 error, power and sample size ....... 130
   10.1 Introduction .......................................... 130
   10.2 Type 1 error .......................................... 130
   10.3 Type 2 error .......................................... 131
   10.4 The power of a test ................................... 135
   10.5 What sample size do you need to ensure the risk of
        Type 2 error is not too high? ......................... 135
   10.6 Type 1 error, Type 2 error and the concept of
        biological risk ....................................... 136
   10.7 Conclusion ............................................ 138
   10.8 Questions ............................................. 139
11 Single-factor analysis of variance ......................... 140
   11.1 Introduction .......................................... 140
   11.2 The concept behind analysis of variance ............... 141
   11.3 More detail and an arithmetic example ................. 147
   11.4 Unequal sample sizes (unbalanced designs) ............. 152
   11.5 An ANOVA does not tell you which particular
        treatments appear to be from different populations .... 153
   11.6 Fixed or random effects ............................... 153
   11.7 Reporting the results of a single-factor ANOVA ........ 154
   11.8 Summary ............................................... 154
   11.9 Questions ............................................. 155
12 Multiple comparisons after ANOVA ........................... 157
   12.1 Introduction .......................................... 157
   12.2 Multiple comparison tests after a Model I ANOVA ....... 157
   12.3 An a posteriori Tukey comparison following
        a significant result for a single-factor Model I
        ANOVA ................................................. 160
   12.4 Other a posteriori multiple comparison tests .......... 162
   12.5 Planned comparisons ................................... 162
   12.6 Reporting the results of a posteriori comparisons ..... 164
   12.7 Questions ............................................. 166
13 Two-factor analysis of variance ............................ 168
   13.1 Introduction .......................................... 168
   13.2 What does a two-factor ANOVA do? ...................... 170
   13.3 A pictorial example ................................... 174
   13.4 How does a two-factor ANOVA separate out the effects
        of each factor and interaction? ....................... 176
   13.5 An example of a two-factor analysis of variance ....... 180
   13.6 Some essential cautions and important complications ... 181
   13.7 Unbalanced designs .................................... 192
   13.8 More complex designs .................................. 192
   13.9 Reporting the results of a two-factor ANOVA ........... 193
   13.10 Questions ............................................ 194
14 Important assumptions of analysis of variance,
   transformations, and a test for equality of variances ...... 196
   14.1 Introduction .......................................... 196
   14.2 Homogeneity of variances .............................. 196
   14.3 Normally distributed data ............................. 197
   14.4 Independence .......................................... 201
   14.5 Transformations ....................................... 201
   14.6 Are transformations legitimate? ....................... 203
   14.7 Tests for heteroscedasticity .......................... 204
   14.8 Reporting the results of transformations and the
        Levene test ........................................... 205
   14.9 Questions ............................................. 207
15 More complex ANOVA ......................................... 209
   15.1 Introduction .......................................... 209
   15.2 Two-factor ANOVA without replication .................. 209
   15.3 A posteriori comparison of means after a two-factor
        ANOVA without replication ............................. 214
   15.4 Randomised blocks ..................................... 214
   15.5 Repeated-measures ANOVA ............................... 216
   15.6 Nested ANOVA as a special case of a single-factor
        ANOVA ................................................. 222
   15.7 A final comment on ANOVA - this book is only an
        introduction .......................................... 229
   15.8 Reporting the results of two-factor ANOVA without
        replication, randomised blocks design,
        repeated-measures ANOVA and nested ANOVA .............. 229
   15.9 Questions ............................................. 230
16 Relationships between variables: correlation and
   regression ................................................. 233
   16.1 Introduction .......................................... 233
   16.2 Correlation contrasted with regression ................ 234
   16.3 Linear correlation .................................... 234
   16.4 Calculation of the Pearson r statistic ................ 235
   16.5 Is the value of r statistically significant? .......... 241
   16.6 Assumptions of linear correlation ..................... 241
   16.7 Summary and conclusion ................................ 242
   16.8 Questions ............................................. 242
17 Regression ................................................. 244
   17.1 Introduction .......................................... 244
   17.2 Simple linear regression .............................. 244
   17.3 Calculation of the slope of the regression line ....... 246
   17.4 Calculation of the intercept with the Taxis ........... 249
   17.5 Testing the significance of the slope and the
        intercept ............................................. 250
   17.6 An example - mites that live in the hair follicles .... 258
   17.7 Predicting a value of Y from a value of X ............. 260
   17.8 Predicting a value of X from a value of Y ............. 260
   17.9 The danger of extrapolation ........................... 262
   17.10 Assumptions of linear regression analysis ............ 263
   17.11 Curvilinear regression ............................... 266
   17.12 Multiple linear regression ........................... 273
   17.13 Questions ............................................ 281
18 Analysis of covariance ..................................... 284
   18.1 Introduction .......................................... 284
   18.2 Adjusting data to remove the effect of a confounding
        factor ................................................ 285
   18.3 An arithmetic example ................................. 288
   18.4 Assumptions of ANCOVA and an extremely important
        caution about parallelism ............................. 289
   18.5 Reporting the results of ANCOVA ....................... 295
   18.6 More complex models ................................... 296
   18.7 Questions ............................................. 296
19 Non-parametric statistics .................................. 298
   19.1 Introduction .......................................... 298
   19.2 The danger of assuming normality when a population is
        grossly non-normal .................................... 298
   19.3 The advantage of making a preliminary inspection
        of the data ........................................... 300
20 Non-parametric tests for nominal scale data ................ 301
   20.1 Introduction .......................................... 301
   20.2 Comparing observed and expected frequencies: the
        chi-square test for goodness of fit ................... 302
   20.3 Comparing proportions among two or more independent
        samples ............................................... 305
   20.4 Bias when there is one degree of freedom .............. 308
   20.5 Three-dimensional contingency tables .................. 312
   20.6 Inappropriate use of tests for goodness of fit and
        heterogeneity ......................................... 312
   20.7 Comparing proportions among two or more related
        samples of nominal scale data ......................... 314
   20.8 Recommended tests for categorical data ................ 316
   20.9 Reporting the results of tests for categorical data ... 316
   20.10 Questions ............................................ 318
21 Non-parametric tests for ratio, interval or ordinal scale
   data ....................................................... 319
   21.1 Introduction .......................................... 319
   21.2 A non-parametric comparison between one sample and
        an expected distribution .............................. 320
   21.3 Non-parametric comparisons between two independent
        samples ............................................... 325
   21.4 Non-parametric comparisons among three or more
        independent samples ................................... 331
   21.5 Non-parametric comparisons of two related samples ..... 335
   21.6 Non-parametric comparisons among three or more
        related samples ....................................... 338
   21.7 Analysing ratio, interval or ordinal data that show
        gross differences in variance among treatments and
        cannot be satisfactorily transformed .................. 341
   21.8 Non-parametric correlation analysis ................... 342
   21.9 Other non-parametric tests ............................ 344
   21.10 Questions ............................................ 344
22 Introductory concepts of multivariate analysis ............. 346
   22.1 Introduction .......................................... 346
   22.2 Simplifying and summarising multivariate data ......... 347
   22.3 An R-mode analysis: principal components analysis ..... 348
   22.4 Q-mode analyses: multidimensional scaling ............. 361
   22.5 Q-mode analyses: cluster analysis ..................... 368
   22.6 Which multivariate analysis should you use? ........... 372
   22.7 Questions ............................................. 374
23 Choosing a test ............................................ 375
   23.1 Introduction .......................................... 375

   Appendix: Critical values of chi-square, t and F ........... 388
   References ................................................. 394
   Index ...................................................... 396

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