Experiments in ecology : their logical design and interpretation using analysis of variance / A. J. Underwood.
Editor: Cambridge : Cambridge University Press, c1997Descripción: xvii, 504 p. : il. ; 23 cmISBN: 0521556961 (pbk); 0521553296 (hbk)Otra clasificación: 62J10 (62P10 92D40)1 Introduction [1] 2 A framework for investigating biological patterns and processes [7] 2.1 Introduction [7] 2.2 Observations [8] 2.3 Models, theories, explanations [10] 2.3.1 Models of physiological stress [10] 2.3.2 Models based on competition [10] 2.3.3 Grazing models [10] 2.3.4 Models to do with hazards [11] 2.3.5 Models of failure of recruitment [11] 2.4 Numerous competing models [12] 2.5 Hypotheses, predictions [13] 2.6 Null hypotheses [15] 2.7 Experiments and their interpretation [16] 2.8 What to do next? [17] 2.9 Measurements, gathering data and a logical structure [19] 2.10 A consideration: why are you measuring things? [21] 2.11 Conclusion: a plea for more thought [22] 3 Populations, frequency distributions and samples [24] 3.1 Introduction [24] 3.2 Variability in measurements [24] 3.3 Observations and measurements as frequency distributions [25] 3.4 Defining the population to be observed [27] 3.5 The need for samples [30] 3.6 The location parameter [30] 3.7 Sample estimate of the location parameter [33] 3.8 The dispersion parameter [34] 3.9 Sample estimate of the dispersion parameter [36] 3.10 Degrees of freedom [37] 3.11 Representative sampling and accuracy of samples [38] 3.12 Other useful parameters [44] 3.12.1 Skewness [44] 3.12.2 Kurtosis [47] 4 Statistical tests of null hypotheses [50] 4.1 Why a statistical test? [50] 4.2 An example using coins [51] 4.3 The components of a statistical test [55] 4.3.1 Null hypothesis [55] 4.3.2 Test statistic [56] 4.3.3 Region of rejection and critical value [56] 4.4 Type I error or rejection of a true null hypothesis [57] 4.5 Statistical test of a theoretical biological example [58] 4.5.1 Transformation of a normal distribution to the standard normal distribution [59] 4.6 One- and two-tailed null hypotheses [62] 5 Statistical tests on samples [65] 5.1 Repeated sampling [65] 5.2 The standard error from the normal distribution of sample means [70] 5.3 Confidence intervals for a sampled mean [70] 5.4 Precision of a sample estimate of the mean [73] 5.5 A contrived example of use of the confidence interval of sampled means [74] 5.6 Student’s t-distribution [76] 5.7 Increasing precision of sampling [77] 5.7.1 The chosen probability used to construct the confidence interval [78] 5.7.2 The sample size (n) [78] 5.7.3 The variance of the population (σ2) [80] 5.8 Description of sampling [81] 5.9 Student’s t-test for a mensurative hypothesis [82] 5.10 Goodness-of-fit, mensurative experiments and logic [84] 5.11 Type I and Type II errors in relation to a null hypothesis [87] 5.12 Determining the power of a simple statistical test [91] 5.12.1 Probability of Type I error [92] 5.12.2 Size of experiment (n) [93] 5.12.3 Variance of the population [95] 5.12.4 ‘Effect size’ [97] 5.13 Power and alternative hypotheses [97] 6 Simple experiments comparing the means of two populations [100] 6.1 Paired comparisons [100] 6.2 Confounding and lack of controls [104] 6.3 Unpaired experiments [106] 6.4 Standard error of the difference between two means [107] 6.4.1 Independence of samples [108] 6.4.2 Homogeneity of variances [109] 6.5 Allocation of sample units to treatments [114] 6.6 Interpretation of a simple ecological experiment [118] 6.7 Power of an experimental comparison of two populations [124] 6.8 Alternative procedures [128] 6.8.1 Binomial (sign) test for paired data [128] 6.8.2 Other alternative procedures [130] 6.9 Are experimental comparisons of only two populations useful? [132] 6.9.1 The wrong population is being sampled [132] 6.9.2 Modifications to the t-test to compare more than two populations [137] 6.9.3 Conclusion [139] 7 Analysis of variance [140] 7.1 Introduction [140] 7.2 Data collected to test a single-factor null hypothesis [141] 7.3 Partitioning of the data: the analysis of variation [143] 7.4 A linear model [145] 7.5 What do the sums of squares measure? [149] 7.6 Degrees of freedom [152] 7.7 Mean squares and test statistic [153] 7.8 Solution to some problems raised earlier [154] 7.9 So what happens with real data? [155] 7.10 Unbalanced data [156] 7.11 Machine formulae [157] 7.12 Interpretation of the result [157] 7.13 Assumptions of analysis of variance [158] 7.14 Independence of data [159] 7.14.1 Positive correlation within samples [160] 7.14.2 Negative correlation within samples [166] 7.14.3 Negative correlation among samples [168] 7.14.4 Positive correlation among samples [172] 7.15 Dealing with non-independence [179] 7.16 Heterogeneity of variances [181] 7.16.1 Tests for heterogeneity of variances [183] 7.17 Quality control [184] 7.18 Transformations of data [187] 7.18.1 Square-root transformation of counts (or Poisson data) [188] 7.18.2 Log transformation for rates, ratios, concentrations and other data [189] 7.18.3 Arc-sin transformation of percentages and proportions [192] 7.18.4 No transformation is possible [192] 7.19 Normality of data [194] 7.20 The summation assumption [195] 8 More analysis of variance [198] 8.1 Fixed or random factors [198] 8.2 Interpretation of fixed or random factors [204] 8.3 Power of an analysis of a fixed factor [209] 8.3.1 Non-central F-ratio and power [209] 8.3.2 Influences of α, n, σ2e and Ai values [211] 8.3.3 Construction of an alternative hypothesis [214] 8.4 Power of an analysis of a random factor [216] 8.4.1 Central F-ratios and power [216] 8.4.2 Influences of α, n, σ2e , σ2A and a [218] 8.4.3 Construction of an alternative hypothesis [220] 8.5 Alternative analysis of ranked data [223] 8.6 Multiple comparisons to identify the alternative hypothesis [224] 8.6.1 Introduction [224] 8.6.2 Problems of excessive Type I error [225] 8.6.3 A priori versus a posteriori comparisons [226] 8.6.4 A priori procedures [227] 8.6.5 A posteriori comparisons [234] 9 Nested analyses of variance [243] 9.1 Introduction and need [243] 9.2 Hurlbert’s ‘pseudoreplication’ [245] 9.3 Partitioning of the data [245] 9.4 The linear model [250] 9.5 Degrees of freedom and mean squares [254] 9.6 Tests and interpretation: what do the nested bits mean? [259] 9.6.1 F-ratio of appropriate mean squares [259] 9.6.2 Solution to confounding [260] 9.6.3 Multiple comparisons [261] 9.6.4 Variability among replicated units [261] 9.7 Pooling of nested components [268] 9.7.1 Rationale and procedure [268] 9.7.2 Pooling, Type II and Type I errors [269] 9.8 Balanced sampling [273] 9.9 Nested analyses and spatial pattern [275] 9.10 Nested analysis and temporal pattern [279] 9.11 Cost-benefit optimization [283] 9.12 Calculation of power [289] 9.13 Residual variance and an ‘error’ term [291] 10 Factorial experiments [296] 10.1 Introduction [296] 10.2 Partitioning of variation when there are two experimental factors [300] 10.3 Appropriate null hypotheses for a two-factor experiment [305] 10.4 A linear model and estimation of components by mean squares [306] 10.5 Why do a factorial experiment? [312] 10.5.1 Information about interactions [313] 10.5.2 Efficiency and cost-effectiveness of factorial designs [316] 10.6 Meaning and interpretation of interactions [318] 10.7 Interactions of fixed and random factors [323] 10.8 Multiple comparisons for two factors [331] 10.8.1 When there is a significant interaction [331] 10.8.2 When there is no significant interaction [331] 10.8.3 Control of experiment-wise probability of Type I error [333] 10.9 Three or more factors [335] 10.10 Interpretation of interactions among three factors [335] 10.11 Power and detection of interactions [340] 10.12 Spatial replication of ecological experiments [342] 10.13 What to do with a mixed model [344] 10.14 Problems with power in a mixed analysis [346] 10.15 Magnitudes of effects of treatments [347] 10.15.1 Magnitudes of effects of fixed treatments [348] 10.15.2 Some problems with such measures [348] 10.15.3 Magnitudes of components of variance of random treatments [351] 10.16 Problems with estimates of effects [355] 10.16.1 Summation and interactions [355] 10.16.2 Comparisons among experiments or areas [356] 10.16.3 Conclusions on magnitudes of effects 357j 11 Construction of any analysis from general principles [358] 11.1 General procedures [358] 11.2 Constructing the linear model [361] 11.3 Calculating the degrees of freedom [362] 11.4 Mean square estimates and F-ratios [364] 11.5 Designs seen before [370] 11.5.1 Designs with two factors [370] 11.5.2 Designs with three factors [370] 11.6 Construction of sums of squares using orthogonal designs [375] 11.7 Post hoc pooling [375] 11.8 Quasi F-ratios [377] 11.9 Multiple comparisons [378] 11.10 Missing data and other practicalities [380] 11.10.1 Loss of individual replicates [382] 11.10.2 Missing sets of replicates [383] 12 Some common and some particular experimental designs [385] 12.1 Unreplicated randomized blocks design [385] 12.2 Tukey’s test for non-additivity [389] 12.3 Split-plot designs [391] 12.4 Latin squares [401] 12.5 Unreplicated repeated measures [403] 12.6 Asymmetrical controls: one factor [408] 12.7 Asymmetrical controls: fixed factorial designs [409] 12.8 Problems with experiments on ecological competition [414] 12.9 Asymmetrical analyses of random factors in environmental studies [415] 13 Analyses involving relationships among variables [419] 13.1 Introduction to linear regression [419] 13.2 Tests of null hypotheses about regressions [422] 13.3 Assumptions underlying regression [424] 13.3.1 Independence of data at each X [425] 13.3.2 Homogeneity of variances at each X [427] 13.3.3 X values are not fixed [428] 13.3.4 Normality of errors in T [429] 13.4 Analysis of variance and regression [431] 13.5 How good is the regression? [431] 13.6 Multiple regressions [434] 13.7 Polynomial regressions [439] 13.8 Other, non-linear regressions [444] 13.9 Introduction to analysis of covariance [444] 13.10 The underlying models for covariance [447] 13.10.1 Model 1: Regression in each treatment [448] 13.10.2 Model 2: A common regression in each treatment [449] 13.10.3 Model 3: The total regression, all data combined [454] 13.11 The procedures: making adjustments [457] 13.12 Interpretation of the analysis [462] 13.13 The assumptions needed for an analysis of covariance [464] 13.13.1 Assumptions in regressions [464] 13.13.2 Assumptions in analysis of variance [465] 13.13.3 Assumptions specific to an analysis of covariance [466] 13.14 Alternatives when regressions differ [471] 13.14.1 A two-factor scenario [471] 13.14.2 The Johnson-Neyman technique [473] 13.14.3 Comparisons of regressions [474] 13.15 Extensions of analysis of covariance to other designs [474] 13.15.1 More than one covariate [475] 13.15.2 Non-linear relationships [476] 13.15.3 More than one experimental factor [476] 14 Conclusions: where to from here? [478] 14.1 Be logical, be eco-logical [478] 14.2 Alternative models and hypotheses [480] 14.3 Pilot experiments: all experiments are preliminary [481] 14.4 Repeated experimentation [481] 14.5 Criticisms and the growth of knowledge [484] References [486] Author index [496] Subject index [499]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 62 Un56 (Browse shelf) | Available | A-8088 |
Incluye referencias bibliográficas (p. 486-495) e índices.
1 Introduction [1] --
2 A framework for investigating biological patterns and processes [7] --
2.1 Introduction [7] --
2.2 Observations [8] --
2.3 Models, theories, explanations [10] --
2.3.1 Models of physiological stress [10] --
2.3.2 Models based on competition [10] --
2.3.3 Grazing models [10] --
2.3.4 Models to do with hazards [11] --
2.3.5 Models of failure of recruitment [11] --
2.4 Numerous competing models [12] --
2.5 Hypotheses, predictions [13] --
2.6 Null hypotheses [15] --
2.7 Experiments and their interpretation [16] --
2.8 What to do next? [17] --
2.9 Measurements, gathering data and a logical structure [19] --
2.10 A consideration: why are you measuring things? [21] --
2.11 Conclusion: a plea for more thought [22] --
3 Populations, frequency distributions and samples [24] --
3.1 Introduction [24] --
3.2 Variability in measurements [24] --
3.3 Observations and measurements as frequency distributions [25] --
3.4 Defining the population to be observed [27] --
3.5 The need for samples [30] --
3.6 The location parameter [30] --
3.7 Sample estimate of the location parameter [33] --
3.8 The dispersion parameter [34] --
3.9 Sample estimate of the dispersion parameter [36] --
3.10 Degrees of freedom [37] --
3.11 Representative sampling and accuracy of samples [38] --
3.12 Other useful parameters [44] --
3.12.1 Skewness [44] --
3.12.2 Kurtosis [47] --
4 Statistical tests of null hypotheses [50] --
4.1 Why a statistical test? [50] --
4.2 An example using coins [51] --
4.3 The components of a statistical test [55] --
4.3.1 Null hypothesis [55] --
4.3.2 Test statistic [56] --
4.3.3 Region of rejection and critical value [56] --
4.4 Type I error or rejection of a true null hypothesis [57] --
4.5 Statistical test of a theoretical biological example [58] --
4.5.1 Transformation of a normal distribution to the standard normal distribution [59] --
4.6 One- and two-tailed null hypotheses [62] --
5 Statistical tests on samples [65] --
5.1 Repeated sampling [65] --
5.2 The standard error from the normal distribution of sample means [70] --
5.3 Confidence intervals for a sampled mean [70] --
5.4 Precision of a sample estimate of the mean [73] --
5.5 A contrived example of use of the confidence interval of sampled means [74] --
5.6 Student’s t-distribution [76] --
5.7 Increasing precision of sampling [77] --
5.7.1 The chosen probability used to construct the confidence interval [78] --
5.7.2 The sample size (n) [78] --
5.7.3 The variance of the population (σ2) [80] --
5.8 Description of sampling [81] --
5.9 Student’s t-test for a mensurative hypothesis [82] --
5.10 Goodness-of-fit, mensurative experiments and logic [84] --
5.11 Type I and Type II errors in relation to a null hypothesis [87] --
5.12 Determining the power of a simple statistical test [91] --
5.12.1 Probability of Type I error [92] --
5.12.2 Size of experiment (n) [93] --
5.12.3 Variance of the population [95] --
5.12.4 ‘Effect size’ [97] --
5.13 Power and alternative hypotheses [97] --
6 Simple experiments comparing the means of two populations [100] --
6.1 Paired comparisons [100] --
6.2 Confounding and lack of controls [104] --
6.3 Unpaired experiments [106] --
6.4 Standard error of the difference between two means [107] --
6.4.1 Independence of samples [108] --
6.4.2 Homogeneity of variances [109] --
6.5 Allocation of sample units to treatments [114] --
6.6 Interpretation of a simple ecological experiment [118] --
6.7 Power of an experimental comparison of two populations [124] --
6.8 Alternative procedures [128] --
6.8.1 Binomial (sign) test for paired data [128] --
6.8.2 Other alternative procedures [130] --
6.9 Are experimental comparisons of only two populations useful? [132] --
6.9.1 The wrong population is being sampled [132] --
6.9.2 Modifications to the t-test to compare more than two populations [137] --
6.9.3 Conclusion [139] --
7 Analysis of variance [140] --
7.1 Introduction [140] --
7.2 Data collected to test a single-factor null hypothesis [141] --
7.3 Partitioning of the data: the analysis of variation [143] --
7.4 A linear model [145] --
7.5 What do the sums of squares measure? [149] --
7.6 Degrees of freedom [152] --
7.7 Mean squares and test statistic [153] --
7.8 Solution to some problems raised earlier [154] --
7.9 So what happens with real data? [155] --
7.10 Unbalanced data [156] --
7.11 Machine formulae [157] --
7.12 Interpretation of the result [157] --
7.13 Assumptions of analysis of variance [158] --
7.14 Independence of data [159] --
7.14.1 Positive correlation within samples [160] --
7.14.2 Negative correlation within samples [166] --
7.14.3 Negative correlation among samples [168] --
7.14.4 Positive correlation among samples [172] --
7.15 Dealing with non-independence [179] --
7.16 Heterogeneity of variances [181] --
7.16.1 Tests for heterogeneity of variances [183] --
7.17 Quality control [184] --
7.18 Transformations of data [187] --
7.18.1 Square-root transformation of counts (or Poisson data) [188] --
7.18.2 Log transformation for rates, ratios, concentrations and other data [189] --
7.18.3 Arc-sin transformation of percentages and proportions [192] --
7.18.4 No transformation is possible [192] --
7.19 Normality of data [194] --
7.20 The summation assumption [195] --
8 More analysis of variance [198] --
8.1 Fixed or random factors [198] --
8.2 Interpretation of fixed or random factors [204] --
8.3 Power of an analysis of a fixed factor [209] --
8.3.1 Non-central F-ratio and power [209] --
8.3.2 Influences of α, n, σ2e and Ai values [211] --
8.3.3 Construction of an alternative hypothesis [214] --
8.4 Power of an analysis of a random factor [216] --
8.4.1 Central F-ratios and power [216] --
8.4.2 Influences of α, n, σ2e , σ2A and a [218] --
8.4.3 Construction of an alternative hypothesis [220] --
8.5 Alternative analysis of ranked data [223] --
8.6 Multiple comparisons to identify the alternative hypothesis [224] --
8.6.1 Introduction [224] --
8.6.2 Problems of excessive Type I error [225] --
8.6.3 A priori versus a posteriori comparisons [226] --
8.6.4 A priori procedures [227] --
8.6.5 A posteriori comparisons [234] --
9 Nested analyses of variance [243] --
9.1 Introduction and need [243] --
9.2 Hurlbert’s ‘pseudoreplication’ [245] --
9.3 Partitioning of the data [245] --
9.4 The linear model [250] --
9.5 Degrees of freedom and mean squares [254] --
9.6 Tests and interpretation: what do the nested bits mean? [259] --
9.6.1 F-ratio of appropriate mean squares [259] --
9.6.2 Solution to confounding [260] --
9.6.3 Multiple comparisons [261] --
9.6.4 Variability among replicated units [261] --
9.7 Pooling of nested components [268] --
9.7.1 Rationale and procedure [268] --
9.7.2 Pooling, Type II and Type I errors [269] --
9.8 Balanced sampling [273] --
9.9 Nested analyses and spatial pattern [275] --
9.10 Nested analysis and temporal pattern [279] --
9.11 Cost-benefit optimization [283] --
9.12 Calculation of power [289] --
9.13 Residual variance and an ‘error’ term [291] --
10 Factorial experiments [296] --
10.1 Introduction [296] --
10.2 Partitioning of variation when there are two experimental factors [300] --
10.3 Appropriate null hypotheses for a two-factor experiment [305] --
10.4 A linear model and estimation of components by mean squares [306] --
10.5 Why do a factorial experiment? [312] --
10.5.1 Information about interactions [313] --
10.5.2 Efficiency and cost-effectiveness of factorial designs [316] --
10.6 Meaning and interpretation of interactions [318] --
10.7 Interactions of fixed and random factors [323] --
10.8 Multiple comparisons for two factors [331] --
10.8.1 When there is a significant interaction [331] --
10.8.2 When there is no significant interaction [331] --
10.8.3 Control of experiment-wise probability of --
Type I error [333] --
10.9 Three or more factors [335] --
10.10 Interpretation of interactions among three factors [335] --
10.11 Power and detection of interactions [340] --
10.12 Spatial replication of ecological experiments [342] --
10.13 What to do with a mixed model [344] --
10.14 Problems with power in a mixed analysis [346] --
10.15 Magnitudes of effects of treatments [347] --
10.15.1 Magnitudes of effects of fixed treatments [348] --
10.15.2 Some problems with such measures [348] --
10.15.3 Magnitudes of components of variance of random treatments [351] --
10.16 Problems with estimates of effects [355] --
10.16.1 Summation and interactions [355] --
10.16.2 Comparisons among experiments or areas [356] --
10.16.3 Conclusions on magnitudes of effects 357j --
11 Construction of any analysis from general principles [358] --
11.1 General procedures [358] --
11.2 Constructing the linear model [361] --
11.3 Calculating the degrees of freedom [362] --
11.4 Mean square estimates and F-ratios [364] --
11.5 Designs seen before [370] --
11.5.1 Designs with two factors [370] --
11.5.2 Designs with three factors [370] --
11.6 Construction of sums of squares using orthogonal designs [375] --
11.7 Post hoc pooling [375] --
11.8 Quasi F-ratios [377] --
11.9 Multiple comparisons [378] --
11.10 Missing data and other practicalities [380] --
11.10.1 Loss of individual replicates [382] --
11.10.2 Missing sets of replicates [383] --
12 Some common and some particular experimental designs [385] --
12.1 Unreplicated randomized blocks design [385] --
12.2 Tukey’s test for non-additivity [389] --
12.3 Split-plot designs [391] --
12.4 Latin squares [401] --
12.5 Unreplicated repeated measures [403] --
12.6 Asymmetrical controls: one factor [408] --
12.7 Asymmetrical controls: fixed factorial designs [409] --
12.8 Problems with experiments on ecological competition [414] --
12.9 Asymmetrical analyses of random factors in environmental studies [415] --
13 Analyses involving relationships among variables [419] --
13.1 Introduction to linear regression [419] --
13.2 Tests of null hypotheses about regressions [422] --
13.3 Assumptions underlying regression [424] --
13.3.1 Independence of data at each X [425] --
13.3.2 Homogeneity of variances at each X [427] --
13.3.3 X values are not fixed [428] --
13.3.4 Normality of errors in T [429] --
13.4 Analysis of variance and regression [431] --
13.5 How good is the regression? [431] --
13.6 Multiple regressions [434] --
13.7 Polynomial regressions [439] --
13.8 Other, non-linear regressions [444] --
13.9 Introduction to analysis of covariance [444] --
13.10 The underlying models for covariance [447] --
13.10.1 Model 1: Regression in each treatment [448] --
13.10.2 Model 2: A common regression in each treatment [449] --
13.10.3 Model 3: The total regression, all data combined [454] --
13.11 The procedures: making adjustments [457] --
13.12 Interpretation of the analysis [462] --
13.13 The assumptions needed for an analysis of covariance [464] --
13.13.1 Assumptions in regressions [464] --
13.13.2 Assumptions in analysis of variance [465] --
13.13.3 Assumptions specific to an analysis of covariance [466] --
13.14 Alternatives when regressions differ [471] --
13.14.1 A two-factor scenario [471] --
13.14.2 The Johnson-Neyman technique [473] --
13.14.3 Comparisons of regressions [474] --
13.15 Extensions of analysis of covariance to other designs [474] --
13.15.1 More than one covariate [475] --
13.15.2 Non-linear relationships [476] --
13.15.3 More than one experimental factor [476] --
14 Conclusions: where to from here? [478] --
14.1 Be logical, be eco-logical [478] --
14.2 Alternative models and hypotheses [480] --
14.3 Pilot experiments: all experiments are preliminary [481] --
14.4 Repeated experimentation [481] --
14.5 Criticisms and the growth of knowledge [484] --
References [486] --
Author index [496] --
Subject index [499] --
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