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Preface | |
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Introduction | |
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What do we mean by statistics? | |
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Why is statistics necessary? | |
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Statistics in field biology | |
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The limitations of statistics | |
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The purpose of this text | |
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Measurement and Sampling Concepts | |
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Populations, samples and observations | |
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Counting things--the sampling unit | |
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Random sampling | |
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Random numbers | |
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Independence | |
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Statistics and parameters | |
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Descriptive and inferential statistics | |
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Parametric and non-parametric statistics | |
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Processing Data | |
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Scales of measurement | |
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The nominal scale | |
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The ordinal scale | |
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The interval scale | |
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The ratio scale | |
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Conversion of interval observations to an ordinal scale | |
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Derived variables | |
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The precision of observations | |
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How precise should we be? | |
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The frequency table | |
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Aggregating frequency classes | |
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Frequency distribution of count observations | |
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Dispersion | |
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Bivariate data | |
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Presenting Data | |
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Introduction | |
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Dot plot or line plot | |
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Bar graph | |
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Histogram | |
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Frequency polygon and frequency curve | |
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Scattergram (scatter plot) | |
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Circle or pie graph | |
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Measuring the Average | |
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What is an average? | |
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The mean | |
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The median--a resistant statistic | |
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The mode | |
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Relationship between the mean, median and mode | |
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Measuring Variability | |
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Variability | |
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The range | |
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The standard deviation | |
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Calculating the standard deviation | |
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Calculating the standard deviation from grouped data | |
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Variance | |
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An alternative formula for calculating the variance and standard deviation | |
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Obtaining the standard deviation, variance and the sum of squares from a calculator | |
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Degrees of freedom | |
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The coefficient of variation | |
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Probability | |
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The meaning of probability | |
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Compound probabilities | |
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Probability distribution | |
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Models of probability distribution | |
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The binomial probability distribution | |
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The Poisson probability distribution | |
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The negative binomial probability distribution | |
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Critical probability | |
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Probability Distributions as Models of Dispersion | |
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Dispersion | |
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An Index of Dispersion | |
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Choosing a model of dispersion | |
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The binomial model | |
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Poisson model | |
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The negative binomial model | |
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Deciding the goodness of fit | |
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The Normal Distribution | |
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The normal curve | |
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Some mathematical properties of the normal curve | |
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Standardizing the normal curve | |
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Two-tailed or one-tailed? | |
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Small samples: the t-distribution | |
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Are our data 'normal'? | |
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Data Transformation | |
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The need for transformation | |
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The logarithmic transformation | |
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When there are zero counts--the arcsinh transformation | |
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The square root transformation | |
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The arcsine transformation | |
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Back-transforming transformed numbers | |
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Is data transformation really necessary? | |
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How Good are our Estimates? | |
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Sampling error | |
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The distribution of a sample mean | |
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The confidence interval of the mean of a large sample | |
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The confidence interval of the mean of a small sample | |
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The confidence interval of the mean of a sample of count data | |
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The difference between the means of two large samples | |
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The difference between the means of two small samples | |
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Estimating a proportion | |
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Estimating a Lincoln Index | |
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Estimating a diversity index | |
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The distribution of a variance--chi-square distribution | |
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The Basis of Statistical Testing | |
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Introduction | |
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The experimental hypothesis | |
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The statistical hypothesis | |
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Test statistics | |
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One-tailed tests and two-tailed tests | |
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Hypothesis testing and the normal curve | |
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Type 1 and type 2 errors | |
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Parametric and non-parametric statistics: some further observations | |
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The power of a test | |
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Analysing Frequencies | |
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The chi-square test | |
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Calculating the x[superscript 2] test statistic | |
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A practical example of a test for homogeneous frequencies | |
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The problem of independence | |
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One degree of freedom--Yates' correction | |
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Goodness of fit tests | |
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Tests for association--the contingency table | |
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The r [times] c contingency table | |
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The G-test | |
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Applying the G-test to a one-way classification of frequencies | |
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Applying the G-test to a 2 [times] 2 contingency table | |
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Applying the G-test to an r [times] c contingency table | |
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Advice on analysing frequencies | |
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Measuring Correlations | |
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The meaning of correlation | |
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Investigating correlation | |
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The strength and significance of a correlation | |
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Covariance | |
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The Product Moment Correlation Coefficient | |
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The coefficient of determination r[superscript 2] | |
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The Spearman Rank Correlation Coefficient r[subscript s] | |
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Advice on measuring correlations | |
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Regression Analysis | |
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Introduction | |
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Gradients and triangles | |
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Dependent and independent variables | |
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A perfect rectilinear relationship | |
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The line of least squares | |
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Simple linear regression | |
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Fitting the regression line to the scattergram | |
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The error of a regression line | |
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Confidence limits of an individual estimate | |
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The significance of the regression line | |
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The difference between two regression lines | |
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Dealing with curved relationships | |
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Transformation of both axes | |
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Regression through the origin | |
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An alternative line of best fit | |
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Advice on using regression analysis | |
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Comparing Averages | |
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Introduction | |
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Matched and unmatched observations | |
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The Mann--Whitney U-test for unmatched samples | |
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Advice on using the Mann--Whitney U-test | |
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More than two samples--the Kruskal--Wallis test | |
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Advice on using the Kruskal--Wallis test | |
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The Wilcoxon test for matched pairs | |
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Advice on using the Wilcoxon test for matched pairs | |
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Comparing means--parametric tests | |
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The F-test (two-tailed) | |
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The z-test for comparing the means of two large samples | |
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The t-test for comparing the means of two small samples | |
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The t-test for matched pairs | |
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Advice on comparing means | |
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Analysis of Variance--ANOVA | |
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Why do we need ANOVA? | |
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How ANOVA works | |
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Procedure for computing one-way ANOVA | |
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Procedure for computing the Tukey test | |
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Two-way ANOVA | |
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Procedure for computing two-way ANOVA | |
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Procedure for computing the Tukey test in two-way ANOVA | |
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Two-way ANOVA with single observations | |
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The randomized block design | |
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The Latin square | |
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Analysis of variance in regression | |
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Advice on using ANOVA | |
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Multivariate Analysis | |
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Introduction | |
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What is information? | |
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Making large problems manageable | |
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Are there three groups or four? | |
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Learning from experience? | |
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Variations on a theme | |
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Summary | |
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Appendices | |
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Table of random numbers | |
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t-distribution | |
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X[superscript 2]-distribution | |
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Critical values of Spearman's Rank Correlation Coefficient | |
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Product moment correlation values at the 0.05 and 0.01 levels of significance | |
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Mann--Whitney U-test values (two-tailed test) P = 0.05 | |
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Critical values of T in the Wilcoxon test for two matched samples | |
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F-distribution, 0.05 level of significance, two-tailed test | |
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Critical values of F[subscript max] 0.05 level of significance | |
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F-distribution | |
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Tukey test | |
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Symbols | |
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Matrices and vectors | |
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Computer packages | |
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Bibliography and further reading | |
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Index | |