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PAST PAleontological STatistics Version 3.0 Reference manual Øyvind Hammer Natural History Museum University of Oslo [email protected] 1999-2013 1 Contents Welcome to the PAST! .............................................................................................................................

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PAST PAleontological STatistics

Version 3.0

Reference manual Øyvind Hammer Natural History Museum University of Oslo [email protected]

1999-2013

1

Contents Welcome to the PAST! .......................................................................................................................... 10 Installation ............................................................................................................................................. 11 The spreadsheet and the Edit menu ..................................................................................................... 12 Entering data ..................................................................................................................................... 12 Selecting areas................................................................................................................................... 12 Moving a row or a column ................................................................................................................ 13 Renaming rows and columns ............................................................................................................ 13 Increasing the size of the array ......................................................................................................... 13 Cut, copy, paste ................................................................................................................................. 13 Remove.............................................................................................................................................. 13 Row colors and symbols .................................................................................................................... 13 Selecting datatypes for columns, and specifying groups .................................................................. 13 Remove uninformative rows/columns .............................................................................................. 14 Transpose .......................................................................................................................................... 14 Grouped columns to multivar ........................................................................................................... 14 Grouped rows to multivar ................................................................................................................. 15 Observations to contingency table ................................................................................................... 15 Stack grouped rows into columns ..................................................................................................... 15 Samples to events (UA to RASC)........................................................................................................ 15 Events to samples (RASC to UA) ........................................................................................................ 15 Loading and saving data .................................................................................................................... 15 Importing data from Excel ................................................................................................................. 16 Reading and writing Nexus files ........................................................................................................ 16 2

Importing text files ............................................................................................................................ 17 Counter .............................................................................................................................................. 17 Transform menu .................................................................................................................................... 18 Logarithm .......................................................................................................................................... 18 Subtract mean ................................................................................................................................... 18 Remove trend .................................................................................................................................... 18 Box-Cox .............................................................................................................................................. 18 Row percentage................................................................................................................................. 19 Row normalize length........................................................................................................................ 19 Abundance to presence/absence...................................................................................................... 19 Procrustes fitting ............................................................................................................................... 19 Bookstein fitting ................................................................................................................................ 20 Project to tangent space ................................................................................................................... 20 Remove size from landmarks ............................................................................................................ 21 Transform landmarks ........................................................................................................................ 21 Remove size from distances .............................................................................................................. 21 Sort ascending and descending ......................................................................................................... 22 Regular interpolation ........................................................................................................................ 22 Evaluate expression ........................................................................................................................... 22 Plot menu .............................................................................................................................................. 24 Graph ................................................................................................................................................. 24 XY graph............................................................................................................................................. 25 XY graph with error bars ................................................................................................................... 26 Histogram .......................................................................................................................................... 27 Bar chart/box plot ............................................................................................................................. 28 Percentiles ......................................................................................................................................... 29 Missing values are deleted. ............................................................................................................... 29 3

Normal probability plot ..................................................................................................................... 30 Ternary .............................................................................................................................................. 31 Bubble plot ........................................................................................................................................ 32 Matrix ................................................................................................................................................ 33 Surface ............................................................................................................................................... 34 Statistics menu ...................................................................................................................................... 35 Univariate .......................................................................................................................................... 35 Two-sample tests .............................................................................................................................. 39 t test and related tests for equal means ....................................................................................... 39 F test for equal variances .............................................................................................................. 41 Mann-Whitney test for equal medians ......................................................................................... 42 Kolmogorov-Smirnov test for equal distributions ......................................................................... 43 Coefficient of variation (Fligner-Kileen test) ................................................................................. 44 Two-sample paired tests (t, sign, Wilcoxon) ..................................................................................... 46 Several-sample tests.......................................................................................................................... 48 One-way ANOVA ........................................................................................................................... 48 Kruskal-Wallis ................................................................................................................................ 51 Several-samples repeated measures tests ........................................................................................ 53 Tukey’s pairwise post-hoc tests .................................................................................................... 54 Friedman test ................................................................................................................................ 54 Two-way ANOVA ............................................................................................................................... 57 Two-way ANOVA without replication ............................................................................................... 60 One-way ANCOVA ............................................................................................................................. 61 Correlation table ............................................................................................................................... 62 Intraclass correlation ......................................................................................................................... 65 Normality tests .................................................................................................................................. 67 Contingency table (chi2 etc.) ............................................................................................................. 70 4

Risk/odds ........................................................................................................................................... 72 Survival analysis (Kaplan-Meier curves, log-rank test etc.) ............................................................... 74 Combine errors.................................................................................................................................. 76 Multivar menu ....................................................................................................................................... 77 Principal components ........................................................................................................................ 77 Principal coordinates ......................................................................................................................... 81 Non-metric MDS ................................................................................................................................ 82 Taguchi, Y.-H., Oono, Y. 2005. Relational patterns of gene expression via non-metric multidimensional scaling analysis. Bioinformatics 21:730-40.Correspondence analysis ................. 83 Correspondence analysis................................................................................................................... 84 Detrended correspondence analysis ................................................................................................. 86 Canonical correspondence ................................................................................................................ 87 Seriation ............................................................................................................................................ 88 CABFAC factor analysis, NOT YET IN PAST 3 ...................................................................................... 89 Discriminant analysis ......................................................................................................................... 90 Two-block PLS .................................................................................................................................... 92 Cluster analysis .................................................................................................................................. 93 Neighbour joining .............................................................................................................................. 95 K-means clustering ............................................................................................................................ 96 Multivariate normality ...................................................................................................................... 97 Box’s M .............................................................................................................................................. 98 MANOVA ........................................................................................................................................... 99 One-way ANOSIM ............................................................................................................................ 100 One-way PERMANOVA .................................................................................................................... 101 Two-way ANOSIM............................................................................................................................ 102 Two-way PERMANOVA.................................................................................................................... 103 Mantel test and partial Mantel test ................................................................................................ 104 5

SIMPER ............................................................................................................................................ 106 Paired Hotelling ............................................................................................................................... 107 Modern Analog Technique .............................................................................................................. 108 Similarity and distance indices ........................................................................................................ 110 Genetic sequence stats ................................................................................................................... 116 Model menu ........................................................................................................................................ 117 Linear, bivariate ............................................................................................................................... 117 Linear, multivariate (one independent, n dependent).................................................................... 121 Linear, multiple (one dependent, n independent) .......................................................................... 122 Linear, multivariate multiple (m independent, n dependent) ........................................................ 123 Generalized Linear Model ............................................................................................................... 124 Polynomial regression ..................................................................................................................... 126 Nonlinear ......................................................................................................................................... 127 Linear ........................................................................................................................................... 127 Quadratic ..................................................................................................................................... 127 Power........................................................................................................................................... 128 Exponential .................................................................................................................................. 128 Von Bertalanffy............................................................................................................................ 128 Michaelis-Menten ....................................................................................................................... 128 Logistic ......................................................................................................................................... 128 Gompertz ..................................................................................................................................... 129 Gaussian ...................................................................................................................................... 129 Sinusoidal regression....................................................................................................................... 130 Smoothing spline ............................................................................................................................. 132 LOESS smoothing ............................................................................................................................. 133 Mixture analysis .............................................................................................................................. 134 Abundance models NOT YET IN PAST 3........................................................................................... 136 6

Species packing (Gaussian) NOT YET IN PAST 3 .............................................................................. 138 Logarithmic spiral ............................................................................................................................ 139 Diversity menu .................................................................................................................................... 140 Diversity indices............................................................................................................................... 140 Quadrat richness ............................................................................................................................. 142 Beta diversity ................................................................................................................................... 145 Taxonomic distinctness ................................................................................................................... 147 Individual rarefaction ...................................................................................................................... 149 Sample rarefaction (Mao’s tau)....................................................................................................... 151 SHE analysis ................................................