Analyzing Data with GraphPad Prism A companion to GraphPad Prism version 3 Harvey Motulsky President GraphPad Software Inc. [email protected] GraphPad Software, Inc. © 1999 GraphPad Software, Inc. All rights reserved. All Rights Reserved. GraphPad Prism, Prism and InStat are registered trademarks of GraphPad Contents Software, Inc. GraphPad is a trademark of GraphPad Software, Inc. Use of the software is subject to the restrictions contained in the Preface.........................................................................................................2 accompanying software license agreement. Introduction to statistical comparisons..........................................................3 Garbage in, garbage out ...................................................................................3 Citation: H.J. Motulsky, Analyzing Data with GraphPad Prism, 1999, When do you need statistical calculations? ........................................................3 The key concept: Sampling from a population....................................................4 GraphPad Software Inc., San Diego CA, www.graphpad.com. Confidence intervals ........................................................................................8 P values ..........................................................................................................9 Hypothesis testing and statistical significance................................................... 11 Acknowledgements: The following individuals made substantial Statistical power ............................................................................................ 13 contributions towards development of this book: Arthur Christopoulos A Bayesian perspective on interpreting statistical significance............................ 15 (Neuroscience Research in Psychiatry, Univ. Minnesota), Lee Limbird Beware of multiple comparisons ..................................................................... 17 (Dept. Pharmacology, Vanderbilt University), Rick Neubig (Dept. Outliers......................................................................................................... 18 Pharmacology, Univ. Michigan), Paige Searle (Vice-president GraphPad Analyzing one group...................................................................................23 Software). Entering data to analyze one group ................................................................. 23 How to reach GraphPad: Frequency distributions .................................................................................. 24 Column statistics............................................................................................ 25 Phone: 858-457-3909 (619-457-3909 before June 12, 1999) Interpreting descriptive statistics...................................................................... 26 Fax: 858-457-8141 (619-457-8141 before June 12, 1999) The results of normality tests........................................................................... 29 The results of a one-sample t test..................................................................... 30 Email: [email protected] or [email protected] The results of a Wilcoxon rank sum test........................................................... 34 Web: www.graphpad.com Row means and totals .................................................................................... 37 Mail: GraphPad Software, Inc. t tests and nonparametric comparisons .......................................................39 5755 Oberlin Drive #110 Introduction to comparing of two groups ......................................................... 39 San Diego, CA 92121 USA Entering data to compare two groups with a t test (or a nonparametric test) ........ 39 Choosing an analysis to compare two groups................................................... 41 The results of an unpaired t test....................................................................... 45 The results of a paired t test ............................................................................ 51 The results of a Mann-Whitney test ................................................................. 57 The results of a Wilcoxon matched pairs test.................................................... 59 One-way ANOVA and nonparametric comparisons .....................................65 Introduction to comparisons of three or more groups........................................ 65 Choosing one-way ANOVA and related analyses ............................................. 67 The results of one-way ANOVA ...................................................................... 72 The results of repeated measures one-way ANOVA .......................................... 82 The results of a Kruskal-Wallis test .................................................................. 85 The results of a Friedman test.......................................................................... 89 Two-way analysis of variance......................................................................93 Introduction to two-way ANOVA.................................................................... 93 Entering data for two-way ANOVA.................................................................. 93 Choosing the two-way ANOVA analysis .......................................................... 94 Interpreting the results of nonlinear regression..........................................207 The results of two-way ANOVA ...................................................................... 97 Approach to interpreting nonlinear regression results...................................... 207 Do the nonlinear regression results make sense? ............................................ 208 Survival curves .........................................................................................109 How certain are the best-fit values? ............................................................... 209 Introduction to survival curves ...................................................................... 109 How good is the fit?..................................................................................... 212 Entering survival data ................................................................................... 109 Does the curve systematically deviate from the data?...................................... 214 Choosing a survival analysis ......................................................................... 112 Could the fit be a local minimum? ................................................................ 216 Interpreting survival analysis......................................................................... 113 Have you violated an assumption of nonlinear regression?.............................. 217 Graphing survival curves.............................................................................. 120 Have you made a common error when using nonlinear regression?................. 218 Contingency tables ...................................................................................121 Comparing two curves..............................................................................221 Introduction to contingency tables ................................................................ 121 Comparing the fits of two models.................................................................. 221 Entering data into contingency tables ............................................................ 122 Comparing fits to two sets of data (same equation).......................................... 224 Choosing how to analyze a contingency table................................................ 123 Interpreting analyses of contingency tables .................................................... 124 The distributions of best-fit values.............................................................229 The confidence interval of a proportion ......................................................... 131 Why care about the distribution of best-fit values ........................................... 229 Using simulations to determine the distribution of a parameters ...................... 229 Correlation...............................................................................................135 Example simulation 1. Dose-response curves. ................................................ 230 Introduction to correlation............................................................................ 135 Example simulation 2. Exponential decay. ..................................................... 231 Entering data for correlation.......................................................................... 135 Detailed instructions for comparing parameter distributions ............................ 234 Choosing a correlation analysis..................................................................... 136 Results of correlation.................................................................................... 137 Analyzing radioligand binding data ...........................................................237 Introduction to radioligand binding ............................................................... 237 Linear regression ......................................................................................141 Law of mass action....................................................................................... 238 Introduction to linear regression.................................................................... 141 Nonspecific binding....................................................................................