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Prism 4 Statistics Guide −Statistical Analyses for Laboratory and Clinical Researchers

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Prism 4 Statistics Guide −Statistical Analyses for Laboratory and Clinical Researchers Version 4.0 Statistics Guide Statistical analyses for laboratory and clinical researchers Harvey Motulsky 1999-2005 GraphPad Software, Inc. All rights reserved. Third printing February 2005 GraphPad Prism is a registered trademark of GraphPad Software, Inc. GraphPad is a trademark of GraphPad Software, Inc. Citation: H.J. Motulsky, Prism 4 Statistics Guide −Statistical analyses for laboratory and clinical researchers. GraphPad Software Inc., San Diego CA, 2003, www.graphpad.com. This book is a companion to the computer program GraphPad Prism version 4, which combines scientific graphics, basic biostatistics, and nonlinear regression (for both Windows and Macintosh). Prism comes with three volumes in addition to this one: The Prism 4 User’s Guide, Prism 4 Step-by-Step Examples, and Fitting Models to Biological Data using Linear and Nonlinear Regression. You can learn more about Prism, and download all four volumes as Acrobat (pdf) files, from www.graphpad.com To contact GraphPad Software, email [email protected] or [email protected]. Table of Contents Statistical Principles ......................................................................................9 1. Introduction to Statistical Thinking .....................................................9 Garbage in, garbage out .............................................................................................9 When do you need statistical calculations? ...............................................................9 The key concept: Sampling from a population ........................................................10 What are samples and populations?...................................................................10 The need for independent samples.....................................................................10 How you can use statistics to extrapolate from sample to population................11 Confidence intervals..................................................................................................11 Limitations of statistics............................................................................................ 12 2. The Gaussian Distribution.................................................................. 13 Importance of the Gaussian distribution................................................................. 13 Origin of the Gaussian distribution ......................................................................... 13 The Central Limit Theorem of statistics .................................................................. 15 3. P Values and Statistical Hypothesis Testing........................................ 16 What is a P value? .................................................................................................... 16 What is a null hypothesis? .................................................................................. 16 Common misinterpretation of a P value............................................................. 16 One-tail vs. two-tail P values.................................................................................... 16 Hypothesis testing and statistical significance........................................................ 17 Statistical hypothesis testing .............................................................................. 17 Statistical significance in science........................................................................18 “Extremely significant” results ...........................................................................18 Report the actual P value .................................................................................... 19 4. Interpreting P Values and Statistical Significance................................20 Statistical power...................................................................................................... 20 Type II errors and power ................................................................................... 20 Example of power calculations .......................................................................... 20 A Bayesian perspective on interpreting statistical significance .............................. 21 Beware of multiple comparisons..............................................................................23 5. Outliers ..............................................................................................25 What is an outlier? ...................................................................................................25 Detecting outliers with Grubbs’ test ........................................................................26 Statistical tests that are robust to the presence of outliers.................................28 Excluding outliers in Prism......................................................................................28 Continuous Data ..........................................................................................29 6. Descriptive Statistics...........................................................................29 Choosing column statistics ......................................................................................29 Interpreting descriptive statistics ............................................................................29 Standard deviation (SD) .....................................................................................29 Standard error of the mean (SEM) .....................................................................30 The difference between the SD and SEM ...........................................................30 95% confidence interval (CI) .............................................................................. 31 Coefficient of variation (CV) ............................................................................... 31 Quartiles and range............................................................................................. 31 Geometric mean..................................................................................................32 Skewness and kurtosis ........................................................................................32 The results of normality tests...................................................................................32 How the normality test works.............................................................................32 How to think about results from a normality test ..............................................32 Row means and totals ..............................................................................................33 7. Comparing a Mean or Median to a Hypothetical Value ........................ 35 Choosing a one-sample t test or Wilcoxon rank sum test .......................................35 The results of a one-sample t test ............................................................................35 How a one-sample t test works...........................................................................35 How to think about results from the one-sample t test......................................35 Checklist: Is a one-sample t test the right test for these data?...........................37 The results of a Wilcoxon rank sum test..................................................................38 How the Wilcoxon rank sum test works .............................................................38 How to think about the results of a Wilcoxon rank sum test .............................39 Checklist: Is the Wilcoxon test right for these data? ..........................................39 8. t Tests and Nonparametric Comparisons ........................................... 40 Introduction to comparing two groups................................................................... 40 Entering data to compare two groups with a t test (or a nonparametric test)....... 40 Indexed data....................................................................................................... 40 Choosing an analysis to compare two groups.......................................................... 41 Paired or unpaired test?...................................................................................... 41 t test or nonparametric test?...............................................................................42 Assume equal variances? ....................................................................................43 One- or two-tail P value? ....................................................................................43 Confirm test selection .........................................................................................43 The results of an unpaired t test ..............................................................................44 How the unpaired t test works............................................................................44 How to think about results from an unpaired t test ...........................................44 Checklist: Is an unpaired t test the right test for these data?.............................46 The results of a paired t test.....................................................................................48 How a paired t test works ...................................................................................48 How to think about results of a paired t test ......................................................49 Checklist: Is the paired t test the right test for these data? ................................50 Ratio t tests for paired data.....................................................................................
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