GraphPad Statistics Guide
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PRINCIPLES OF STATISTICS
The big picture
When do you need statistical calculations?
The essential concepts of statistics
Extrapolating from 'sample' to 'population'
Why statistics can be hard to learn
Don't be a P-hacker
How to report statistical results
Ordinal, interval and ratio variables
The need for independent samples
Intuitive Biostatistics (the book)
Essential Biostatistics (the book)
The Gaussian distribution
Importance of the Gaussian distribution
Origin of the Gaussian distribution
The Central Limit Theorem of statistics
Standard Deviation and Standard Error of the Mean
Key concepts: SD
Computing the SD
How accurately does a SD quantify scatter?
Key concepts: SEM
Computing the SEM
The SD and SEM are not the same
Advice: When to plot SD vs. SEM
Alternatives to showing the SD or SEM
The lognormal distribution and geometric mean and SD
The lognormal distribution
The geometric mean and geometric SD factor
Confidence intervals
Key concepts: Confidence interval of a mean
Interpreting a confidence interval of a mean
Other confidence intervals
Advice: Emphasize confidence intervals over P values
One sided confidence intervals
Compare confidence intervals, prediction intervals, and tolerance intervals
Confidence interval of a standard deviation
P Values
What is a P value?
The most common misinterpretation of a P value
More misunderstandings of P values
One-tail vs. two-tail P values
Advice: Use two-tailed P values
Advice: How to interpret a small P value
Advice: How to interpret a large P value
Decimal formatting of P values
How Prism computes exact P values
Hypothesis testing and statistical significance
Statistical hypothesis testing
Asterisks
Advice: Avoid the concept of 'statistical significance' when possible
The false discovery rate and statistical signficance
A legal analogy: Guilty or not guilty?
Advice: Don't P-Hack
Advice: Don't keep adding subjects until you hit 'significance'.
Advice: Don't HARK
Statistical power
Key concepts: Statistical Power
An analogy to understand statistical power
Type I, II (and III) errors
Using power to evaluate 'not significant' results
Why doesn't Prism compute the power of tests
Advice: How to get more power
Choosing sample size
Overview of sample size determination
Why choose sample size in advance?
Choosing alpha and beta for sample size calculations
What's wrong with standard values for effect size?
Sample size for nonparametric tests
Multiple comparisons
The problem of multiple comparisons
The multiple comparisons problem
Lingo: Multiple comparisons
Three approaches to dealing with multiple comparisons
Approach 1: Don't correct for multiple comparisons
When it makes sense to not correct for multiple comparisons
Example: Planned comparisons
Fisher's Least Significant Difference (LSD)
Approach 2: Control the Type I error rate for the family of comparisons
What it means to control the Type I error for a family
Multiplicity adjusted P values
Bonferroni and Sidak methods
The Holm-Sidak method
Tukey and Dunnett methods
Dunn's multiple comparisons after nonparametric ANOVA
Newman-Keuls method
Approach 3: Control the False Discovery Rate (FDR)
What it means to control the FDR
Key facts about controlling the FDR
Pros and cons of the three methods used to control the FDR
Testing for equivalence
Key concepts: Equivalence
Testing for equivalence with confidence intervals or P values
Nonparametric tests
Key concepts: Nonparametric tests
Advice: Don't automate the decision to use a nonparametric test
The power of nonparametric tests
Nonparametric tests with small and large samples
Advice: When to choose a nonparametric test
Lingo: The term "nonparametric"
Outliers
An overview of outliers
Advice: Beware of identifying outliers manually
Advice: Beware of lognormal distributions
How it works: Grubb's test
How it works: ROUT method
The problem of masking
Simulations to compare the Grubbs' and ROUT methods
Analysis checklists
Unpaired t test
Paired t test
Ratio t test
Mann-Whitney test
Wilcoxon matched pairs test
One-way ANOVA
Repeated measures one-way ANOVA
Kruskal-Wallis test
Friedman's test
Two-way ANOVA
Repeated measures two-way ANOVA
Contingency tables
Survival analysis
Outliers
STATISTICS WITH PRISM 8
Getting started with statistics with Prism
What happened to the "Column statistics" analysis?
Statistical analyses with Prism
Guided examples: Statistical analyses
Descriptive statistics
How to: Descriptive statistics
Analysis checklist: Descriptive statistics
Interpreting results: Quartiles and the interquartile range
Interpreting results: Mean, SD, SEM
Interpreting results: Median and its CI
Interpreting results: Coefficent of Variation
Interpreting results: Geometric mean and its CI
Interpreting results: Skewness
Interpreting results: Kurtosis
Harmonic, quadratic, trimmed, and windsorized mean
Row statistics
Overview: Side-by-side replicates
Row means and totals
Frequency Distributions
Visualizing scatter and testing for normality without a frequency distribution
How to: Frequency distribution
Graphing tips: Frequency distributions
Fitting a Gaussian distribution to a frequency distribution
Analyzing curves
Smoothing, differentiating and integrating curves
Area under the curve
Normality (and lognormality) tests
How to: Normality test
Choosing a normality test
Testing for lognormality
Comparing normal and lognormal distributions
QQ plot
Interpreting results: Normality tests
Q&A: Normality tests
Identifying outliers
How to: Identify outliers
Analysis checklist: Outliers
One sample t test and Wilcoxon signed rank test
How to: One-sample t test and Wilcoxon signed rank test
Experimental design tab
Options tab
Interpreting results: One-sample t test
Interpreting results: Wilcoxon signed rank test
t tests, Mann-Whitney and Wilcoxon matched pairs test
Running a t test (or related nonparametric test)
Entering data for a t test
Experimental design tab: t tests
Options tab: t tests
Residuals tab: t tests
Q&A: Choosing a test to compare two groups
The advantage of pairing
Unpaired t test
How to: Unpaired t test from raw data
How to: Unpaired t test from averaged data
Interpreting results: Unpaired t
What to do when the groups have different standard deviations?
The unequal variance Welch t test
Graphing tips: Unpaired t
Advice: Don't pay much attention to whether error bars overlap
Analysis checklist: Unpaired t test
Paired or ratio t test
How to: Paired t test
Testing if pairs follow a Gaussian distribution
Interpreting results: Paired t
Analysis checklist: Paired t test
Graphing tips: Paired t
Paired or ratio t test?
How to: Ratio t test
Interpreting results: Ratio t test
Analysis checklist: Ratio t test
Mann-Whitney or Kolmogorov-Smirnov test
Choosing between the Mann-Whitney and Kolmogorov-Smirnov tests
How to: MW or KS test
Interpreting results: Mann-Whitney test
The Mann-Whitney test doesn't really compare medians
Analysis checklist: Mann-Whitney test
Why the results of Mann-Whitney test can differ from prior versions of Prism
Interpreting results: Kolmogorov-Smirnov test
Analysis checklist: Kolmogorov-Smirnov test
Wilcoxon matched pairs test
"The Wilcoxon test" can refer to several statistical tests
How to: Wilcoxon matched pairs test
Results: Wilcoxon matched pairs test
Analysis checklist: Wilcoxon matched pairs test
How to handle rows where the before and after values are identical
Multiple t tests
How to: Multiple t tests
Options for multiple t tests
Interpreting results: Multiple t tests
Volcano plot from multiple t tests
Nested t tests and ANOVA
Overview of nested factors
Example of a nested design with two treatments
Example of a nested design with three treatments
Lingo: Nested t test and Nested one-way ANOVA
How Prism performs the nested t test and one-way ANOVA
If P is high, should you pool?
Nested t test
How to: Nested t test
Interpreting results: Nested t test
Another example of a nested t test
Analysis checklist: Nested t test
Nested one-way ANOVA
How to: Nested one-way ANOVA
Interpreting results: Nested one-way ANOVA
Analysis checklist: Nested one-way ANOVA
Multiple comparisons after ANOVA
Overview on followup tests after ANOVA
Which multiple comparisons tests does Prism offer?
Relationship between overall ANOVA and multiple comparisons tests
Relationship between multiple comparisons tests and t tests
Correcting the main ANOVA P values for multiple comparisons?
Interpreting results from multiple comparisons after ANOVA
Statistical significance from multiple comparisons
Confidence intervals from multiple comparisons tests
Exact P values from multiple comparisons tests
False Discovery Rate approach to multiple comparisons
How the various multiple comparisons methods work
The pooled standard deviation
The SE of the difference between means
How the Tukey and Dunnett methods work
How the Fisher LSD method works
How the Holm-Sidak method works
How the Bonferroni and Sidak methods work
How the Dunn method for nonparametric comparisons works
How the Dunnett T3, Games and Howell, and Tamhane T2 tests work
How the methods used to control the FDR work
Mathematical details
Repeated measures ANOVA and mixed model analysis
What is repeated measures experimental design?
Missing values in repeated measures ANOVA
The mixed model approach to analyzing repeated measures data
Sphericity and compound symmetry
Quantifying violations of sphericity with epsilon
Analysis details for fitting the mixed model
"Not positive definite" ?
One-way ANOVA, Kruskal-Wallis and Friedman tests
How to: One-way ANOVA and mixed model
Entering data for one-way ANOVA and related tests
Experimental design tab: One-way ANOVA
Repeated measures tab
Multiple comparisons tab: One-way ANOVA
Options tab: Multiple comparisons: One-way ANOVA
Options tab: Graphing and output: One-way ANOVA
Residuals tab: One-way ANOVA
Q&A: One-way ANOVA
One-way ANOVA results
Interpreting results: One-way ANOVA
Analysis checklist: One-way ANOVA
Welch and Browne-Forsythe ANOVA
Interpreting results: Welch and Browne-Forsythe tests
Analysis checklist: Welch and Browne-Forsythe tests
Repeated-measures one-way ANOVA or mixed model
What is repeated measures?
Multiple comparisons after repeated measures one-way ANOVA
Interpreting results: Repeated measures one-way ANOVA
Interpreting results: Mixed model one-way
Interpreting results: Test for trend
Overview: Test for linear trend
Results from test for trend
How the test for trend works
Analysis checklist: Repeated-measures one way ANOVA
Kruskal-Wallis test
Interpreting results: Kruskal-Wallis test
Analysis checklist: Kruskal-Wallis test
Friedman's test
Interpreting results: Friedman test
Analysis checklist: Friedman's test
Two-way ANOVA
How to: Two-way ANOVA
Notes of caution for statistical novices
Deciding which factor defines rows and which defines columns?
Entering data for two-way ANOVA (not repeated measures)
Entering repeated measures data
Missing values and two-way ANOVA
Point of confusion: ANOVA with a quantitative factor
Repeated measures design tab: Two-way ANOVA
Repeated measures analysis tab: Two-way ANOVA
Factor names tab: Two-way ANOVA
Multiple comparisons tab: Two-way ANOVA
Options tab: Multiple comparisons: Two-way ANOVA
Summary of multiple comparisons available (two-way)
Options tab: Other choices
Residual tab: Two-way ANOVA
Q&A: Two-way ANOVA
Intepreting ordinary (not repeated measures) two-way ANOVA results
Interpreting results: Two-way ANOVA
Two-way ANOVA without replication
Graphing tips: Two-way ANOVA
Beware of using multiple comparisons tests to compare dose-response curves or time courses
How Prism computes two-way ANOVA
Table of means (or predicted means)
When there are only two rows
When there are two rows and two columns
Analysis checklist: Two-way ANOVA
Interpreting repeated measures two-way ANOVA results
Interpreting results: Repeated measures two-way ANOVA
ANOVA table in two ways RM ANOVA
Intepreting results: Mixed model two-way
Graphing tips: Repeated measures two-way ANOVA
Table of means or predicted means
Analysis checklist: Repeated measures two-way ANOVA (and mixed model)
Three-way ANOVA
How to: Three-way ANOVA
Note of caution for statistical novices
What is three-way ANOVA used for?
Three way ANOVA may not answer your scientific questions
Entering data for three-way ANOVA
Repeated measures design tab: Three-way ANOVA
Repeated measures analysis tab
Factor names tab: Three-way ANOVA
Multiple comparisons tab: Three-way ANOVA
Options tab: Multiple comparisons: Three-way ANOVA
Options tab: Graphing and output: Three-way ANOVA
Residuals tab: Three-way ANOVA
Consolidate tab: Three-way ANOVA
Interpreting results: Three-way ANOVA
Interpreting results: Three-way ANOVA
Analysis checklist: Three-way ANOVA
Categorical outcomes
The Confidence Interval of a proportion
How Prism can compute a confidence interval of a proportion
Three methods for computing the CI of a proportion
The meaning of “95% confidence” when the numerator is zero
What are binomial variables
Contingency tables
Key concepts: Contingency tables
How to: Contingency table analysis
Fisher's test or chi-square test?
Interpreting results: P values from contingency tables
Interpreting results: Attributable risk
Interpreting results: Relative risk
Interpreting results: Odds ratio
Interpreting results: Sensitivity and specificity
Analysis checklist: Contingency tables
Graphing tips: Contingency tables
Compare observed and expected distributions
How to: Compare observed and expected distributions
How the chi-square goodness of fit test works
The binomial test
McNemar's test
Don't confuse with related analyses
Analysis Checklist: Comparing observed and expected distributions
Survival analysis
How to: Survival analysis
Key concepts. Survival curves
How to: Survival analysis
Q & A: Entering survival data
Example of survival data from a clinical study
Example of survival data from an animal study
Analysis choices for survival analysis
Intepreting results: Survival analysis
Interpreting results: Survival proportions
What determines how low a survival curve gets?
Interpreting results: Number at risk
Interpreting results: P Value
Interpreting results: The hazard ratio
Interpreting results: Median survival times
Intepreting results: Ratio of median survival times
Interpreting results: Comparing >2 survival curves
The logrank test for trend
Multiple comparisons of survival curves
Analysis checklist: Survival analysis
Graphing tips: Survival curves
Q&A: Survival analysis
Determining the median followup time
Correlation
Key concepts: Correlation
How to: Correlation
Interpreting results: Correlation
Analysis checklist: Correlation
Correlation matrix
The difference between correlation and regression
Diagnostic lab analyses
ROC Curves
Key concepts: Receiver-operating characteristic (ROC) curves
How to: ROC curve
Interpreting results: ROC curves
Analysis checklist: ROC curves
Calculation details for ROC curves
Computing predictive values from a ROC curve
Comparing ROC curves
Comparing Methods with a Bland-Altman Plot
How to: Bland-Altman plot
Interpreting results: Bland-Altman
Analysis checklist: Bland-Altman results
Analyzing a stack of P values
Key concepts: Analyzing a stack P values
How to: Analyzing a stack of P values
Interpreting results: Analyzing a stack of P values
Simulating data and Monte Carlo simulations
Simulating a XY data table
Simulating a Column data table
Simulating a Contingency data table
How to: Monte Carlo analyses
Monte Carlo example: Accuracy of confidence intervals
Monte Carlo example: Power of unpaired t test
Using a script to simulate many data sets
How Prism generates random numbers
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