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Statistical Comparisons

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  • Paired or unpaired t tests. Reports P values and confidence intervals
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  • Automatically generate volcano plot (difference vs. P value) from multiple t test analysis
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  • Nonparametric Mann-Whitney test, including confidence interval of difference of medians
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  • Kolmogorov-Smirnov test to compare two groups
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  • Wilcoxon test with confidence interval of median
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  • Perform many t tests at once, using False Discovery Rate (or Bonferroni multiple comparisons) to choose which comparisons are discoveries to study further
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  • Ordinary or repeated measures ANOVA followed by the Tukey, Newman-Keuls, Dunnett, Bonferroni or Holm-Sidak multiple comparison tests, the post-test for trend, or Fisher’s Least Significant tests
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  • One-way ANOVA without assuming populations with equal standard deviations using Brown-Forsythe and Welch ANOVA, followed by appropriate comparisons tests (Games-Howell, Tamhane T2, Dunnett T3)
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  • Many multiple comparisons test are accompanied by confidence intervals and multiplicity adjusted P values
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  • Greenhouse-Geisser correction so repeated measures one-, two-, and three-way ANOVA do not have to assume sphericity. When this is chosen, multiple comparison tests also do not assume sphericity
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  • Kruskal-Wallis or Friedman nonparametric one-way ANOVA with Dunn’s post test
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  • Fisher’s exact test or the chi-square test. Calculate the relative risk and odds ratio with confidence intervals
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  • Two-way ANOVA, even with missing values with some post tests
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  • Two-way ANOVA, with repeated measures in one or both factors. Tukey, Newman-Keuls, Dunnett, Bonferroni, Holm-Sidak, or Fisher’s LSD multiple comparisons testing main and simple effects
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  • Three-way ANOVA (limited to two levels in two of the factors, and any number of levels in the third)
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  • Analysis of repeated measures data (one-, two-, and three-way) using a mixed effects model (similar to repeated measures ANOVA, but capable of handling missing data)
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  • Kaplan-Meier survival analysis. Compare curves with the log-rank test (including test for trend)
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  • Comparison of data from nested data tables using nested t test or nested one-way ANOVA (using mixed effects model)
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Nonlinear Regression

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  • Fit one of our 105 built-in equations, or enter your own. Now including family of growth equations: exponential growth, exponential plateau, Gompertz, logistic, and beta (growth and then decay)
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  • Enter differential or implicit equations
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  • Enter different equations for different data sets
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  • Global nonlinear regression – share parameters between data sets
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  • Robust nonlinear regression
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  • Automatic outlier identification or elimination
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  • Compare models using extra sum-of-squares F test or AICc
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  • Compare parameters between data sets
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  • Apply constraints
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  • Differentially weight points by several methods and assess how well your weighting method worked
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  • Accept automatic initial estimated values or enter your own
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  • Automatically graph curve over specified range of X values
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  • Quantify precision of fits with SE or CI of parameters. Confidence intervals can be symmetrical (as is traditional) or asymmetrical (which is more accurate)
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  • Quantify symmetry of imprecision with Hougaard’s skewness
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  • Plot confidence or prediction bands
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  • Test normality of residuals
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  • Runs or replicates test of adequacy of model
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  • Report the covariance matrix or set of dependencies
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  • Easily interpolate points from the best fit curve
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  • Fit straight lines to two data sets and determine the intersection point and both slopes
 

Simulations

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  • Simulate XY, Column or Contingency tables
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  • Repeat analyses of simulated data as a Monte-Carlo analysis
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  • Plot functions from equations you select or enter and parameter values you choose

Principal Component Analysis (PCA)

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  • Component selection via Parallel Analysis (Monte Carlo simulation), Kaiser criterion (Eigenvalue threshold), Proportion of Variance threshold, and more
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  • Automatically generated Scree Plots, Loading Plots, Biplots, and more
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  • Use results in downstream applications like Principal Component Regression
 

Multiple Variable Graphing

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  • Specify variables defining axis coordinates, color, and size
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  • Create Bubble Plots
 

Column Statistics

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  • Calculate descriptive statistics: min, max, quartiles, mean, SD, SEM, CI, CV, skewness, kurtosis
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  • Mean or geometric mean with confidence intervals
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  • Frequency distributions (bin to histogram), including cumulative histograms
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  • Normality testing by four methods (new: Anderson-Darling)
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  • Lognormality test and likelihood of sampling from normal (Gaussian) vs. lognormal distribution
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  • Create QQ Plot as part of normality testing
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  • One sample t test or Wilcoxon test to compare the column mean (or median) with a theoretical value
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  • Identify outliers using Grubbs or ROUT method
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  • Analyze a stack of P values, using Bonferroni multiple comparisons or the FDR approach to identify “significant” findings or discoveries
 

Simple Linear Regression and Correlation

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  • Calculate slope and intercept with confidence intervals
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  • Force the regression line through a specified point
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  • Fit to replicate Y values or mean Y
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  • Test for departure from linearity with a runs test
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  • Calculate and graph residuals in four different ways (including QQ plot)
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  • Compare slopes and intercepts of two or more regression lines
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  • Interpolate new points along the standard curve
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  • Pearson or Spearman (nonparametric) correlation
 

Generalized Linear Models (GLMs)

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  • Generate models relating multiple independent variables to a single dependent variable using the new multiple variables data table
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  • Multiple linear regression (when Y is continuous)
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  • Poisson regression (when Y is counts; 0, 1, 2, …)
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  • Logistic regression (when Y is binary; yes/no, pass/fail, etc.)
 

Clinical (Diagnostic) Lab Statistics

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  • Bland-Altman plots
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  • Receiver operator characteristic (ROC) curves
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  • Deming regression (type ll linear regression)
 

Other Calculations

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  • Area under the curve, with confidence interval
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  • Transform data
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  • Normalize
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  • Identify outliers
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  • Normality tests
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  • Transpose tables
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  • Subtract baseline (and combine columns)
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  • Compute each value as a fraction of its row, column or grand total