# Statistics

Note: sv_simfit has a simplified version of this program with fewer options
Abstract

The main Simfit statistical program is called Simstat and there are test files to demonstrate every option. Also, note that the reference manual contains the theory for all of the procedures supported by Simfit together with worked examples. In addition there are numerous dedicated programs that often have additional statistical options.

Program Simstat

1. The Simstat data exploration options
   Exhaustive-analysis: arbitrary vector
   Exhaustive-analysis: arbitrary matrix
   Exhaustive-analysis: multivariate-normal matrix
   All possible pairwise MWU/KS2/t-tests
   Robust analysis: one sample
   Robust analysis: two samples
2. The Simstat standard tests options
   1-sample t test
   1-sample Kolmogorov-Smirnov test
   1-sample normal distribution test
   1-sample Poisson distribution test
   2-sample unpaired t test
   2-sample paired t test
   2-sample Kolmogorov-Smirnov test
   2-sample Wilcoxon-Mann-Whitney-U test
   2-sample Wilcoxon signed-rank test
   Chi-sq./Fisher-exact/log-linear contingency table
   McNemar test on paired frequencies
   Cochran Q test (on 0/1 integer matrix)
   Binomial test: K successes in N trials
   Sign test: known number of +/- signs
   Runs test: known number of +/-, runs
   F test for excess variance: two WSSQ
3. The Simstat Analysis of Variance options (ANOVA)
   Bartlett and Levene tests for homogeneity of variance
   1-way and Kruskal-Wallis nonparametric
   1-way only
   1-way Kruskal-Wallis only
   2-way and Friedman nonparametric
   2-way only
   2-way Friedman only
   Latin Square
   Groups and subgroups
   Factorial design
   Repeated measures
4. The Simstat Analysis of Proportions options
   Analysis of proportions
   Cochran-Mantel-Haenszel Meta Analysis
   Bioassay, Dose response and LD50
5. The Simstat multivariate statistics options
   Correlation: Pearson Product Moment
   Correlation: Spearman and Kendall-tau
   Correlation: canonical (2 subgroups)
   Correlation: partial (>2 variables))
   Clusters: dendrograms (arbitrary matrix)
   Clusters: scaling from (arbitrary matrix)
   Clusters: dendrograms and scaling (distance matrix)
   Clusters: K-means
   Principal components analysis: PCA
   Rotation: Procrustes analysis
   Rotation: Varimax or Quartimax
   Compare groups: MANOVA/means/profiles
   Compare groups: canonical variates/PCA
   Compare groups: distances/allocations
   Factor analysis
   Biplots
6. The Simstat regression options
   Fit a line (simple least squares)
   Fit a line (simple reduced major axis)
   Fit a line (simple orthogonal)
   Fit a line (advanced least squares)
   Fit a line (advanced reduced major axis)
   Fit a line (advanced orthogonal)
   Fit a line/calibrate (simple)
   Fit a line/calibrate (advanced)
   Fit a polynomial/calibrate (x,y)
   Fit a polynomial/calibrate (g(x),f(y))
   Fit a multilinear model f(x1,x2,...,xn)
   Fit a dose-response curve (LD50 by GLM)
   Fit logistic regression models (by GLM)
   Fit Cox proportional hazards model
   Compare 2 regression parameters
   Compare 2 sets of regression parameters
7. The Simstat Generalized Linear Model Options
   Comprehensive GLM options
   Logistic regression
   Binary logistic regression (no strata)
   Binary logistic regression (with strata)
   Polynomial logistic regression
   Exponential survival
   Weibull survival
   Extreme value survival
   Cox proportional hazard survival
   Contingency table analysis
   Bioassay (percentiles/EC50/LD50)
8. The Simstat time series and survival options
   Data smoothing
   Lags, ACF and PACF
   Fit and predict by ARIMA
   Survival curves (Kaplan-Meier)
   Survival analysis (GLM techniques)
   Cox proportional hazard analysis
9. The Simstat statistical calculations options
   Statistical power and sample size
   Estimate parameter confidence limits
   Robust calculations for one sample
   Robust calculations for two samples
   Shannon/Brillouin diversity indices
   Plot/evaluate Standard distributions
   Plot/evaluate Non-central distributions
   Quantify ligand binding cooperativity
   Random numbers/permutions/Latin-Squares
   Kernel density estimation
10. The Simstat numerical analysis options
    Polynomial: calculate zeros
    Matrix: determinant/eigenvalues/inverse
    Matrix: singular value decomposition
    Matrix: LU factorisation/norms/cond.no.
    Matrix: QR factorisation
    Matrix: Cholesky factorisation
    Solve: Ax = b (A nonsingular)
    Solve: Ax = b (L_1 norm overdetermined)
    Solve: Ax = b (L_2 norm overdetermined)
    Solve: Ax = b (L_i norm overdetermined)
    Calculate: (y^T)Ay, (y^T)(A^{-1})y
    Calculate: AB,(A^T)B,A(B^T),(A^T)(B^T)
    Calculate: Ax = lambda*Bx (B pos.def.)
    Rotation: Orthomax
    Rotation: Procrustes

Advanced statistics programs with additional options

- Program RSTEST
  Nonparametric statistics, e.g., runs, signs, Kolmogorov-Smirnov, Mann-Whitney, Kruskal-Wallis, Friedman, regression on ranks, etc.
- Program BINOMIAL
  The binomial, Poisson, and non-central beta distributions.
- Program CHISQD
  The chi-square and non-central chi-square distributions.
- Program FTEST
  The F and non-central F distributions.
- Program RANNUM
  Pseudo random vectors, matrices, Latin squares, and random walks in 1, 2, or 3 dimensions.
- Program LINFIT
  Comprehensive linear regression techniques, e.g., L_1, L_2, L_infinity, Robust (M-estimates).
- Program NORMAL
  The normal distribution.
- Program GCFIT
  Nonlinear growth curves, survival curves, and survival analysis
- Program TTEST
  The t and non-central t distributions.
- Program SPLINE Fitting least squares, smoothing, or cross-validatory splines to calibrate, or estimate derivatives, areas, arc length, curvatures, etc.

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