# SIMSTAT: Statistical Calculations

Power and Sample Size
This option is used to calculate statistical power given sample size or sample size needed for a given power when designing clinical trials. Be careful to select the correct distribution and options and make sure the parameters used in the calculation (mean, standard deviation, n) supplied as defaults have been adjusted for your own data. All parameters used are printed so you can check interactively or retrospectively that a correct parameter set has been used. The way these options work is that there will be a set of, say k, conditions and, by fixing any k - 1, the remaining parameter can be calculated by an iterative procedure, using integer arithmetic for the sample size component.
The most valuable way to use these options is to plot power as a function of sample size, then observe what happens to the power function as you change the parameters involved, such as the assumed variance or minimum difference detectable.

Parameter Confidence Limits
You provide data to estimate parameters and confidence limits for the standard distributions, e.g. normal, binomial, Poisson, etc. The significance level for these confidence limits can be set interactively.
If you have estimated x, y and z = N - (x + y) for a series of trinomial distributions, you can input a file like trinom.tf1, with columns of x, y and N, to perform a chi-square test for homogeneity and then visualise the probability contours. If the contours do not overlap, then the sample is not homogeneous, and the atypical trinomial parameters can be identified from the disjoint contours. The significance level can be altered independently of the others in this section.

Robust calculations with one sample
You input a sample with suspected outliers that would lead to bias when calculating the usual sample statistics. This procedure then calculates the median, median absolute deviation, robust standard deviation estimate, together with the trimmed and winsorized means and variance estimates. The Hodges-Lehmann location estimator and 95% confidence limits are calculated for cases where the sample distribution is presumed to be symmetrical. This is useful where a vector of differences is available, such as when using the Wilcoxon signed rank test for H0: X is distributed F(x) and Y is distributed F(x - theta).

Robust calculations with two samples
Two samples are input and the differences in locations (theta) is estimated along with confidence limits and the corresponding limiting U values in a Mann-Whitney U test for testing H0: X is distributed F(x) and Y is distributed F(x - theta).

Diversity indices
Given a set of positive integer frequencies, e.g. for the occurrence of events (species) within groups (regions), the Shannon, Brillouin, Pielou, and Simpson measures of diversity are calculated.

Ligand Binding Cooperativity
You input overall binding constants and a cooperativity analysis is done. This includes transforming the binding polynomial constants into all the alternative spaces, plotting species fractions and transforms of the saturation function, estimating minmax Hill slopes, and zeros of the binding polynomial and Hessian.

Standard distributions
You can input parameters then calculate pds, cdfs and percentage points for the normal, t, chi-square, F, beta or gamma distributions, to avoid table look up when exploring the results of testing.

Non central distributions
You can input parameters then calculate probabilities for the non-central t, chi-square, beta and F distributions, to avoid table look up when doing advanced power/sample-size calculations.

Random numbers, permutations and Latin Squares
When designing experiments it is often necessary to generate random numbers of various types. For instance, random permutations of an integer or alphabetical vector are used to assign subjects to groups, and random Latin Squares are required when distributing treatments for ANOVA. This option allows you to generate uniformly distributed numbers or integers, normally distributed numbers, and uniformly distributed permutations of integer sequences or Latin Squares. Further options are provided by program RANNUM.

Kernel density estimation
Given a sample of size n, the number of bins for plotting, and the number of density points required, a Gaussian kernel density estimate can be calculated then plotted as a pdf against the sample histogram, and as a cdf against the sample cumulative distribution function.

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