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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