altFrequencyMat {PoolBal}

Identify a region of plausible alternative hypotheses in the proportion, strength of non-null evidence space

Description

This function provides a convenient way to interact with simulations performed over a grid of possible alternatives spanning the proportion (eta) and strength (KL divergence) of evidence against the null hypothesis under beta alternatives.

Usage

altFrequencyMat(logKappaRange, logW = FALSE)

Arguments

logKappaRange

pair of numeric values

logW

logical, should the log scale simulation be used?

Details

The simulation this function summarized used a range of eta, w, and KL divergence values to generate thousands of potential alternative distributions. The power of each chi-squared pooled p-value for 161 kappa values ranging from exp(-8) to exp(8) selected uniformly on the log scale was then computed for each alternative using 10,000 simulated examples. Every choice of kappa was compared to the maximum power across all kappas for each setting using a binomial test of differences. This same simulation was repeated twice: once for w values selected uniformly from 0 to 1 and another where selection was uniform on the log scale. The internal data summarizes the results by reporting the count of instances in w (or logw) where a given kappa value was most powerful for a given eta and KL divergence.

Though the simulation data is not exported to users and so cannot be accessed directly, this function allows a user to query the data with a range of kappa values (corresponding to those where a given sample seems most powerful) and returns the count of cases in w where a kappa in the corresponding kappa range was most powerful given the eta, KL-divergence combination with beta alternatives. The simulations only spanned kappa values from exp(-8) to exp(8), so providing values outside this range will give very inaccurate results.

Value

An 81 by 81 matrix giving summarized counts of cases.

Author(s)

Chris Salahub

Examples

altFrequencyMat(c(-1, 1), logW = FALSE)
altFrequencyMat(c(-1, 1), logW = TRUE)