# BTD_cov: Bayesian Test of Deficit with Covariates In singcar: Comparing Single Cases to Small Samples

## Description

Takes a single observation and compares it to a distribution estimated by a control sample, while controlling for the effect of covariates, using Bayesian methodology. This test is used when assessing a case conditioned on some other variable, for example, assessing abnormality when controlling for years of education or sex. Under the null hypothesis the case is an observation from the distribution of scores from the task of interest coming from observations having the same score as the case on the covariate(s). Returns a significance test, point and interval estimates of difference between the case and the mean of the controls as well as point and interval estimates of abnormality, i.e. an estimation of the proportion of controls that would exhibit a more extreme conditioned score. This test is based on random number generation which means that results may vary between runs. This is by design and the reason for not using `set.seed()` to reproduce results inside the function is to emphasise the randomness of the test. To get more accurate and stable results please increase the number of iterations by increasing `iter` whenever feasible. Developed by Crawford, Garthwaite and Ryan (2011).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```BTD_cov( case_task, case_covar, control_task, control_covar, alternative = c("less", "two.sided", "greater"), int_level = 0.95, iter = 10000, use_sumstats = FALSE, cor_mat = NULL, sample_size = NULL ) ```

## Arguments

 `case_task` The case score from the task of interest. Must be a single value. `case_covar` A vector containing the case scores on all covariates included. Can be of any length except 0, in that case use `BTD`. `control_task` A vector containing the scores from the controls on the task of interest. Or a vector of length 2 containing the mean and standard deviation of the task. In that order. `control_covar` A vector, matrix or dataframe containing the control scores on the covariates included. If matrix or dataframe each column represents a covariate. Or a matrix or dataframe containing summary statistics where the first column represents the means for each covariate and the second column represents the standard deviation. `alternative` A character string specifying the alternative hypothesis, must be one of `"two.sided"` (default), `"greater"` or `"less"`. You can specify just the initial letter. `int_level` The probability level on the Bayesian credible intervals, defaults to 95%. `iter` Number of iterations to be performed. Greater number gives better estimation but takes longer to calculate. Defaults to 10000. `use_sumstats` If set to `TRUE`, `control_tasks` and `control_covar` are treated as matrices with summary statistics. Where the first column represents the means for each variable and the second column represents the standard deviation. `cor_mat` A correlation matrix of all variables included. NOTE: the first variable should be the task of interest. `sample_size` An integer specifying the sample size of the controls.

## Details

Uses random generation of inverse wishart distributions from the CholWishart package (Geoffrey Thompson, 2019).

## Value

A list with class `"htest"` containing the following components:

 `statistic` the average z-value over `iter` number of iterations. `parameter` the degrees of freedom used to specify the posterior distribution. `p.value` the average p-value over `iter` number of iterations. `estimate` case scores expressed as z-scores on task X and Y. Standardised effect size (Z-CCC) of task difference between case and controls and point estimate of the proportion of the control population estimated to show a more extreme task difference. `null.value` the value of the difference between tasks under the null hypothesis. `interval` named numerical vector containing level of confidence and confidence intervals for both effect size and p-value. `desc` data frame containing means and standard deviations for controls as well as case scores. `cor.mat` matrix giving the correlations between the task of interest and the covariates included. `sample.size` number of controls.. `alternative` a character string describing the alternative hypothesis. `method` a character string indicating what type of test was performed. `data.name` a character string giving the name(s) of the data

## References

Crawford, J. R., Garthwaite, P. H., & Ryan, K. (2011). Comparing a single case to a control sample: Testing for neuropsychological deficits and dissociations in the presence of covariates. Cortex, 47(10), 1166-1178. doi: 10.1016/j.cortex.2011.02.017

Geoffrey Thompson (2019). CholWishart: Cholesky Decomposition of the Wishart Distribution. R package version 1.1.0. https://CRAN.R-project.org/package=CholWishart

## Examples

 ```1 2 3 4``` ```BTD_cov(case_task = size_weight_illusion[1, "V_SWI"], case_covar = size_weight_illusion[1, "YRS"], control_task = size_weight_illusion[-1, "V_SWI"], control_covar = size_weight_illusion[-1, "YRS"], iter = 100) ```

singcar documentation built on March 1, 2021, 5:07 p.m.