# BTD: Bayesian Test of Deficit In singcar: Comparing Single Cases to Small Samples

## Description

Takes a single observation and compares it to a distribution estimated by a control sample using Bayesian methodology. Calculates standardised difference between the case score and the mean of the controls and proportions falling above or below the case score, as well as associated credible intervals. This approach was developed by Crawford and Garthwaite (2007) but converge to the results of `TD()`, which is faster. Returns the point estimate of the standardised difference between the case score and the mean of the controls and the point estimate of the p-value (i.e. the percentage of the population that would be expected to obtain a lower or higher score, depending on the alternative hypothesis). 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.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```BTD( case, controls, sd = NULL, sample_size = NULL, alternative = c("less", "greater", "two.sided"), int_level = 0.95, iter = 10000, na.rm = FALSE ) ```

## Arguments

 `case` Case observation, can only be a single value. `controls` Numeric vector of observations from the control sample. If single value, treated as mean. `sd` If input of controls is single value, the standard deviation of the sample must be given as well. `sample_size` If input of controls is single value, the size of the sample must be given as well. `alternative` A character string specifying the alternative hypothesis, must be one of `"less"` (default), `"greater"` or `"two.sided"`. You can specify just the initial letter. `int_level` Level of confidence for credible intervals, defaults to 95%. `iter` Number of iterations. Set to higher for more accuracy, set to lower for faster calculations. `na.rm` Remove `NA`s from controls.

## Value

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

 `statistic` the mean z-value over `iter` number of iterations `parameter` the degrees of freedom used to specify the posterior distribution. `p.value` the mean p-value for all simulated Z-scores. `estimate` estimated standardised difference (Z-CC) and point estimate of p-value. `null.value` the value of the difference under the null hypothesis. `interval` named numerical vector containing credibility level and intervals for both Z-CC and estimated proportion. `desc` named numerical containing descriptive statistics: mean and standard deviations of controls as well as sample size. `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 as well as summaries.

## References

Crawford, J. R., & Garthwaite, P. H. (2007). Comparison of a single case to a control or normative sample in neuropsychology: Development of a Bayesian approach. Cognitive Neuropsychology, 24(4), 343-372. doi: 10.1080/02643290701290146

## Examples

 ```1 2 3 4``` ```BTD(case = -2, controls = 0, sd = 1, sample_size = 20, iter = 1000) BTD(case = size_weight_illusion[1, "V_SWI"], controls = size_weight_illusion[-1, "V_SWI"], alternative = "l", iter = 1000) ```

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