associationMatrix produces a matrix with confidence intervals for effect sizes, point estimates for those effect sizes, and the p-values for the test of the hypothesis that the effect size is zero, corrected for multiple testing.

```
associationMatrix(
dat = NULL,
x = NULL,
y = NULL,
conf.level = 0.95,
correction = "fdr",
bootstrapV = FALSE,
info = c("full", "ci", "es"),
includeSampleSize = "depends",
bootstrapV.samples = 5000,
digits = 2,
pValueDigits = digits + 1,
colNames = FALSE,
type = c("R", "html", "latex"),
file = "",
statistic = associationMatrixStatDefaults,
effectSize = associationMatrixESDefaults,
var.equal = TRUE
)
# S3 method for associationMatrix
print(x, type = x$input$type, info = x$input$info, file = x$input$file, ...)
# S3 method for associationMatrix
pander(x, info = x$input$info, file = x$input$file, ...)
```

- dat
A dataframe with the variables of interest. All variables in this dataframe will be used if both x and y are NULL. If dat is NULL, the user will be presented with a dialog to select a datafile.

- x
If not NULL, this should be a character vector with the names of the variables to include in the rows of the association table. If x is NULL, all variables in the dataframe will be used.

- y
If not NULL, this should be a character vector with the names of the variables to include in the columns of the association table. If y is NULL, the variables in x will be used for the columns as well (which produces a symmetric matrix, similar to most correlation matrices).

- conf.level
Level of confidence of the confidence intervals.

- correction
Correction for multiple testing: an element out of the vector c("holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none"). NOTE: the p-values are corrected for multiple testing; The confidence intervals are not!

- bootstrapV
Whether to use bootstrapping to compue the confidence interval for Cramer's V or whether to use the Fisher's Z conversion.

- info
Information to print: either both the confidence interval and the point estimate for the effect size (and the p-value, corrected for multiple testing), or only the confidence intervals, or only the point estimate (and the corrected p-value). Must be on element of the vector c("full", "ci", "es").

- includeSampleSize
Whether to include the sample size when the effect size point estimate and p-value are shown. If this is "depends", it will depend on whether all associations have the same sample size (and the sample size will only be printed when they don't). If "always", the sample size will always be added. If anything else, it will never be printed.

- bootstrapV.samples
If using boostrapping for Cramer's V, the number of samples to generate.

- digits
Number of digits to round to when printing the results.

- pValueDigits
How many digits to use for formatting the p values.

- colNames
If true, the column heading will use the variables names instead of numbers.

- type
Type of output to generate: must be an element of the vector c("R", "html", "latex").

- file
If a file is specified, the output will be written to that file instead of shown on the screen.

- statistic
This is the complicated bit; this is where associationMatrix allows customization of the used statistics to perform null hypothesis significance testing. For everyday use, leaving this at the default value, associationMatrixStatDefaults, works fine. In case you want to customize, read the 'Notes' section below.

- effectSize
Like the 'statistics' argument, 'effectSize also allows customization, in this case of the used effect sizes. Again, the default value, associationMatrixESDefaults, works for everyday use. Again, see the 'Notes' section below if you want to customize.

- var.equal
Whether to test for equal variances ('test'), assume equality ('yes'), or assume unequality ('no').

- ...
Addition arguments are passed on to the

`print()`

amd`pander::pander()`

functions.

An object with the input and several output variables, one of which is a dataframe with the association matrix in it. When this object is printed, the association matrix is printed to the screen. If the 'file' parameter is specified, a file with this matrix will also be written to disk.

The 'statistic' and 'effectSize' parameter make it possible to use different functions to conduct null hypothesis significance testing and compute effect sizes. In both cases, the parameter needs to be a list containing four lists, named 'dichotomous', 'nominal', 'ordinal', and 'interval'. Each of these lists has to contain four elements, character vectors of length one (i.e. just one string value), again named 'dichotomous', 'nominal', 'ordinal', and 'interval'.

The combination of each of these names (e.g. 'dichotomous' and 'nominal', or 'ordinal' and 'interval', etc) determine which test should be done when computing the p-value to test the association between two variables of those types, or which effect sizes to compute. When called, associationMatrix determines the measurement levels of the relevant variables. It then uses these two levels (their string representation, e.g. 'dichotomous' etc) to find a string in the 'statistic' and 'effectSize' objects. Two functions with these names are then called from two lists, 'computeStatistic' and computeEffectSize. These lists list contain functions that have the same names as the strings in the 'statistic' list.

For example, when the default settings are used, the string (function name)
found for two dichotomous variables when searching in
associationMatrixStatDefaults is 'chisq', and the string found in
associationMatrixESDefaults is 'v'. associationMatrix then calls
`computeStatistic[['chisq']]`

and `computeEffectSize[['v']]`

, providing the two
variables as arguments, as well as passing the 'conf.level' argument. These
two functions then each return an object that associationMatrix extracts the
information from. Inspect the source code of these functions (by typing
their names without parentheses in the R prompt) to learn how this object
should look, if you want to write your own functions.

```
### Generate a simple association matrix using all three variables in the
### Orange tree dataframe
associationMatrix(Orange);
#> 1. 2. 3.
#> 1. Tree
#>
#> 2. age e=[0; NA]
#> e=0, p=1
#> 3. circumference e=[0; 0.19] r=[0.83; 0.96]
#> e=0.11, p=.728 r=0.91, p<.001
### Or four variables from infert:
associationMatrix(infert, c("education", "parity",
"induced", "case"), colNames=TRUE);
#> education parity induced case
#> education
#>
#> parity e=[0.09; 0.23]
#> e=0.16, p<.001
#> induced e=[0.01; 0.08] r=[0.34; 0.54]
#> e=0.04, p=.011 r=0.45, p<.001
#> case e=[0; NA] r=[-0.12; 0.13] r=[-0.11; 0.14]
#> e=0, p=.999 r=0.01, p=.999 r=0.02, p=.999
### Use variable names in the columns and generate html
associationMatrix(Orange, colNames=TRUE, type='html');
#> Tree age circumference
#> Tree "" "" ""
#> <!-- Variable 1 --> "" "" ""
#> age "e=[0; NA]" "" ""
#> <!-- Variable 2 --> "e=0, p=1" "" ""
#> circumference "e=[0; 0.19]" "r=[0.83; 0.96]" ""
#> <!-- Variable 3 --> "e=0.11, p=.728" "r=0.91, p<.001" ""
```