# L_OR: Likelihood Support for Odds Ratio (OR) In likelihoodR: Likelihood Analyses for Common Statistical Tests

## Description

This function calculates the support for an OR from a 2 x 2 categorical data table. An expected OR can be specified and the support calculated for this relative to the observed and null (which is assumed to be 1, but can also be specified) values. A likelihood function is plotted for the obtained OR with a specified likelihood interval, and expected OR, if specified. Chi-squared and likelihood ratio test (G) statistics are also provided and a likelihood-based % confidence interval. It uses the optimize function to locate desired limits for both intervals and other support calculations.

## Usage

 `1` ```L_OR(table, null=1, exp.OR=NULL, L.int=2, alpha=0.05, cc=FALSE, toler=0.0001, verb=TRUE) ```

## Arguments

 `table` a 2 x 2 matrix or contingency table containing counts. `null` the value against which the obtained OR is tested, default = 1. `exp.OR` an expected or hypothetical OR. `L.int` likelihood interval given as support values, e.g. 2 or 3, default = 2. `alpha` the significance level used, 1 - alpha interval calculated, default = 0.05. `cc` logical indicating whether to apply continuity correction, default = FALSE. `toler` the desired accuracy using optimise, default = 0.0001. `verb` show output, default = TRUE.

## Value

\$S.val - support for observed OR from expected.

\$df - degrees of freedom.

\$exp.OR - expected OR.

\$S.exp.ORvsObs - support for expected OR versus observed.

\$S.exp.ORvsNull - support for expected OR versus the null.

\$L.int - likelihood interval of observed OR for specified level of support.

\$S_int - specified likelihood interval in units of support.

\$observed - observed frequencies.

\$expected - the expected values for null hypothesis of no interaction.

\$chi.sq - chi-squared statistic.

\$corrected - whether chi-squared was corrected, default = FALSE.

\$p.value - p value.

\$LR.test = the likelihood ratio test statistic.

\$lrt.p = the p value for the likelihood ratio test statistic

\$residuals - the Pearson residuals.

\$alpha - specified significance level.

\$conf.int - likelihood-based confidence interval for observed RR.

\$all.err.acc - error accuracy for each application of the optimize function.

## References

Aitkin, M. et al (1989) Statistical Modelling in GLIM, Clarendon Press, ISBN : 978-0198522041

Cahusac, P.M.B. (2020) Evidence-Based Statistics, Wiley, ISBN : 978-1119549802

Royall, R. M. (1997). Statistical evidence: A likelihood paradigm. London: Chapman & Hall, ISBN : 978-0412044113

Edwards, A.W.F. (1992) Likelihood, Johns Hopkins Press, ISBN : 978-0801844430

Dienes, Z. (2008) Understanding Psychology as a Science: An Introduction to Scientific and Statistical Inference, Palgrave, MacMillan, ISBN : 978-0230542303

## Examples

 ```1 2 3 4``` ```# for folic acid and neural tube defects example, p 146 tab <- as.table(rbind(c(6,587),c(21,581))) dimnames(tab) <- list(Treatment=c("Folic acid","None"),Defect=c("Yes","No")) L_OR(tab, exp.OR = 0.5, L.int = 2) ```

likelihoodR documentation built on Dec. 11, 2021, 9:42 a.m.