# erpavetest: Significance testing of averaged ERPs. In ERP: Significance Analysis of Event-Related Potentials Data

## Description

The function first calculates averaged ERP values within a predetermined number of equally-spaced intervals then tests for significance of the relationship between averaged ERPs and covariates in a linear model framework.

## Usage

 ```1 2``` ```erpavetest(dta, design, design0 = NULL, nintervals = 10, method = c("none","BH","holm","hochberg","hommel","bonferroni","BY","fdr"),alpha = 0.05) ```

## Arguments

 `dta` Data frame containing the ERP curves: each column corresponds to a time frame and each row to a curve. `design` Design matrix of the nonnull model for the relationship between the ERP and the experimental variables. Typically the output of the function model.matrix `design0` Design matrix of the null model. Typically a submodel of the nonnull model, obtained by removing columns from design. Default is NULL, corresponding to the model with no covariates. `nintervals` Number of intervals in the partition of the whole interval of observation. Default is 10. `method` FDR- or FWER- controlling multiple testing procedures as available in the function p.adjust. Default is "none", for no multiplicity correction. `alpha` The FDR or FWER control level. Default is 0.05

## Value

 `pval` p-values of the tests. `correctedpval` Corrected p-values, for the multiplicity of tests. Depends on the multiple testing method (see function p.adjust). `significant` Indices of the time points for which the test is positive. `segments` Factor giving the membership of timepoints to each interval in the partition. `breaks` Breakpoints of the partition. `test` Pointwise F-statistics if p>1, where p is the difference between the numbers of parameters in the nonnull and null models. Otherwise, if p=1, the function returns pointwise t-statistics (signed square-roots of F-statistics). `df1` Residual degrees of freedom for the nonnull model. `df0` Residual degrees of freedom for the null model. `signal` Estimated signal: a pxT matrix, where T the number of frames. `r2` R-squared values for each of the T linear models.

## Author(s)

David Causeur, IRMAR, UMR 6625 CNRS, Agrocampus Ouest, Rennes, France.

`erptest`, `erpfatest`, `gbtest`, `p.adjust`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```data(impulsivity) # Paired t-tests for the comparison of the ERP curves in the two conditions, # within experimental group High, at channel CPZ erpdta.high = impulsivity[impulsivity\$Group=="High",5:505] # ERP curves for subjects in group 'High' covariates.high = impulsivity[impulsivity\$Group=="High",1:4] # Experimental covariates for subjects in group 'High' design = model.matrix(~C(Subject,sum)+Condition,data=covariates.high) # Design matrix to compare ERP curves in the two conditions design0 = model.matrix(~C(Subject,sum),data=covariates.high) # Design matrix for the null model (no condition effect) tests = erpavetest(erpdta.high,design,design0) time_pt = seq(0,1000,2) # sequence of time points (1 time point every 2ms in [0,1000]) nbs = 20 # Number of B-splines for the plot of the effect curve effect=which(colnames(design)=="ConditionSuccess") erpplot(erpdta.high,design=design,frames=time_pt,effect=effect,xlab="Time (ms)", ylab=expression(Effect~curve~(mu~V)),bty="l",ylim=c(-3,3),nbs=nbs, cex.axis=1.25,cex.lab=1.25,interval="simultaneous") # with interval="simultaneous", both the pointwise and the simultaneous confidence bands # are plotted abline(v=time_pt[tests\$breaks],lty=2,col="darkgray") # Add a grid to show breakpoints points(time_pt[tests\$significant],rep(0,length(tests\$significant)),pch=16,col="blue") # Identifies significant time points by blue dots title("Success-Failure effect curve with 95 percent C.I.",cex.main=1.25) mtext(paste("12 subjects - Group 'High' - ",nbs," B-splines",sep=""),cex=1.25) ```