reg.param.t.test: T-test of two regression slopes or intercepts

In jacobmaugoust/ULT: Useful Little Things

T-test of two regression slopes or intercepts

Description

This function performs a t-test to test whether two regression slopes or two regression intercepts are equal or not. It can also be used to test whether a regression slope or intercept is equal to a given value.

Usage

reg.param.t.test(x, y, factor, x2, y2, object_1, object_2, delta, parameter)

Arguments

x	the x-values to be used. Can contain the two groups of data if the parameter factor is provided. Otherwise, contain the x-values for the first group.
y	the y-values to be used. As for x, it can contain the two groups of data if the parameter factor is provided. Otherwise, contain the y-values for the first group.
factor	mandatory if providing x and y data to separate two groups.
x2	the x-values to be used for the second group.
y2	the y-values to be used for the second group.
object_1	the output of the linear model for the first group; can be an output of "lm" or of "summary(lm)"
object_2	the output of the linear model for the second group; can be an output of "lm" or of "summary(lm)"
delta	An optional level value to compare a single slope with.
parameter	the parameter of the regression line to be tested; by default the "slope", otherwise can be the "intercept"

Details

The t-test can be performed on two x and y value vectors if also bringing a factor vector separating the x and y data in two subgroups. It can also be performed on two independant x and y value vectors, that are x, y, x2 and y2. Finally, it can be performed on two lm outputs (no matter if the output comes from lm() or summary(lm())).

Value

Returns an object containing the absolute difference between the two estimated parameters ($Estimate), the standard error of this difference ($Std. Error), the t-value of the t-test ($t value), the degrees of freedom of the test ($df) and the p-value of the bilateral t-test ($p-value).

Examples

## To test a pre-established vs estimated parameter
x<-c(sort(runif(100,0,100)))
y<-c()
slope<-runif(1,-100,100)
intercept<-runif(1,-100,100)
for (i in 1:length(x)){
  y[i]<-x[i]*slope+intercept+runif(1,-abs(slope)/100,abs(slope)/100)
}
parameter<-"slope"
reg.param.t.test(x,y,slope,parameter="intercept")
reg.param.t.test(y~x,slope,"slope")
reg.param.t.test(lm(y~x),slope,parameter) ## This tests if the function retrieves the original defined slope as equal to the slope of
reg.param.t.test(lm(y~x),intercept,"intercept") ## This tests if the function retrieves the original defined intercept as equal to the intercept of lm()
reg.param.t.test(lm(y~x),0,parameter)[c(1,2,3,5)]==summary(lm(y~x))$coefficients[2,]
reg.param.t.test(lm(y~x),0,"intercept")[c(1,2,3,5)]==summary(lm(y~x))$coefficients[1,]

## To compare two pre-established slopes
x1<-sort(runif(50,0,20))
x2<-sort(runif(50,0,20))
slope1<-runif(1,-100,100)
intercept<-runif(1,-100,100)
slope2<-runif(1,-100,100)
y1<-c()
y2<-c()
for (i in 1:length(x1)){
  y1[i]<-x1[i]*slope1+intercept+runif(1,-abs(slope1)/100,abs(slope1)/100)
  y2[i]<-x2[i]*slope2+intercept+runif(1,-abs(slope2)/100,abs(slope2)/100)
}
x12<-c(x1,x2)
y12<-c(y1,y2)
fac<-c(rep("1",50),rep("2",50))
parameter<-"slope"
object_1<-summary(lm(y12[fac==levels(factor(fac))[1]]~x12[fac==levels(factor(fac))[1]]))
object_2<-summary(lm(y12[fac==levels(factor(fac))[2]]~x12[fac==levels(factor(fac))[2]]))
plot(x1,y1,type="l",col="blue",ylim=c(min(min(y1),min(y2)),max(max(y1),max(y2))))
points(x2,y2,type="l",col="red")
reg.param.t.test(x12,y12,fac,parameter)
reg.param.t.test(y12~x12,fac,parameter)
reg.param.t.test(y1~x1,y2~x2,parameter)
reg.param.t.test(x1,y1,x2,y2,parameter)
reg.param.t.test(object_1,object_2,parameter)
summary(lm(y12~x12*fac))$coefficients[4,] ## Results do not perfectly fit but are roughly the same, don't know why now...

jacobmaugoust/ULT documentation built on May 16, 2023, 1:29 p.m.