R day 3
In clinical trial studies, Pvalue is critical for measuring drug efficacy. Typically, the statistical analysis Plan will describe statistical significance as: Pvalue <0.05 for twotailed Log Rank Test.
Recently, I came across a study with the statistical significance as Pvalue <0.025 for onetailed Log Rank test in the analysis plan.
Question:
Does twotailed Pvalue= 0.05 means the same as Onetailed Pvalue =0.025 ?
If they are not the same? what are the differences?
let’s trying to figure out these questions by the following procedures.

What does Pvalue mean

What does twotailed Pvalue mean

What does onetailed Pvalue mean
Without loss of generality, Pvalue is the probability of the test results observed assuming the null hypothesis is correct.
Null hypothesis: the mean value is the same for Group A and Group B
H0: mean(Group A) = Mean(Group B)
m< 100 s< 30 x< seq(from=m5*s, to=m+5*s, by=1) y< dnorm(x,mean=m,sd=s) plot(x,y,type="l", col="darkgreen", lwd=2,las=1, main="TwoTailed") abline(v=m+2*s, col="orange",lwd=3) abline(v=m2*s, col="orange",lwd=3) polygon(c(x[x>=160],160),c(y[x>=160],y[x==0]),col="lightblue") polygon(c(x[x<=40],40),c(y[x<=40],y[x==0]),col="lightblue")
Twotailed Pvalue Test:
Pvalue (<0.05) reject or accept (p> 0.05) the Null hypothesis.
Pvalue >0.05, accept Null hypothesis, which means mean value is the same for Group A and Group B.
Pvalue <0.05, Reject the Null hypothesis, mean value of Group A is different from the mean value in Group B.
 Key interpretation: this part only stated the mean value for two Groups are not the same, but we can not take for grant that mean(group A) > mean(group B) or mean(group B) > mean(group A)
Onetailed Pvalue Test
Pvalue (<0.025) reject or accept (p> 0.025) the Null hypothesis
Pvalue <0.025, accept Null hypothesis, the mean value for Group A strictly greater the mean value for Group B.
m< 100 s< 30 x< seq(from=m5*s, to=m+5*s, by=1) y< dnorm(x,mean=m,sd=s) plot(x,y,type="l", col="darkgreen", lwd=2,las=1, main="OneTailed") abline(v=m+2*s,col="purple",lwd=3) polygon(c(x[x>=160],160),c(y[x>=160],y[x==0]),col="lightblue")
Summary:
In most cases, if the variable is continuous, a Onetailed pvalue is the same as Twotailed pvalue/2. But for noninferiority studies, we prefer to use Onetailed pvalue.
Thanks Jun and Renee 5 for the pvalue knowledge with me .
Happy Studying!