Dear Greg: H0: Mean 1- Mean 2 = 0 Ha: Mean 1 - Mean 2 ! = 0
with many thanks abou ______________________ *AbouEl-Makarim Aboueissa, PhD* *Professor, Statistics and Data Science* *Graduate Coordinator* *Department of Mathematics and Statistics* *University of Southern Maine* On Fri, Nov 6, 2020 at 12:35 PM Greg Snow <538...@gmail.com> wrote: > A p-value is for testing a specific null hypothesis, but you do not > state your null hypothesis anywhere. > > It is the null value that needs to be subtracted from the bootstrap > differences, not the observed difference. By subtracting the observed > difference you are setting a situation where the p-value will always > be about 0.5 or about 1 (depending on 1 tailed or 2 tailed). If > instead you subtract a null value (such as 0), then the p-values will > be closer to what you are expecting. > > On Fri, Nov 6, 2020 at 9:44 AM AbouEl-Makarim Aboueissa > <abouelmakarim1...@gmail.com> wrote: > > > > *Dear All:* > > > > *I am trying to compute the p-value of the bootstrap test; please see > > below.* > > > > *In example 1 the p-value agrees with the confidence interval.* > > *BUT, in example 2 the p-value DOES NOT agree with the confidence > > interval. In Example 2, the p-value should be zero or close to zero.* > > > > *I am not sure what went wrong, or not sure if I missed something.* > > > > *any help would be appreciated.* > > > > > > *with many thanks* > > *abou* > > > > > > > > ##### Two - Sample Bootstrap > > > > ##### Source: > > http://www.ievbras.ru/ecostat/Kiril/R/Biblio_N/R_Eng/Chernick2011.pdf > > > > ##### Example 1: > > ##### ---------- > > > > > > > > set.seed(1) > > > > n1 <- 29 > > n1 > > x1 <- rnorm(n1, 1.143, 0.164) #some random normal variates: mean1 = 1.143 > > x1 > > > > n2 <- 33 > > n2 > > x2 <- rnorm(n2, 1.175, 0.169) #2nd random sample: mean2 = 1.175 > > x2 > > > > obs.diff.theta <- mean(x1) - mean(x2) > > obs.diff.theta > > > > theta <- as.vector(NULL) #### vector to hold difference estimates > > > > iterations <- 1000 > > > > for (i in 1:1000) { #bootstrap resamples > > xx1 <- sample(x1, n1, replace = TRUE) > > xx2 <- sample(x2, n2, replace = TRUE) > > theta[i] <- mean(xx1) - mean(xx2) > > } > > > > > > > > ##### Confidence Interval: > > ##### -------------------- > > > > > > quantile(theta, probs = c(.025,0.975)) #Efron percentile CI on difference > > in means > > > > ##### 2.5% 97.5% > > ##### - 0.1248539 0.0137601 > > > > > > ##### P-Value > > ##### ------- > > > > p.value <- (sum (abs(theta) >= obs.diff.theta) + 1)/ (iterations+1) > > > > ##### p.value <- (sum (theta >= obs.diff.theta) + 1)/ (iterations+1) > > > > p.value > > > > > > > > #### R OUTPUT > > > > #### > quantile(theta, probs = c(.025,0.975)) > > #### 2.5% 97.5% > > #### -0.12647744 0.02099391 > > > > #### > p.value <- (sum (abs(theta) >= obs.diff.theta) + 1)/ > (iterations+1) > > #### > p.value > > #### [1] 1 > > > > ##### Example 2: > > ##### ---------- > > > > > > set.seed(5) > > > > n1 <- 29 > > ### n1 > > x1 <- rnorm(n1, 10.5, 0.15) ###### sample 1 with mean1 = 10.5 > > ### x1 > > > > n2 <- 33 > > ### n2 > > x2 <- rnorm(n2, 1.5, 0.155) ##### Sample 2 with mean2 = 1.5 > > ### x2 > > > > obs.diff.theta <- mean(x1) - mean(x2) > > obs.diff.theta > > > > theta <- as.vector(NULL) #### vector to hold difference estimates > > > > iterations <- 1000 > > > > ##### bootstrap resamples > > > > for (i in 1:1000) { > > xx1 <- sample(x1, n1, replace = TRUE) > > xx2 <- sample(x2, n2, replace = TRUE) > > theta[i] <- mean(xx1) - mean(xx2) > > } > > > > > > > > ##### Confidence Interval: > > ##### -------------------- > > > > > > ###### CI on difference in means > > > > quantile(theta, probs = c(.025,0.975)) > > > > > > > > ##### P-Value > > ##### ------- > > > > p.value <- (sum (abs(theta) >= obs.diff.theta) + 1)/ (iterations+1) > > > > ##### p.value <- (sum (theta >= obs.diff.theta) + 1)/ (iterations+1) > > > > p.value > > > > ##### R OUTPUT > > > > #### > ###### CI on difference in means > > #### > > > #### > quantile(theta, probs = c(.025,0.975)) > > #### 2.5% 97.5% > > #### 8.908398 9.060601 > > > > #### > ##### P-Value > > #### > p.value <- (sum (abs(theta) >= obs.diff.theta) + 1)/ > (iterations+1) > > > > #### > p.value > > #### [1] 0.4835165 > > > > ______________________ > > > > > > *AbouEl-Makarim Aboueissa, PhD* > > > > *Professor, Statistics and Data Science* > > *Graduate Coordinator* > > > > *Department of Mathematics and Statistics* > > *University of Southern Maine* > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > > and provide commented, minimal, self-contained, reproducible code. > > > > -- > Gregory (Greg) L. Snow Ph.D. > 538...@gmail.com > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
