Confidence interval to check for difference: Use 1.96 SE and not 1.96 SD !

Let create two variables of length 100, one with mean 10 (A) and one with mean 12 (B) both with SD=2. Of course the two variables overlap.

A <- rnorm(100, 10, 2)

B <- rnorm(100, 12, 2)

library(HelpersMG)

barplot_errbar(c(mean(A) ,mean(B)), errbar.y = c(1.96*sd(A), 1.96*sd(B)), las=1, ylim=c(0, 20), main="1.96 x SD")

Now do a t test. It is highly significant:

t.test(A, B)


Welch Two Sample t-test


data:  A and B

t = -7.8344, df = 197.93, p-value = 2.82e-13

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

 -2.737632 -1.636588

sample estimates:

mean of x mean of y 

 9.741912 11.929021 

Then if you want use the overall of confidence interval, use SE:

barplot_errbar(c(mean(A) ,mean(B)), errbar.y = c(1.96*sd(A)/sqrt(length(A)),  1.96*sd(B)/sqrt(length(A))), las=1, ylim=c(0, 12), main="1.96 x SE")

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