Why is bootci giving different interval than prctile?

I was trying to show confidence interval on a histogram with the following code.

n = 10e3;
data = randn(n,1);

alpha = 0.05;
nboot = 10e3;
mu = mean(data);

[ci,bootstat] = bootci(nboot,{@mean,data},"Alpha",alpha,"Type","percentile");
bootstat = bootstat-mu;
ci = ci-mu;

figure
histogram(bootstat,"Normalization","cdf")
hold on
yline(alpha, "Color","#D95319")
yline(1-alpha, "Color","#D95319")
xline(ci(1), "Color","#D95319")
xline(ci(2), "Color","#D95319")

The computed confidence interval does not aligne with the "cdf" histogram. But when I compute the interval using the following function, then it aligns as expected.

ci = prctile(bootstat, [alpha*100,(1-alpha)*100]);

Does anybody know, why is that the case?

Answer 1

[Adam Danz]

You're using two different alpha values.

When you call bootci, you specify alpha as 0.05 or 5%.

When you call prctile, you're setting the p endpoints to 5% and 95% which is a 10% alpha value.

Instead,

ci = prctile(bootstat, [alpha/2,1-alpha/2]*100);

Remember, when alpha equal 5, that means the interval is the middle 95% of your data. The remaining 5% is split up on each side of the distribution with 2.5% on each side. So, the left bound will be at 2.5% and the right bound at 100-2.5 or 97.5%.

[Jakub]

Thanks for clarifying! I see that I did not understand the meaning of alpha.

Answer 2

[the cyclist]

Because your prctile calculation should be

ci = prctile(bootstat, [(alpha/2)*100,(1-(alpha/2))*100]);