# [R] Variance Computing- - HELP!!!!!!!!!!!!!!!!!!

Richard A. O'Keefe ok at cs.otago.ac.nz
Wed Aug 20 04:32:26 CEST 2003

```"Padmanabhan, Sudharsha" <sudAR_80 at neo.tamu.edu>
We know trhat as the sample size increases, the variance should
decrease,

Should it?

I can paraphrase his test case thus:

v100 <- sapply(1:100, function(i) var(rnorm(100, 0, 3)))
# We expect the elements of v100 to cluster around 3^2
v1000 <- sapply(1:1000, function(i) var(rnorm(1000, 0, 3)))
# We expect the elements of v1000 to cluster around 3^2 too.
fivenum(v100)
=>    6.469134  7.884637  8.916314 10.189463 13.897817
#                    ^^^^^^^^
fivenum(v1000)
=>    7.874345  8.692326  8.967684  9.268955 10.503038
#		     ^^^^^^^^

The population parameter sigma-squared is 3^2 = 9.
The estimates are 8.92 in one case and 8.97 in the other;

Looking at density(v100) and density(v1000) is enlightening.

Means and standard deviations:

mean(v100)		var(v100)
=>  9.080676		2.376193
mean(v1000)		var(v1000)
=>  8.98147		0.1721246

Are these not pretty much as expected?  Not that a t-test is the
ideal test for the distributions involved, but it's familiar and
since the distribution is pretty bell-shaped, it may be usable as
a rough guide to whether to be worried or not.

> t.test(v100, v1000)

Welch Two Sample t-test

data:  v100 and v1000
t = 0.6413, df = 100.439, p-value = 0.5228
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.2077100  0.4061231
sample estimates:
mean of x mean of y
9.080676  8.981469

```