Standard error bigger than variance

Question

I am trying to compute the paramaters of a sample mean, but I found a standard error (0.02463249) bigger than variance (0.0006067597).

Maybe I made an error into my r code but I don't find it. Someone could give a hand to me please ?

Here my code :

x.s <- sample.mean[,'value'] ; m.s <- 1000 ; mu.s <- mean(x.s) ; var.s <- var(x.s)/m.s ; sd.s <- sd(x.s)/sqrt(m.s)

x.s is my samples means values and m.s the number of simulation.

closely related: https://stats.stackexchange.com/questions/89683/standard-deviation-for-values-below-1/ — Glen_b, Aug 17 '17 at 11:12
Maybe I should be worried that my height is larger than my weight? — whuber, Aug 17 '17 at 13:43

score 5 · Accepted Answer · answered Aug 17 '17 at 10:40

5

Variance is the square of the standard error. For a positive number less than 1, the square of that number is smaller than the number itself. Hence variance is smaller than standard error.

$$ 0.02463249^2 = 0.02463249 \times 0.02463249 = 0.0006067597 $$

answered Aug 17 '17 at 10:40

Greenparker

15,588

2

Although mathematically correct, this answer misses the point: the variance and standard deviation are different quantities altogether and in general cannot be compared. For instance, when the data are measured in meters, the SD is in meters but the variance is in square meters: what sense would it make to compare a length to an area at all?? – whuber Aug 17 '17 at 13:44

Standard error bigger than variance

1 Answers1