How to calculate variance?

September 15, 2010 9:23 PM

How do I calculate the between-groups variance (Vb)?

I've just started a research methods class, and have a problem set due, and haven't any idea how to do it.


I've got to calculate the means and variances for the two groups, as well as the between-groups variance (Vb), and the total variance (Vt), then I've got to describe and explain the results of Vt=Vb +Vw in these circumstances.

How do I calculate these things? (I know how to calculate the mean)

posted by taltalim to Science & Nature (8 answers total)

This is where I think you might start.
posted by ptm at 9:36 PM on September 15, 2010

I'd start with my textbook or class notes.
posted by sanko at 9:40 PM on September 15, 2010 [1 favorite]

Just take the second moment of the distribution.

∫[(x-c)^2]f(x) dx where c is the mean and f(x) is the probability density function.
posted by mr_roboto at 9:47 PM on September 15, 2010

If your textbook is not clear on these matters, I highly recommend Gravetter and Walnau's "Statistics for the Behavioral Sciences". I taught myself out of it. Old editions are just as good as new ones.
posted by fake at 9:52 PM on September 15, 2010 [1 favorite]

Response by poster: Thank you, ptm. But I think it was much simpler than that page makes it.

Is variance just the sum of the data points, less the mean, squared, and divided by two? And based on that how do I calculate the between-groups variance and total variance?

To others: I appreciate the suggestion to start with my textbook or class notes, as I never could have thought of that on my own. There is no textbook for the course, and my notes for this day of class are less than sufficient.
posted by taltalim at 5:13 AM on September 16, 2010

The variance is the mean of the squares of (i - M), where the "i"s are the data values and M is the mean of all data points.

If your data are 9, 10, 11, then the mean is 10; the squares of (i-M) are 1, 0, and 1; the variance is (1+0+1)/3 = 0.66

If your data are 5, 10, and 15, then the mean is still 10; the squares of (i-M) are 25, 0, and 25; the variance is (25 + 0 + 25) /3 = 16

I assume that you're getting "2" from some example, but that number should be either N or N-1. Can't help you with why it's sometimes N-1 rather than N.
posted by endless_forms at 7:01 AM on September 16, 2010

What I should have said in the first place is that if you were one of my students, I'd much rather you came to me with questions.

Between-groups variance is conceptually the same thing as within-group variance, but it's handled on the group means rather than the individual values.

So let's say you had the groups 9, 10, 11; 4, 5, 6; and 18, 20, 22.

The first group has the mean of 10. The second group has a mean of 5. The third group has a mean of 20.

The Grand Mean of these is 11.66

The between-groups variance is the sum of n_i * ( (mean_i - Grand_mean) ^2 ).

so in this example, it's [3 * (1.66)^2 ] + [3 * 6.66^2] + [3 * 8.33^2].

Try this page: http://people.richland.edu/james/lecture/m170/ch13-1wy.html or this page: http://www.sjsu.edu/faculty/gerstman/StatPrimer/anova-a.pdf

Where I am likely to have led you astray is the difference between using N or N-1 to divide by. I am no stats god; this is meant as a starting point and not an ending point. I am likely to have gotten something kind of wrong, but maybe it will feel less mysterious.
posted by endless_forms at 7:13 AM on September 16, 2010

Although this is probably too late for you, the magic search term is one-way anova or one-way classification.

People didn't directly answer your question because answering homework questions is contrary to the guidelines. There are several good reasons for that.
posted by a robot made out of meat at 9:19 AM on September 18, 2010