# Measure of variance between two populations

I have a set of genes, each of which composed of $10$ values, $5$ coming from population $a$ and $5$ coming from population $b$. I would like to define a measure of the variation between the two populations. In particular, I am interested in "recognising" a sort of behavioral jump between the two populations.

For example, if in population $a$ the values of $gene_1$ are $[0.3, 0.4, 0.3, 0.4, 0.2]$, and in population $b$ the values are $[0.8, 0.9, 1.1, 0.7, 0.8]$, I would expect a high value of variation compared to the case in which the values in population $b$ are $[0.2, 0.1, 0.4, 0.3, 0.3]$. This could be explained as a change in expression (low-expressed vs high-expressed) of that gene.

T-test is useful to analyze the statistical significance of variation between the two means, but I need simply a value describing this variation.

Using the variance between two numbers (the two means) seems a bit weird. I could use $\frac{mean_a-mean_b}{mean_a}$.

Is there any "measure" of the variance between two populations?

• might the groups be different sizes, or will it always be 5 vs 5? – Glen_b Dec 16 '14 at 3:57
• It's a bit hard to tell what you need. e.g. What about $\left(\frac{\bar{x}_a-\bar{x}_b}{\bar{x}_\text{combined}}\right)^2$? Or $\left(\frac{\bar{x}_a-\bar{x}_b}{\bar{x}_a+\bar{x}_b}\right)^2$? Do they do what you want, or not? – Glen_b Dec 16 '14 at 4:05
• The size could be different between the two groups (indeed it is often different). – no_name Dec 16 '14 at 4:18
• What about a squared t-statistic? It's a measure of variation between the means divided by variation about the means. – Glen_b Dec 16 '14 at 5:13
• Do you mean to use the t value of the t-statistic? – no_name Dec 16 '14 at 5:30