How can I tell if I can assume equal population standard deviations? If I have $\bar{X} = 0.14$ and $\bar{Y} = 0.139$ and the population SD of $X$ is $0.0026$ and the population SD of $Y$ is $0.0024$. 
The population for both statistics is $6$.
How can I construct a test to see if I can assume equal population standard deviations? 
Here is what I did.
Degrees of Freedom for $X$ = $5$
Degrees of Freedom for $Y$ = $5$
$F=\frac{(0.0026)^2}{(0.0024)^2} = 1.173611$
Using the F-statistic chart I see the critical value is $3.45298$ for $5$ degrees of freedom each.
Since $1.173611 < 3.45298$ does that mean I cannot assume equal population standard deviations?
I'm lost... and have put work in... Any idea?
 A: There are many issues to deal with, so I will number them


*

*You don't perform inference on population values. You state: "the Population SD of X is 0.0026" "the Population SD of Y is 0.0024". If those are really population standard deviations there's no reason to do a hypothesis test t infer whether they're different -- you already know they differ. 

*However, the more important question isn't whether the population variances are identical -- this is in practice going to be almost never exactly true. If you're doing this to decide whether you can apply some equal variance procedure, such a tiny difference in variability will be of little consequence for the subsequent inference.

*My guess is that you probably don't know the population variances; might these actually be sample variances?

*The F-test is very sensitive to the assumption of normality. Its properties (significance level and power) are badly affected by non-normality and usually avoided. If you must test, there are choices generally regarded as better. (However, if you're doing this for an exercise for a class this is a different matter; a similar caveat applies to items 2,6 and 7)

*You reject when the ratio of variances is far from 1, not close to 1. the critical value you gave is the cut off point. 

*Hypothesis tests of assumptions don't necessarily help -- they actually lead to taking the wrong action a lot of the time, since in large samples they'll cause you to reject trivial differences in variance (when it doesn't matter) and in small samples they'll cause you to do nothing when there's more serious issues. The problem you're trying to solve is one of effect size (how much difference will it make?) rather than significance.

*If you can't reasonably make the assumption of equality of variance (based on subject matter knowledge for example), there's no need to assume it at all.

*"the population size for both statistics is 6". Again, if you really have the whole population, you have nothing to test (either in respect of the variance or anything else) -- you already have the quantities about which you need to make inference. Please consider whether 6 might be a sample size instead.
