1-Tailed Levene Test

#1
I am interested in testing if the variance of one data set is bigger than another set. I thought about using a simple F-test, but I am not sure the populations are normal. Is there a 1-tailed variant of the Levene Test for Equality of Variances?

I understand that the Levene Test performs a 1-way ANOVA on the calculated dispersion data. Could I just perform a 1-tailed t-test instead of the ANOVA? Alternatively, can I just cut the calculated probability in half?

Please forgive my limited statistical background and thank you for your help!
 
#2
If no one knows about that modification to the Levene test, can anyone tell me if there any 1-tailed test for comparing variance other than the F-test? Or is the F-test a reasonable choice even of that data may not by normal?
 
#4
Thank you for your suggestion. Yes, you can have a [tex] k= 2[/tex] groups in the Levene test. However, it is only setup to regect the hypotheses [tex]\sigma_1 = \sigma_2[/tex]. I would like a 1-sided test for [tex]\sigma_1 \le \sigma_2[/tex].