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I have five groups of data and I want to test if their variance is significantly different or not. The data are normally distributed and I do not have any repeated measurements in any groups. What sort of analysis should I use?

Tukey's test compares the means, but how can I compare their variances?

For example I have 3 groups A, B and C. In groups A, B and C I have 30, 50 and 20 observations (which are stored as double-precision numeric variables in R).

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    $\begingroup$ you should use ANOVA (analysis of variance), or its non-parametric equivalent according to variable distribution. Can you tell more about your data, or post it here? (maybe you have repeated measures which must be taken into account) $\endgroup$ – Ladislav Naďo Jan 29 '14 at 9:13
  • $\begingroup$ what exactly do you mean by: "double variable"? $\endgroup$ – Ladislav Naďo Jan 29 '14 at 9:19
  • $\begingroup$ I have edited the question and added a simple example. $\endgroup$ – user1436187 Jan 29 '14 at 9:19
  • $\begingroup$ I mean Double-Precision in R programming language. $\endgroup$ – user1436187 Jan 29 '14 at 9:21
  • $\begingroup$ Not even double-precision mean something to me. Most helpful will be if you post at least part of your data. Or describe the aim of analysis (what you are trying to do and experimental design) $\endgroup$ – Ladislav Naďo Jan 29 '14 at 9:23
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To assess whether variance differs between groups, you need to use something like Levene's test or the Brown-Forsythe test. I discuss these in my answer here: Why Levene test of equality of variances rather than F ratio? You can perform these tests in R with ?leveneTest in the car package (which actually performs the B-F test by default).

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Levene's test or the Brown Forsythe test is certainly appropriate, but if the data are normally distributed, I believe Bartlett's test might have greater statistical power. You may want to run a Bartlett test on the data and see if it comes up significant.

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