I would like to determine whether or not the standard deviations obtained for a category of problem significantly differ from the standard deviations obtained for another group. Do you know a way to do so ?
That could be done using Levene's test http://en.wikipedia.org/wiki/Levene%27s_test
or Bartlett's test for more than two groups http://en.wikipedia.org/wiki/Bartlett%27s_test
Catherine, there is in fact a well-known test for two variances, the F-ratio test. By taking the ratio of two variances one may determine if they are significantly different or not. The details for this test can be found in any book on statistics under the Hypothesis test section. A good book to reference is Ostle's "Statistics in Research"
Use the following address: http://en.wikipedia.org/wiki/Levene%27s_test
Levene's test
Hi Catherine. Are you interested in comparing dispersion between two or more samples? If so, Bartlett's or Levene's test should work. Are you working with SPSS, right? SPSS only uses the Levene Test. According to Zar (1999) , Bartlett's test for homogeneity is better, particularly when the underlying distribution can be assumed to be near normal, but SPSS has no packaged Bartlett test.
If you want to perform a Levene's test in SPSS, you can go to the Menu Analyze, then descritive statistics and finally explore. In Spread vs Level with Levene Test, the none option is selected by default. Please select untransformed. Done! Or simply perform a t-test or a ANOVA (in options don't forget to select the homogeneity of variance test box). Hope it helps. Cheers.
Hello Catherine. The 2nd paragraph of the Wiki entry states the caution I was going to add, namely that Bartlett's test is VERY sensitive to departures from normality. In other words, a 'significant' outcome MAY mean that the population variances differ, or that one or both depart from normality (worse if they do so in different ways), or that the variances AND distributions differ. As always, proceed with caution.
The para above was written just before I was whisked away on a holiday to the UK (from the Gold Coast, Australia). I wanted to add a couple of examples in which the theoretical populations have different skewness and hence would set the Bartlett alarm bell ringing, misleadingly. So, sitting in our London apartment awaiting the days's activities, I thought I'd better finish what I'd started.
Example 1: Think of two versions of an ability or knowledge test which, for their intended audience, would be too difficult and too easy, respectively. The difficult test would result in positive skew (of the theoretical population of tests scores), whereas the easy test would result in negative skew. Both populations of scores could well have the same variance, but Bartlett's test would be likely to say otherwise.
Example 2: Think of two experimental conditions that are predicted to impede or enhance reaction times, respectively. The hypothetical populations of 'raw' RTs would again differ in skewness (slower condition -> positive skew; faster condition -> negative skew), with the same implications for the Bartlett test.
I could add more about the inappropriateness of population models for the social and behavioural sciences (see my answers to another of Catherine's questions) and about the cautions to take if you're tempted to apply transforms to the raw data, but the day is now upon me. So, more some other time.
P.S. if you have several groups to test, then an ANOVA test is just that! It tests several groups and their respective variances... i.e. Analysis of Variance (ANOVA).
@Luisiana, that's not true, at least for the standard ANOVA, which assumes independently and identically distributed error terms. Consequently you just get one within-group variance term, not a variance for each group.
Eik, you're right... ANOVA assumes homegeniety across the groups... you'll need to test each group of interest.
Howevet the levene's test is the simple comparison of two variable when at each item was subtracted the mean.
On the other hand levene's test is a t-test when each item was x'=x-x(mean).
With this basis you could apply different test like Welch ANOVA or welch t-test.
You can consider the coefficient of variation (CV= Standard Deviation/Mean) of each problem and compare across groups using Mean mean Difference or ANOVA. The lesser the CV, the more stable and lesser the variation of the item/ problem. I do not know whether I have understood your problem correctly. Damodar Suar
There is an R package at https://github.com/benmarwick/cvequality that has two methods for testing for differences in the CV (or spread) or 2 or more groups.
Hi Catherine Thevenot , you may be interested in my calculator, which corrects for differences in group variances even if those differences are negligible. The calculator also has an in-built Levene's test, among other features:
Research Welch's t-test for comparing two independent groups: An Exce...
Cole, T. J., Faith, M. S., Pietrobelli, A., & Heo, M. (2005). What is the best measure of adiposity change in growing children: BMI, BMI%, BMI z-score or BMI centile?. European journal of clinical nutrition, 59(3), 419.
So this paper describes a strategy applied to the field of nutrition for examining differences in variability. Sorry I've not personally examined this problem ...but intending to.
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