Question about homoscedasticity test one of the reviewer of a paper of mine suggested to perform a homoscedasticity test between the results of two experiments, testing the same thing in two conditions. The experiments consisted in ratings along a 7 points Likert-scale.
One of the experiment results were distributed on a large range of values, while the other showed a tendency towards the center of the Likert-scale range (i.e. 3.5). The reviewer argued that the latter behaviour could be due to the fact that participants answered more randomly, and he suggested that to verify this possibility, an homoscedasticity test should be performed comparing the two conditions.
Now, I would like to understand this comment. In relation to my case, what does it mean that the variances of the two conditions are significantly different?
What instead if they are equal?
Secondly and more importantly, which test for homoscedasticity do you suggest I perform?
I use R. Can you suggest the function more suitable for my case? I saw that there are many.
 A: I think this question has been addressed a few times before although not in the context of your paper.  Even though the likert scale is ordinal, some people here argue that average scores can be looke at as numerical (interval).  Ascribing to that theory the variance of the averages has some meaning. Also a Likert scale even though it is discrete the individual scores could be thought of as interval if you believe that respondents think the change from 2 to 3 is the same as from 3 to 4 etc.  This may be a stretch.  Of course if the raw data were normally distributed you could use the F test for comparing two normally distributed variables.  Unless the sample size is large it is difficult to reject homoscedasticity. it has also been pointed out that the F test is not robust to depatures from normality.  So it is safer to use a robust test.  Levene's test is one of the most common ones  and there are modifications to it that have been proposed. Still you may be uncomfortable treating ordinal data as though it was were interval.  So maybe a nonparametric test based only on ranking the data or on permutations would be suitable.  then you really are asking if the distributions have different scales.
There are apparently three well-known nonparametric tests for equality of scale in two distributions with well-known properties and some new one appearing in the literature. A Google search using "nonparametric tests of scale" turns up a lot of interesting links.  There is even one that discuss whether or not Likert scales should be viewed parametrically or nonparametrically with a paper like yours instigating the discussion.  Do the search.
But to help out here are links to a few papers.  Full pdfs are not available


*

*Mathur

*Klotz

*Penfield.

A: According to the comments above reported I found that the solution is to use mood.test().
The result is
> mood.test(scrd_non_interactive$Response,scrd_interactive$Response)

Mood two-sample test of scale

data:  scrd_non_interactive$Response and scrd_interactive$Response 
Z = 0.3895, p-value = 0.6969
alternative hypothesis: two.sided 

From this I conclude that the variance of the two groups is not statistically different.
