Test for significant differences for data between 0 and 1

Question

I have to test for significant differences between scenarios. Data consist of the length of a segment divided by the total length of the network. They are distributed between 0 (never equal to 0) and 1, with the length of the network changing. My data contains also many 1s. An example is:

basin	scenario 1	scenario 2	scenario 3	Network length
1	1.00	0.11	0.5	15
2	0.95	0.7	0.13	1500

I tried a GLM with quasi-binomial family in R with model 'data ~ scenario' The summary is :

Coefficients:

	Estimate Std.	Error t	value	Pr(>t)
(Intercept)	2.91314	0.10747	27.107	<2e-16 ***
scenario 1	-0.05700	0.15008	-0.380	0.704
scenario 2	-0.08756	0.14910	-0.587	0.557
scenario 3	-0.10635	0.14851	-0.716	0.474

------- cut ----------

(Dispersion parameter for quasibinomial family taken to be 0.594791)

Null deviance: 3166.8 on 10539 degrees of freedom.

Residual deviance: 3165.0 on 10530 degrees of freedom

The test is never significant neither for scenarios nor for pairwise comparison (with means). Am I using the correct distribution for these data? Is it fully correct to use a GLM to test for significant differences among groups of data in a case like this?

Answer 1

A suggestion: You could investigate (test via simulation) based on the Triangular Distribution.

Not confident that you get anything useful here (as your data appears to be somewhat sparse), but a simulation exercise could provide insights on expected accuracy as your sample size increases. Results could also be compared (and/or combined) with other approaches.

Background: Per Wikipedia, to quote:

Distribution of the absolute difference of two standard uniform variables

This distribution for a = 0, b = 1 and c = 0 is the distribution of X = |X1 − X2|, where X1, X2 are two independent random variables with standard uniform distribution.

The expected value is 1/3 and associated variance 1/18.

More research here finds the following more precise commentary:

Note that X − Y will only have a triangular distribution if b − a = d − c (that is, the joint support is a square interval), otherwise it will have a trapezoidal distribution.

Note: I am looking at the problem from the perspective that the data may consist inherently of samples taken from, say, a Uniform Distribution (hence, the non-traditional analysis). This may be representative of your data upon excluding your reported presence 'of many ones'.