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I have dataset about vehicles that crossed a certain singalized intersection (each record is vehicle). I want to model the relationship between the entrance time relative to the yellow onset (independent variable) and the number of vehicles (dependent variable). To this end, I use the following logistic model:

I divided the dataset into two, by the length of vehicle (short or long), and I fitted the above model for each subset of data. I want to perform hypothesis test about the B parameter (represents the slope in the inflection point). In simple words, I want to compare the slopes of two models, but I do not know what to compare - means or variances?

In what cases it is better to perform a test that compares two variances (instead of comparing means)? What is the motivation to use a test that compares two variances?

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    $\begingroup$ If you want to look how spread out the data are. $\endgroup$
    – Daeyoung
    Commented Sep 6, 2016 at 15:21
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    $\begingroup$ When your hypothesis of interest is about variances? $\endgroup$
    – Glen_b
    Commented Sep 6, 2016 at 16:02
  • $\begingroup$ @Glen_b - I did not quite understand your question. $\endgroup$
    – Pini
    Commented Sep 6, 2016 at 18:24
  • $\begingroup$ I was indicating the obvious answer. Note that you don't formally do comparisons you're uninterested in -- what you want to compare should relate to what you want to find out. The question mark (indicating 'is this really the kind of answer you want?') was because I believe you will need to reformulate your post to ask a question that doesn't have the obvious answer. In any case, please clarify what it is you seek. ctd ... $\endgroup$
    – Glen_b
    Commented Sep 6, 2016 at 22:41
  • $\begingroup$ ctd ... If an answer along the lines "You compare variances when the information you wish to find out is related to how variances compare" is what you want then I could take it off hold and post something like that as an answer but it seems a little facile without some kind of motivation or context. Please edit your question to make it clearer what you're trying to understand -- what is the source of your question? What makes you ask? Are you just looking for an example of a case when you'd do it, like mdewey posted, or something else? $\endgroup$
    – Glen_b
    Commented Sep 6, 2016 at 22:41

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Let us look at a simple possible example. Suppose you divide your sample of patients into two groups and give one group your new experimental treatment and the other your old boring control treatment. Even the new exciting treatment will not work equally well for everybody so it may well be that when you measure serum whatever after the treatment the results for your treatment group are more variable than for the control group. In such a case you could test for differences in variance.

Having said that, in practice people do not seem to do such a test but just test for differences in location.

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  • $\begingroup$ Part of the art is to work on a scale on which variability differences are small. That often means a logarithmic scale. $\endgroup$
    – Nick Cox
    Commented Sep 6, 2016 at 16:40
  • $\begingroup$ @NickCox I think you perhaps hold the view that differences in variance are usually a nuisance whereas I hold the heretical view that sometimes they may be revealing. I imagine our views can co-exist. $\endgroup$
    – mdewey
    Commented Sep 6, 2016 at 19:51
  • $\begingroup$ Absolutely; the pattern of variability is often of primary interest too. That's another part of the art. $\endgroup$
    – Nick Cox
    Commented Sep 6, 2016 at 20:36
  • $\begingroup$ Finding a scale (a transformation) on which the variability differences are small amounts to a form of model for the variability (in a sense, which transformation does that tells us how variability is related to location). Dealing with changing variability and location separately can be difficult to understand and explain, but if the are connected in this way it makes distributional comparisons much easier to understand and explain. I think this (the model's connection between location and variability) is one reason GLMs are quite attractive as distributional modeling tools. $\endgroup$
    – Glen_b
    Commented Sep 6, 2016 at 22:27

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