# How to statistically compare two independent differences?

Three methods A, B and C are used to measure a continuous variable x for each subject in a study. There are two types of subjects in the study: type1 and type2.

Difference between type

xA1 - xA2 (difference in means of type1 and type2 as measured by method A)

xB1 - xB2

xC1 - xC2

Difference between method

xA - xB (difference in means between the measurements by A and B)

xB - xC

xC - xA

Now, how to statistically compare the difference between type and difference between method?

Bonus question: How to check if the method choice affects the group difference and also quantify it?

One toy example would be an experiment where weights of subjects (male and female) are measured using three different scales. How to statistically compare inter-scale difference with the inter-gender difference?

One approach I am thinking is explained here -> Statistical comparison of 2 independent Cohen's ds But both differences explained in the link are type1 - type2 kind and I am not sure if it is applicable to compare method1 - method2 vs. type1 - type2 differences. Also, I am wondering if there is an alternative way of comparing without calculating Cohen's d.

• What do YOU think? Also if this is homework please add the self-study tag and have a look here. – Stefan Dec 1 '15 at 19:44
• Please see the edited question. – gruangly Dec 1 '15 at 19:57
• What is your rationale choosing the approach you linked above? The type of analysis will also depend on what scale your outcome variable is measured. Statistical tests also come with assumptions which have to be considered as well. You see given your information it's not really possible to give a better answer. – Stefan Dec 1 '15 at 21:23
• Let's assume your outcome was measured on the interval scale and you only have 2 methods (A and B) and no differentiation between types. Which statistical test would you choose? Why did you tag t-test in your question? Maybe this could be a starting point? From there you could add the third method (C) and also add additional types (type1, type2) and work yourself up to an analysis of variance for instance including post-hoc analysis. – Stefan Dec 1 '15 at 21:24