How can I read this decision tree

Question

I'm sorry, I'm trying to learn some statistics in order to help someone I care about. Here's my problem, I have this decision tree below, for which I have no documentation to help. I cannot find out how to read the first row.

My question is only related to the first row. There's no need to understand the whole tree, which basically helps to choose between many different tests. It's in french (englih is not my native language), so I'll translate it :

1. The first item at the uper-left side says "independant variable". You have to choose between "exists" (go down) or "does not exist" (go right).
2. If you go right, the second item says "dependant variable". You have to decide if itss a discrete or continuous variable. If it's discrete, do a adjusted chi-squared test ; if it's continuous, go right.
3. You have then to decide which test to apply depending on what you know about sigma. If you know its value, do a z-test. If you don't, do a Student's t-test.

What my question is : I actually don't know how to read the first item. Since a independant variable represents an input and the dependant variable is an output related to it (by definition) ; how can I tell that a independant variable doesn't exist and then evaluate if a dependant variable is discrete or continuous ?

If a dependant variable can exist by itself, can you give me a concrete exemple ?

I'm sorry if it seems messy or confused, but I cannot find out how to properly read the first row of the tree because of this... I'm stuck.

Many thanks to anyone who can help me.

Answer 1

An independent variable not existing is the same as a one sample procedure, in other words you are dealing with a single sample or group. The null hypothesis is just does the parameter equal a claimed value, not a comparison between groups or relationship with another variable.