Please judge my statistics knowledge based on the following mind map

[Cinitiator]

How bad is my statistics knowledge based on the following mind map? Any concepts which aren't bold are the concepts that I know; the bold ones are the ones I'm currently learning.

The mind map in question:
http://i.imgur.com/4He3f.png

What should I learn next based on my current statistical knowledge?

 

[Number Nine]

Judge in relation to what?
Honestly, the mind map isn't really all that clear. You say you know "regression", but what does that mean, exactly? I've taken several courses devoted exclusively to regression modelling, and I still only consider myself to be familiar with the basics. Are you comfortable with generalized additive models? Do you know what a response surface is? (you should, since you "know ANOVA").

 

[Cinitiator]

Judge in relation to what?
Honestly, the mind map isn't really all that clear. You say you know "regression", but what does that mean, exactly? I've taken several courses devoted exclusively to regression modelling, and I still only consider myself to be familiar with the basics. Are you comfortable with generalized additive models? Do you know what a response surface is? (you should, since you "know ANOVA").

Sorry for using very vague terms. By "regression" I simply mean the lest squared regression lines. And when some branch is linked with another, it means that its children branches are the parts of the concept I'm familiar with. That is, I'm only familiar with a very small part of ANOVA - specified in the children branches on the mind map.

 

[Stephen Tashi]

The map seems to indicate that there are different "types" of probability. The axioms of probability are the same in Bayesian and in frequentist statistics.

 

[chiro]

Hey Cinitiator.

A few comments.

The first one is that you separate conditional probability from probability: I think this is subtle because all conditional probability is, is constrained probability. You have a general space and you constrain it to get a conditional probability.

Also with regard to the function types, you may want to characterize the types by the nature of the process. In other words, what do these particular functions model in terms of an actual tangible process? The binomial models a process with n-trials each completely independent from the other with each trial having the same characteristics.

The other thing is to distinguish between process distributions and statistical/sampling distribution.

Process distributions are based on real processes and statistical/sampling distributions aid in doing theoretical work with regards to sampling and statistical inference. Examples of a process distribution include binomial, multinomial, hypergeometric, negative binomial, Poisson and so on. Examples of a statistical/sampling distribution including chi-square, F-distribution, t-distribution and so on.

For hypothesis testing, one thing that should be pointed out is whether hypotheses are disjoint or not. Usually they are but not always: for example you can get things that "overlap" like H0: theta = 0.6, H1: theta = 0.4 and these will affect how you analyze.

The region is the most important element in a hypothesis test, and also you may want to consider how power and size help define the other attributes.

I'd also echo Stephen Tashi's advice about the Kolmogorov Axioms.

Finally with regards to probability, one of the big things in probability conceptually is the ability to figure out what events are disjoint to others at any level (not necessarily at an atomic one where they can no longer be broken down). This helps establish the addition rule conceptually. The multiplication rule is with regard to independence and this can be related back to tree diagrams conceptually amongst other things.

Again these relate to the kolmogorov axioms (especially the addition rule).