# Calculating significance of distribution

I have the following type of data:

Age    Type
3      A
3      A
3      A
4      A
4      B
4      A
5      A
5      A
5      B
6      A
6      C
6      B
7      A
7      C
7      B


Explanation of the data: essentially, this represents different types of outputs produced by a single child at different ages. For example, at age 3, he can only produce A type output. At age 4 he can start producing B-type output. Once he gets to age 6 he becomes capable of producing C-type output, in addition to the previous two types. The underlying hypothesis is that the child is able to produce C-type output only after they have successfully produced B-type output (which must be preceded by A type, though the hypothesis only entails the relationship between C and B).

The measurements reflect the outputs of a single child, measured over a period of several years.

I am trying to show that the distribution of the types (by age) is not due to chance. My goal is to show that the fact that type C first appears at a later age than type B is not due to chance (i.e. the fact that type B first appears as a result at age 4, while type C first appears at age 6).

What would be the appropriate method to do this?

(I am using R, so any additional input on applying the suggested method there would be appreciated)

• uvm.edu/~dhowell/StatPages/More_Stuff/OrdinalChisq/… Mar 5, 2017 at 16:14
• Could you please explain what "first appears" means? There is no evident way in these data to interpret that phrase.
– whuber
Mar 5, 2017 at 21:45
• @whuber I have edited the post to clarify this. If it still isn't clear, please let me know. Mar 5, 2017 at 22:35
• Thank you. I think it could help to explain what these data mean. We need to understand how there might be statistical dependencies among the data and how the data might have varied. Otherwise there's not enough information to recommend an appropriate procedure.
– whuber
Mar 5, 2017 at 23:04
• Also - are these the same children that you are following over several years, or are these 15 different children? Mar 5, 2017 at 23:29