Tricky little kuznets diagrams
I will try to show in the following demonstration how a
Kuzents diagram/beahvior can appear even in places where it's not inherently there.
What does it mean "not inherently there"?
Where there isn't really a complex fenomena that has non linear charactristics.
Let's say that we are looking at a certain cognitive ability.
Mathematics ability.
I want to assume for the sake for the sake of the trick that we are born with
some sort of a mathematic talent that can be quantified to 0-10 and the talent
is distributed normally.
(Go ahead randomize our test students)
Randomize 100 students
View the students distribution in a Graph
Now: each group like the one we just created has an ability
distribution. (The graph)
but if we want to compare two students groups, it's easier to use Mean value and
Variance to get a feeling about the diffarence between the different groups.
View the group in a Graph
What i want to do now is the following modelling:
1. To create multiple randomize groups.
View the groups
2. To define an augmentation operator (education process) and apply it to the
different groups. (With some variations to model different education qualities)
We'll use simple mulplication.
a student with a 5 point ability will have 5*1.5 = 7.5 ability
View what it does the the distribution
So here is the graph of the different groups (Placed by Mean/Variance
properties) after they've been applied with augmentation factors 1-4
Each group with a different augmentation factor.
View the groups after the factor
As we can see in the graph above - if we look at their real ability we see that
both Mean ability and the variance withing the group are in correlation. (both
correlated to the augmentation factor)
3. Defining test function.
Tests are'nt usually the ideal identity function.
Let's play with some test funtion and see how does their Mean/Variance graph looks like.
(We've seen above how the groups mean & variance are according to the identity test)
Let's look at the following test
you need ability 15 to get 80
you need ability 25 to get 90
you need ability 30 to get 100
Mathematically it would be: (a=ability)
(min(a,15) / 15) * 80 + (min(max(a-15,0),10) / 10) * 10 + (min(max(a-25,0),5) / 5) * 5
View the groups with this test function