14.4 Contingency Tables
Experimental units 1.75m 1.75mDon't forget about the age old question of What is a culture gap?
People short tallWe also discuss several other topics like Describe the characteristics of a moon jellyfish?
Is there any relationship between these two variables? Don't forget about the age old question of What are unattainable and therefore discouraging to most employees?
Usually, we know, women tend to be shorter.
So, Intuitively, they are not independent.
But, what if we choose another variable?Don't forget about the age old question of Why did thousands of people engage in slave trade, even when they considered it to be immoral?
#of kids 3 small
in family > 3 large If you want to learn more check out excitatory cholinergic synapse
We also discuss several other topics like which of the following terms refers to a bass playing equal note values (usually quarter notes) on every beat in an unsyncopated manner:
Intuitively, height and number of kids probably are not dependent.
Now let us look at a concrete example
We wish to classify defects found on furniture produced in a manufacturer, according to two different Methods.
(1) the type of defect
(2) the production shift prob of defect
n = 309 pieces of furniture that are defected
The defects were classified as one of 4 types A, B, C, D and also by Shift 1,2,3.
: that type of defect is independent of production shift.
: that type of defect is dependent of the production shift.
A. column probabilities - we want to test
B. row probabilities - that these are events independent
A: defects from type A
B: defects from shift 1
So, the first box prob. Is
however, we don't know
We must estimate it from the data.
In general i = 1, 2, 3
j= A, B, C, D
Where is the number in respective cell.
We can use a Chi-squared test to test
Because all expected values
Where df. Is (r-1)(c-1)
When is true should be small (3-1)(4-1)
So,we reject when is large. 2x3 = 6 df.
Therefore, since 19.17 > 12.592, we reject the null and conclude that the type of defect and production shift are dependent.
Therefore again, we would conclude that we should reject the null
15 Nonparametric Statistics
15.2 A general two sample shift model
population 1 - mean
population 2 - mean
Note the only difference is the location shift.