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Get Full Access to UA - MATH 452 - Class Notes - Week 9
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UA / Mathematics / MATH 452 / How can you determine relationships between two variables?

How can you determine relationships between two variables? Description

Description: The notes for week 10 cover the classes from 3/29 and 3/31. They cover Contingency Tables to Sign Tests.
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14.4 Contingency Tables

Height

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?

Gender        Female

Male

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.

Restrictions:

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

If independent

Cell Probability

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.

so,

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

• No parameters in the model

15.2 A general two sample shift model

population 1 -        mean

〉~N

population 2 -        mean

<

Note the only difference is the location shift.

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