Contingency Tables

Contingency Table Problems

The table below contains contingency tables for daily co-movement of stock prices with the S&P 500.



Co-movement of Stock Price with S&P 500
Company One
Stock Close<Prior Low
Stock Close Between Prior Low and High
Stock Close>Prior High
S&P Close < Prior Low
12
18
4
S&P Close Between Prior Low & High
26
80
28
S&P Close > Prior High
5
31
48
Company Two
Stock Close<Prior Low
Stock Between Prior Low and High
Stock Close>Prior High
S&P Close < Prior  Low
10
21
3
S&P Close
 Between Prior Low & High
19
68
47
S&P Close
> Prior High
14
48
22


Question One:   A stock moves in tandem with the market in three instances --- (1) stock price close is below previous day’s low, (2) stock price close and S&P 500 close are both between prior low and prior high, and (3) S&P close is greater than prior high.   What is the probability these stocks move in tandem with the market? Is the difference in the likelihoods that these two stocks move in tandem significantly different from zero?

Link for answer to question one is here.




Question Two:   Use the Pearson Chi-Square Test to determine whether there is a significant relationship between stock price movement categories and S&P 500 movement categories for the two companies described above.  

Calculate Kendall Tau's A for these two contingency tables.     Discuss the difference between the Chi-square statistics and Kendall Tau statistics for the two contingency tables.  How might these statistics be used to measure the movement of stock prices with the market?



Question Three: The contingency tables below involve self-perceived general health status and self-perceived mental health status for two age groups   -- young adults 35 years old and under and older adults over age 75.  

Two Contingency Tables
Less Than or Equal to 35
General Health
Mental Health
Excellent
Medium
Poor
Total
Excellent
7,233
2,302
26
9,561
Medium
951
6,966
84
8,001
Poor
20
91
47
158
Total
8,204
9,359
157
Greater than 75
General Health
Mental Health
Excellent
Medium
Poor
Total
Excellent
151
213
8
372
Medium
71
967
62
1,100
Poor
1
38
28
67
Total
223
1,218
98
1,539



Use this data to estimate the joint probability of each self-reported general health and self-reported mental health combination.

Discuss ways the two contingency tables differ and are similar.

Answer for these two questions here.


Other potential problems on general health versus mental health contingency tables:

What it is the probability that general health and mental health move in tandem for the two age groups?

Use the chi-square statistic to test for an association between mental health and general health for the two age groups.

What is Kendal’s Tau A for the two general-health versus mental-health contingency tables?



Question Four:  Using data on the outcomes of presidential elections for Iowa and Wisconsin for every presidential election between 1852 and 2016 inclusive create a two-by-two contingency table describing the relationship between the outcome in Iowa and the outcome in Wisconsin 

Answer to Iowa/Wisconsin Association Problem Here:

http://www.dailymathproblem.com/2016/11/the-relationship-between-electoral.html


Data on Wisconsin and Iowa electoral outcomes:








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