Contingency Table Problems
The table below contains
contingency tables for daily comovement of stock prices with the S&P 500.
Comovement
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 ChiSquare 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 Chisquare 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?
Calculate Kendall Tau's A for these two contingency tables. Discuss the difference between the Chisquare 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?
Link to answer for question two is here:
http://www.dailymathproblem.com/2017/12/thechisquaretestandkendallstau.html
Question Three: The contingency tables below involve selfperceived
general health status and selfperceived 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
selfreported general health and selfreported 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 chisquare 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 generalhealth versus mentalhealth 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 twobytwo 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/therelationshipbetweenelectoral.html
Answer to Iowa/Wisconsin Association Problem Here:
http://www.dailymathproblem.com/2016/11/therelationshipbetweenelectoral.html
Data on Wisconsin and Iowa electoral outcomes:
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