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### 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 ClosePrior 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 ClosePrior 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?

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: