## An “Unusual Episode”

Purpose:

This activity is intended to illustrate the use of contingency tables (two-way tables).

Background:

The tables below contain a data set giving counts for a population at risk and fatalities for an “unusual episode.”  This mortality episode is well known historically.  There were 2201 people at risk.  Those at risk are categorized by economic status (I -- high or rich, II -- medium, III -- low or poor, and Other), age (child or adult), gender (female or male), and survival status (survived or did not survive).  More information cannot be specified about the Other economic status group.  This would give away the answer to what the “unusual episode” describes.

Instructions:

Examine the data carefully.  Look for any interesting features.  To help get a more complete picture of how each of the explanatory variables (economic status, age, and gender) is related to the response variable (survival status), complete the Questions.

After examining the data and completing the Questions, give your best “educated guess” as to what historical episode this data set describes.

Data:

Population at Risk and Deaths for an “Unusual Episode”:

 By Economic Status and Gender Population Exposed to Risk Number of Deaths Economic status Male Female Both Male Female Both I (rich) 180 145 325 118 4 122 II 179 106 285 154 13 167 III (poor) 510 196 706 422 106 528 Other 862 23 885 670 3 673 Total 1731 470 2201 1364 126 1490

 By Economic Status and Gender Population Exposed to Risk Number of Deaths Economic status Male Female Both Male Female Both I (rich) 180 145 325 118 4 122 II 179 106 285 154 13 167 III (poor) 510 196 706 422 106 528 Other 862 23 885 670 3 673 Total 1731 470 2201 1364 126 1490

Questions:

1.

(a)  Calculate the overall percentage of deaths:    _____% of those at risk died.

(b)  Calculate the percentage of the overall deaths that were male and female.

## %                           %

2.  Do you think that there is an association between Gender and Number of Deaths for the “unusual episode?”  Explain.

3.      Construct a two-way table to display the variables Economic Status and Survival Status:

### Status

Survived

4.  Calculate the percentage of deaths in each of the four economic status groups.  You have calculated  the conditional distributions of Survival Status given Economic Status.

5.  Do you think that there is an association between Economic Status and Survival Status for the “unusual episode?”  Explain.

6.      Construct a two-way table to display the variables Economic Status and Male Survival Status:

### Survival

Status          Survived

7.  Calculate the conditional distributions of Male Survival Status given Economic Status.

8.  Do you think that there is an association between Economic Status and Male Survival Status for the “unusual episode?”  Explain.

9.  Construct a two-way table to display the variables Economic Status and Female Survival Status:

### Survival

Status                      Survived

10.  Calculate the conditional distributions of Female Survival Status given Economic Status.

11.  Do you think that there is an association between Economic Status and Female Survival Status for the “unusual episode?”  Explain.

12.  Construct a two-way table to display the variables Economic Status (I, II, III) and Child Survival Status:

### Survival

Status                      Survived      6

13.  Calculate the conditional distributions of Child Survival Status given Economic Status (I, II, III).

14.  Do you think that there is an association between Economic Status and Child Survival Status for the “unusual episode?”  Explain.

·What “unusual episode” in history do you think this data set describes?  Explain.

Answers to Activity Questions and Assessment Question:

Activity Questions.

## 1364/1490 = 92%         126/1490=8%

2.  It appears that there is an association between Gender and Number of Deaths.  The deaths were overwhelmingly male.  (The high mortality rate among males might be the result of the rule of ‘women and children first’.)

### Status

Survived        203       118       178       212

325       285       706       885

### Survival

Status

Survived

5.  It appears that there is an association between Economic Status and Survival Status.  The lower economic status groups (and the Other group) have higher mortality rates.  (The high mortality rate among those in Class III might be explained by the more vulnerable position of the third-class cabins, lower in the hull of the ship.)

### Survival

Status          Survived      62           25         88        192

180         179       510      862

### Survival

Status

Survived

8.  It appears that there is an association between Economic Status and Male Survival Status.  The highest economic status group had the lowest mortality rate.

9.                                                                    Economic Status

### Survival

Status                      Survived      141         93         90         20

145        106        196       23

### Survival

Status

Survived

11.  It appears that there is an association between Economic Status and Female Survival Status.  The lowest economic status group had the highest mortality rate.

12.                                                                  Economic Status

### Survival

Status                      Survived      6             24         27

6            24          79

13.                                                                  Economic Status

### Survival

Status

Survived      100%       100%

14.  It appears that there is an association between Economic Status and Child Survival Status.  The lowest economic status group had the lowest child survival rate.

·The “unusual episode” is the sinking of the ocean liner Titanic after colliding with an iceberg on April 15th, 1912.

Assessment Question.

(a)  The company should calculate the percentage of each claim amount for each type of vehicle.  That is, the company should calculate the conditional distributions of claim amount given type of vehicle.

(b)                                                        Type of Vehicle

Car                               Truck                            Sport Utility

Claim Amount            \$10,000

\$10,000

(c)  It appears that there is an association between the type of vehicle and the claim amount.  Sport utility vehicles have a much higher percentage of claims over \$10,000 than either cars or trucks.