Chapter 1. Tutorial: Simpson's Paradox in Two-Way Tables

1.1 Problem Statement

{125,140,141,144,163,167,173,180,184,191}
rand(0,9)
@students[$studentsindex]
{429,444,445,448,467,471,477,484,488,495}
@table[$studentsindex]
{210,225,226,230,248,252,258,265,269,276}
@never[$studentsindex]
{429,444,445,448,467,471,477,484,488,495}
@occasional[$studentsindex]
{49,51,51,51,53,54,54,55,55,56}
@personalnever[$studentsindex]
{219,234,235,239,257,261,267,274,278,285}
@neither[$studentsindex]
{429,444,445,448,467,471,477,484,488,495}
@both[$studentsindex]
{51,53,53,53,55,55,56,57,57,58}
@studentneither[$studentsindex]
{125,140,141,144,163,167,173,180,184,191}
@studentnever[$studentsindex]
{29,32,32,32,35,35,36,37,38,39}
@neverneither[$studentsindex]

In 1972-1994 a one-in-six survey of the electoral roll, largely concerned with thyroid disease and heart disease was carried out in Wichkham, a mixed urban and rural district near Newcastle-upon-Tyne, in the UK. Twenty years later, a follow-up study was conducted.

Here are the results for two age groups of females. Each table shows the twenty-year survival status for smokers and non-smokers.

Figure 1.1

1.2 Step 1

questions

Question 1.1

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Correct.
Incorrect.

Question 1.2

B0y1NMzTi+BY4pw+406quw6O2whJHVYlXcB+kvBZY+plBmlOKvcNpKjkPW7EhW/Q1GnENuuPgXbcNUP6iYfXAtIGR0DkCi1AYdxk7mBhiAjzbYtVou9HyI90arOtugTKXk+6LTohu+Rxh1oT/4Y4jkOVgz6wqLkLJ8CNAg==
Correct.
Incorrect.

Question 1.3

The 20-year survival rate for female non-smokers aged 55-64 is 96zjfHsrV6vFWL6htplNHzmsNzy2u+q1RraxpKgCE9u3OVIi7MC0Qg== the 20-year survival rate for female smokers aged 55-65. It appears that “smoking is bad for your survival rate”.

Correct.
Incorrect.

1.3 Step 2

Question 1.4

U3JgEE+iitQ9yY8swaTh0vq82EjYLUxamksMWsqBCtLf3fWH5YHYYHA6iRbgs9fMX7BNGzt+S+7tlmGJFHD0sgX+cGxpDvOHAalS7UXtW7Yx1U8CaXiukffU7FY=
Correct.
Incorrect.

Question 1.5

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Correct.
Incorrect.

Question 1.6

The 20-year survival rate for female non-smokers aged 65-74 is 96zjfHsrV6vFWL6htplNHzmsNzy2u+q1RraxpKgCE9u3OVIi7MC0Qg== the 20-year survival rate for female smokers aged 65-74.

Correct.
Incorrect.

Question 1.7

In both cohorts, the 20-year survival rate for female non-smokers is 96zjfHsrV6vFWL6htplNHzmsNzy2u+q1RraxpKgCE9u3OVIi7MC0Qg== the 20-year survival rate for female smokers.

Correct.
Incorrect.

Question 1.8

It appears that q+E4APcKVTpWkxUFgWtimVj4qx5sZMszH4LVf9z1Y8XjkfW9QJKyvE+8Dvf37O6usqzMlUljDK1yNqcIdO8n1EZsmAtIUCXGd6wa+AhUmezoIe45ecnDPclagFZ2tT4BRMfk1X+UZK8Wbu9ouGGkOZ3UEKyq+v7SoPL3VxgcJAQyYqLb6Y8iUw==.

Correct.
Incorrect.

1.4 Step 3

Now pool the tables of both age groups (complete the entries below):

Figure 1.2

Question 1.9

tgIG/lx5aKztz+kr/YNLOjPeLbWcKqEFT6W0LQ==
Correct.
Incorrect.

Question 1.10

bFKaT3BuN8a4wEpqd4SbAhUQc9GG3HkMl4zmZsOMmfs=
Correct.
Incorrect.

Question 1.11

wd17fxsweupStydFjy3gqGA+ysZygxnMbc4PTg==
Correct.
Incorrect.

Question 1.12

OBVuQE5S8OPLQ0rPeJd5ptiOzHIxZuLMR8cCn3fKfLb0AXmlRNairG09pTQXD90+/jVKF6g4lysp0YWcI/K55IOWniILqwdECfz6ueGz6ndtuMIb4Ihxi+I2PSxwxTftf0E/H3R4FRP7hA2k
Correct.
Incorrect.

Question 1.13

HkK/uYGbhSGNZ+1BKu5nOjBxjB4cbZTTucLgACp5g7piGVC7DlqpL8/xnLpzD+LAQsO7W70gz5hkroUzfY2A794pPqewtk/5b40cC2awzMTS9vx6D6bbrqVGm1Ip09RwLfkUFT9RJ5hJtQF+xml+IAW8DNfjPvwnvJbakpLeQ7E7cCBqwwLGVQ==
Correct.
Incorrect.

Question 1.14

The 20-year survival rate for female non-smokers in the combined is dtedc6OYBuNTT7atoTcHDGiv2YbOi4iGRK+/ktkk2tv1+4StajlfWg== the 20-year survival rate for female smokers for the combined cohort.

Correct.
Incorrect.

Question 1.15

It appears that +Es03j93VoSeYHkrxR3hbbdy23jYk01CCRYlAzr/n2P0MOGoUuETePEbHwGikoi7USv88TiOicIliGsCxG727n/xEhT6FeBKejXTcEcFYCgCiCuEiQXh7VGCkBPPYsxY1KskZ5/oXXscyGcu/uX/pA6b+FplYHCUYBvRtA==.

Correct.
Incorrect.

Question 1.16

This is an example of _________ A84Q9wCTVTkyP3c4cAq/OB7espkegUMdP1EoSyDDtejeGdqcUaizAEikQqJGBb2IkDwByBpecFk= where the results of the combined table are “opposite” to the results of the individual tables.

Correct.
Incorrect.