- Below is a data set published by Karl Pearson in 1910 (in Biometrika,
Vol. 7, p. 257), that gives data collected by Dr. John Brownlee on the
relationship between the severity of an attack of smallpox and the length
of time since vaccination. There are five degrees of severity, from most
severe (Haemorrhagic) to least (very sparse). Note that these data are
confined to people who have experienced some form of attack, and that
because the ages of the people are not given there is confounding of age
and years-since-vaccination (no young people could have been vaccinated 45
years before the attack, and it is conceivable that older people are
over-represented in the unvaccinated group). Analyze these data. (Data
are available by rows in the data set
vacc.raw [Source:S Stigler])

[See the asthma example for explanation of how to use the predict command in Stata and how to calculate residuals from a Poisson regression.]- Treating the table as a whole, test the hypothesis of no association, both with the Chisquare test and with the loglikelihood ratio test.
- Form a table of the same form of the Pearson residuals, and look for patterns of deviation. What conclusions do you draw?
- Use the estimated parameters from Stata's
`poisson`command to calculate fitted values for the second and fourth entries in row 2 of the table. Compare your calculations with the result of the Stata's`predict`command. - Repeat the test of no association for the reduced table consisting of the first two rows only. Presumably the people here are more similar in age. Do your conclusions differ? Can you explain why they might?

Severity of Attack Years since Haemorrhagic Confluent Abundant Sparse Very Totals Vacination Sparse ----------------------------------------------------------------------- 0- 10 0 1 6 11 12 30 10 - 25 5 37 114 165 136 457 25 - 45 29 155 299 268 181 932 Over 45 11 35 48 33 28 155 Unvaccinated 4 61 41 7 2 115 ----------------------------------------------------------------------- Totals 49 289 508 484 359 1689

- Agresti, Exercise 4.2
- Agresti, Exercise 4.3
- Agresti, Exercise 4.6

- The textbook is on two-hour reserve in Eckhart library.