The file Aspirin Data, available on the course Wattle page in the Datasets section, contains
a 2 imes 2 imes 2 contingency table with columns defined as follows.
Column 1 V1=Observation number. [Observations 1 to 8.]
Column 2 V2=Count. [Nonnegative integer count for each cell in the Table.]
Column 3 V3=Case/Control Factor. [Factor Level 1 (Controls) and Level 2 (Cases).]
Column 4 V4=Ulcer Type Factor. [Factor Level 1 (Gastric) and Level 2 (Duodenal).]
Column 5 V5=Aspirin Use Factor. [Factor Level 1 (Non-User) and Level 2 (User).]
Further points:
(i) The cases were selected due to having one of two types of ulcer while the controls were
selected from the general population on the basis of having similar demographic
characteristics (and possibly other similar characteristics not related to the presence
or absence of an ulcer) to the cases.
(ii) Do not forget to declare V3,V4 and V5 (or whatever you decide to call these three
variables) as factors.
(iii) There is not necessarily a single correct answer to some of the question parts below.
In part (b), for example, the main requirement is to axplain your thinking.
(iv) Mark Scheme: each question part below is worth 8 marks.
Please provide answers to the following.
(a) Use the Aspirin Data to construct a 2 imes 2 imes 2 table. You should write the table down
with appropriate labelling.
(b) This dataset was collected in a Case-Control study and consequently the Case-Control
factor should definitely be thought of as a covariate factor as opposed to a response
factor. Decide whether the other two factors, Ulcer Type and Aspirin Use, should
be treated as a response factors or covariate factors, briefly explaining your think-
ing. Note that there are three possibilities you should consider: (i) Ulcer Type is a
response factor and Apririn Use is a covariate factor; (ii) Ulcer Type is a covariate
factor and Aspirin Use is a response factor; and (iii) both are response factors.
(c) Fit a suitable sequence of log-linear models suitable for 3-way contingency tables and
use the change-in-deviance criterion for model selection.
(d) Given a brief interpretation of the model you selected in part (c), taking into account
the type of sampling you decided to assume in part (b).
(e) Give a brief report, not more than half a page, of your main findings to the doctor who
asked you to do the analysis. Your report should be as non-technical as possible as
you are not able to assume that the doctor is an expert in Statistics. Note: you are not
expected to restrict your comments to findings which emerged from your analysis in
part (c); you may wish to include discussion of aspects of the table as part of your
summary.
Ihe file Aspirin Data,available on the course Wattle page in the Datasets section,contains a 2 2 2 contingency table with columns defined as follows.
Column 1 V1=Observation number. [Observations 1 to 8.]
Column 2 V2=Count.[Nonnegative integer count for each cell in the Table.
Column 3 V3=Case/Control Factor. [Factor Level 1 (Controls) and Level 2 (Cases).]
Column 4 V4=Ulcer Type Factor.[Factor Level 1 (Gastric and Level 2(Duodenal).]
Column 5 V5=Aspirin Use Factor. [Factor Level 1 (Non-User) and Level 2 (User).]
Further points:
(i The cases were selected due to having one of two types of ulcer while the controls were selected from the general population on the basis of having similar demographic characteristics (and possibly other similar characteristics not related to the presence or absence of an ulcer to the cases.
(ii) Do not forget to declare V3, V4 and V5 (or whatever you decide to call these three variables) as factors
iii There is not necessarily a single correct answer to some of the question parts below In part (b), for example, the main requirement is to axplain your thinking.
iv Mark Scheme: each question part below is worth 8 marks.
Please provide answers to the following.
(a) Use the Aspirin Data to construct a 2 2 2 table. You should write the table down with appropriate labelling.
(b) This dataset was collected in a Case-Control study and consequently the Case-Control factor should definitely be thought of as a covariate factor as opposed to a response factor. Decide whether the other two factors, Ulcer Type and Aspirin Use, should be treated as a response factors or covariate factors, briefly explaining your think- ing. Note that there are three possibilities you should consider: (i Ulcer Type is a response factor and Apririn Use is a covariate factor; (ii) Ulcer Type is a covariate factor and Aspirin Use is a response factor and (iii both are response factors
(c) Fit a suitable sequence of log-linear models suitable for 3-way contingency tables and use the change-in-deviance criterion for model selection.
(d) Given a brief interpretation of the model you selected in part (c), taking into account the type of sampling you decided to assume in part (b).
(e) Give a brief report, not more than half a page, of your main findings to the doctor who asked you to do the analysis. Your report should be as non-technical as possible as you are not able to assume that the doctor is an expert in Statistics. Note: you are not expected to restrict your comments to findings which emerged from your analysis in part (c); you may wish to include discussion of aspects of the table as part of your summary.
