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MATH5945: Categorical Data Analysis

Term 3, 2021

Assignment 1

Submission deadline: Thursday 30 September, 12:05pm

Deliverables: 2 files uploaded to Moodle: (1) PDF file of your worked solutions, and (2) SAS file for ALL computations. Files names should be surname_firstname_z123456789_ASS1.

Assignment length: There is a 5 page limit and minimum 12pt font size. Any pages exceeding this limit or submissions with smaller font sizes will not be marked. Handwritten assignments will not be accepted. This does not include a SAS file of your code. Your document should begin with the Plagiarism Statement below (copy-and-paste it).

SAS code: All computations must be performed using SAS. Your SAS code must run as is and I should not need to modify your code in any way to make it work. You may create a library to import data, but any other code should only use the WORK library (you may assume data files of the same name are in my WORK library). SAS should be used for computing only and answers given only within SAS code will not be marked.

Penalties: Failure to adhere to instructions will result in a minimum 5% mark reduction.

1. The following data was collected for a study on the distances motor vehicles pass a cyclist (infographic on next page).

Use the methods discussed in this course to assess the association between the presence of parked cars and close (<1m) passing distances. Given this result, how comfortable are you cycling near parked cars?

2. A study was conducted to assess whether an operator protective device (OPD) reduces injury severity in a quad bike crash. Cross-tabulated data for OPD use (yes/no) by chest injury severity is given below.

Conduct an appropriate hypothesis test to assess whether quad bikes equipped with an OPD is associated with a reduction in chest injury severity.

3. It is often desirable for the mean and variance of a random variable to be unrelated, such as the normal distribution. This is clearly not true of the binomial distribution where for the variance is

The delta method can be used to motivate a transformation of or such that the resulting distribution will have constant variance. From the lecture notes, the estimator for the transformation with var has asymptotic distribution

(a) Suggest and justify a transformation such that the variance is constant, i.e.,

(b) Using the transformation derived in part (a), derive the asymptotic distribution of and demonstrate this distribution has constant variance.