R 代写代编代码Thinking and Reasoning

日期：2018-04-23 09:57

MAST90044 Thinking and Reasoning with Data

Instructions

• Assignments are to be placed in the appropriate subject and lab box located just inside the north

entrance to the Peter Hall Building. Assignments must be stapled.

• Please label your assignment with the following information:

– your name;

– your student number;

– your lab class;

– your tutor’s name.

• You must sign the plagiarism declaration. The link is available on the LMS.

• Your assignment should show all working and reasoning, as marks will be given for method as well as

for correct answers. Please spell check your document.

• Paste any R code and output into the appropriate places so that it can be seen easily along with your

other work. Graphics from R can be resized within your document; make them smaller as necessary.

• Assignments count for 50% of the assessment in this subject. This one is worth 15%, and covers the

work done in chapters 4 to 6.

• Tutors will not help you directly with assignment questions. However, they may give some help with

R.

• Solutions to the assignment questions will be made available later.

MAST90044 Thinking and Reasoning with Data Assignment 1

Contemporary Issues in Crime and Justice Number 115

May 2008

This bulletin has been independently peer reviewed.

Does circle sentencing reduce Aboriginal

offending?

Jacqueline Fitzgerald

Circle sentencing is an alternative method of sentencing Aboriginal offenders which involves the

offender’s community in the sentencing process. This bulletin considers whether people who

participate in circle sentencing (1) show a reduction in the frequency of their offending, (2) take

longer to reoffend and/or (3) reduce the seriousness of their offending. The results suggest that

circle sentencing has no effect on any of these outcomes. Circle sentencing participants offended

less in the 15 months following their circle. However, the same was also true of Aboriginal people

sentenced in a traditional court setting (the control group). After a range of offender and offence

characteristics were controlled for, we found no difference between the circle sentencing group and

the control group in time to reoffend. Finally, there was no difference between the circle sentencing

group and the control group in the percentage of offenders whose next offence was less serious

than the reference offence.

Introduction

Circle sentencing is an alternative

sentencing process for adult Aboriginal

offenders in New South Wales. It takes

the sentencing process out of the

traditional court setting and allows the

involvement of the offender’s community.

In a circle sentence, the offender,

magistrate, community elders and (on

occasion) the victim and support people

for the offender and/or victim sit in a circle

to discuss the circumstances and impact

of the offence and determine a sentence

tailored to the offender. Circle sentencing

has the full sentencing powers of the

court (Crime Prevention Division 2007).

The first circle sentence in New South

Wales was conducted in Nowra in

February 2002. Since then, with the

exception of an early review of the first

12 months of operation, a rigorous

evaluation of circle sentencing has not

been published. In 2006, the New South

Wales Attorney General’s Department

commissioned a comprehensive

review of the impact of all aspects of

circle sentencing. As part of this review,

the Bureau of Crime Statistics and

Research was asked to analyse the rate

of reoffending among circle sentencing

participants. This bulletin reports the

results of these analyses.

Background

The circle sentencing process that

operates in New South Wales was

adapted from a program that originated

in Canada in the early 1990s for the

sentencing of Indigenous offenders (Potas

et al. 2003). The Canadian program is

based on a restorative model of justice,

which seeks to reconcile the offender and

the victim and actively engage community

members in the rehabilitation of the

accused (LaPrairie 1995).

All Australian jurisdictions, with the

exception of Tasmania, now operate an

Indigenous sentencing court of some

type. The procedures in these courts

generally follow the tenets of restorative

justice, such as, improving communication

between parties, applying procedural

justice (that is, treating people respectfully

and fairly), using persuasion and support

to encourage offenders to be law-abiding

and to avoid incarceration (Marchetti

& Daly 2007). In addition, Indigenous

sentencing courts endeavour to be

culturally appropriate, being inclusive of

both the Indigenous community and the

offender (Marchetti & Daly 2007).

At the time of writing in New South

Wales circle sentencing was operating

in Armidale, Bourke, Brewarrina, Dubbo,

Kempsey, Lismore, Mt Druitt and Nowra.

Nearly half of all circle sentences involve

an offence of common assault; the next

most prevalent offences are unlicensed

driving and breaching an apprehended

violence order.

The eight objectives of circle sentencing

in New South Wales are set out in

Schedule 4 of the NSW Criminal

Procedure Regulation 2005. They are:

To include members of Aboriginal

communities in the sentencing process

To increase the confidence of

Aboriginal communities in the

sentencing process

a)

b)

CRIME AND JUSTICE

Bulletin NSW Bureau of Crime

Statistics and Research

Q1 We will consider issue (3) in the abstract above – whether people who participate in circle sentencing

reduce the seriousness of their subsequent offending. The following table from the article, which considers

subsequent offenders, gives the frequencies and percentages upon which the authors’ conclusion

was based.

B U R E A U O F C R I M E S T A T I S T I C S A N D R E S E A R C H

offence, prior convictions and prior

incarceration, there was no significant

difference between circle sentencing

participants and the control group in

time to reoffend. The answer to the third

question is that there was no significant

difference between the treatment and

the control group in the percentage of

offenders whose next offence was less

serious than the reference offence.

Taken as a whole, the evidence presented

here suggests that circle sentencing

has no effect on the frequency, timing

or seriousness of offending. It could

be argued that these results may have

been different with a more extensive

set of controls. However, this is unlikely

for at least two reasons: the findings

are consistent and an extensive set of

controls were employed in analysing time

to reoffend. The only positive effect for

circle sentencing that even approached

significance was the change in offence

seriousness for circle sentencing

participants, relative to Aboriginal

people dealt with in a conventional court

proceeding (p=0.056 in the one-tailed

Fisher Exact test). Even this effect,

however, might be just a reflection of

regression to the mean.

It should not be concluded that circle

sentencing has no value simply because

it does not appear to have any shortterm

impact on reoffending. Reducing

recidivism is just one of several objectives

of the process. There is nothing in this

analysis to suggest that circle sentencing

is not meeting the other objectives. If it

strengthens the informal social controls

that exist in Aboriginal communities,

circle sentencing may have a crime

prevention value that cannot be quantified

through immediate changes in the risk of

reoffending for individuals.

Given the high priority attached by the

Government to reducing reoffending (see

NSW Government 2006), however, it

would seem prudent to begin considering

ways in which the effectiveness of circle

sentencing in reducing reoffending might

be improved. MacKenzie (2002, p. 385)

argues that, to be effective, rehabilitation

programs must change the characteristics

of offenders that are associated with

their criminal activity (e.g. association

with criminal peers, poor impulse control,

alcohol and drug abuse, unemployment).

The circle sentencing process is not

designed to do this. Instead, it seeks

to, amongst other things, reduce

reoffending by giving Aboriginal people

direct involvement in the sentencing of

Aboriginal offenders. The results reported

here suggest that such direct involvement

is not enough, by itself, to produce a

reduction in reoffending. Consideration

should perhaps be given to combining

circle sentencing with other programs

(e.g. cognitive behavioural therapy, drug

and alcohol treatment, remedial education)

that have been shown to alter the risk

factors for further offending (MacKenzie

2002; Aos, Miller & Drake 2006).

Notes

Another problem is that, from the

Productivity Commission’s published table,

it is unclear how Harris derived an overall

reoffending rate of 29.4% which he cites for

the comparison group.

Offences which were brought to court but

for which the person was not convicted

were not counted. It should be noted

that offences proven in court are not a

precise measure of recidivism as they

exclude crimes for which the offender is

1.

2.

not apprehended. Alternative indicators,

such as police mentions or self-reported

offending, however, have as many, if not

more, problems. Offenders asked to report

on their own offending may not answer

truthfully. Police contacts that do not result

in a conviction may reflect biases in the

exercise of police discretion.

Information on proven offences was

obtained from the Reoffending Database

of the Bureau of Crime Statistics and

Research. See Hua & Fitzgerald 2006 for

details.

A 15-month follow-up period was chosen to

balance the benefits of a reasonable followup

period with the need for a reasonable

sample size. A longer follow-up period

would give a better indication of a person’s

offending patterns. However, it would also

restrict the analysis to a small number of

people circle sentenced in the early days

of the program. For instance, a 30-month

follow-up period would include only 49

individuals who participated in a circle

sentence between 2002 and 2004. Eightyone

individuals participated in a circle

sentence prior to January 2006.

At the time the analysis was conducted

information was only available on court

appearances finalised up to 30 June 2007.

As a result, individuals in both the circle

sentencing group and the control group may

have committed offences in the 15 month

follow-up period which had not yet been

finalised in court by 30 June 2007. The effect

of this on the circle sentencing group and the

control group should be the same.

Offences committed before the circle

sentence (or equivalent reference court

appearance) but finalised in court after it

were counted as prior convictions.

Twenty five percent of both the circle

sentencing group and the control group had

spent time in prison in the five years prior to

the reference court appearance.

An alternative to omitting the seven

individuals for whom an accurate control

group member could not be found, would

have been to relax the matching criteria. It

was decided that it was preferable to have

a slightly smaller sample size with a control

group that precisely represented the circle

sentencing group rather than additional

subjects with a less representative control

group.

Only offences proven in court up to June

2007 were included.

3.

4.

5.

6.

7.

8.

9.

Table 5. Change in offence seriousness by method of disposition

– Circle sentencing group versus Control group

Seriousness of

subsequent offence

Circle sentencing group Control group

No. % No. %

Less serious 34 55.7 3690 44.7

More serious or the same 27 44.3 4560 55.3

Total 61 100 8250

n.s.a

100

a. Not significant: c2

= 2.968, d.f. = 1, p=0.085, Fisher’s Exact Test p=0.056

(a) Enter the data into R and perform a suitable test to examine the association between seriousness

of subsequent offence and sentencing group (Circle vs Control). Interpret the result of the test in

terms of the 0.05 significance level. Give some justification for the test that you have used.

(b) From first principles, calculate the expected frequency for the top left hand cell of the table (Less

serious × Circle sentencing group) under the null hypothesis of no association.

(c) 55.7% of the Circle sentencing group had less serious subsequent offences, but only 44.7% of the

Control group did. The authors concluded that “there was no difference” between the groups (last

sentence of abstract). Were they justified in this conclusion? Briefly explain.

(d) Test whether a claim that “half of those who participate in circle sentencing commit less serious

subsequent offences” is reasonable.

2

MAST90044 Thinking and Reasoning with Data Assignment 1

Q2 An investigator wished to determine whether epinephrine has the effect of elevating plasma cholesterol

levels in humans. Twelve adult males were selected and given both a placebo and the drug. Blood

samples were taken following injection of the placebo and again after injection of epinephrine. Analysis

of the blood samples resulted in the following data:

| Cholesterol Levels (mg/100ml)

Subject | Placebo Epinephrine

--------|--------------------------------

1 | 178 184

2 | 240 243

3 | 210 210

4 | 184 189

5 | 190 200

6 | 181 191

7 | 156 150

8 | 220 226

9 | 210 220

10 | 165 163

11 | 188 192

12 | 214 216

(a) Formulate an appropriate statistical model, defining all the terms. State the null and two-sided

alternative hypotheses which reflect the research question of interest.

(b) Enter the data into R, and calculate the means for placebo and epinephrine. Find a 95% confidence

interval for the mean difference in cholesterol levels between the placebo and epinephrine. Use the

confidence interval to test your null hypothesis.

(c) Would a 99% confidence interval contain zero? Briefly explain. (You don’t need to actually

calculate the 99% confidence interval to answer this question.)

(d) Perform a test which addresses the research question but makes no assumption about the two

populations being normally distributed. Compare the P-value for this test with the P-value found

in (b). Comment on why one is substantially larger than the other.

Q3 A study of customer service compared the waiting time on telephone transactions of two different types.

A random sample of 12 calls to a community information service was taken. A separate random sample

of 12 calls to book AFL final tickets was taken. For each call, the time in minutes spent ‘on hold’ was

recorded. The data are given below.

Community service 11.2 14.1 9.0 6.9 12.6 15.4 18.3 14.3 10.6 9.4 12.1 11.3

AFL final tickets 6.1 4.7 8.3 9.0 10.5 9.2 12.5 6.4 11.6 9.7 12.2 8.6

(a) Enter the data into R. Produce an appropriate graphical display of the data, and calculate the

sample mean and standard deviation for both groups. What conclusions can you draw from these

results?

(b) Find a 95% confidence interval for the difference between the mean waiting times for the two types

of transactions. Is it reasonable to claim that AFL final tickets require a shorter waiting time?

(c) The customer service manager claims that the average waiting time for community service calls is

10 minutes. Is this claim consistent with the data?

3

MAST90044 Thinking and Reasoning with Data Assignment 1

Q4 It is possible to count bunches of grapes long before they are harvested. It would be convenient for

the grower if the weight of the bunches harvested could be reasonably predicted from the number of

the bunches. For this question, we will ignore the treatment and the other explanatory variables in the

data.

For this question you will find the data in the file winery.xls. You will need to figure out how to import

the relevant data into R to answer these questions.

(a) Represent the relationship graphically between the number of bunches harvested and the weight

harvested, for 2001.

(b) Would you describe the relationship as strong? Give a reason, based on a suitable summary

statistic.

(c) Describe an appropriate statistical model for examining the research question, and fit the model in

R. Examine appropriate diagnostic plots, and comment on anything that challenges the assumptions

of the model.

(d) Find a 95% prediction interval for the weight when the number of bunches is 30. Explain its

meaning.

(e) Suppose someone looks at the analysis that you have carried out and comments:

“I don’t understand. If I plug in zero bunches in your estimated model, I don’t get a

prediction of zero weight. How come? That can’t be right!”

Respond to this objection.