plancollectprocessdiscuss start screen what sort of neighbourhood do you live in?

Plan Collect Process Discuss

Start screen

What sort of neighbourhood do

you live in?


Start screen


Start screen

How safe is the area you live in?

What sort of area do you live in?

CollectPlan Process Discuss

Start screen

How safe do you think it

is?

Discuss

Process


Plan

Collect

DHCycleThe Problem Solving Approach

You can build on the first try by

continuing here...

First we decide what problem to

solve and what data we need

Then we collect suitable data.Then we examine

our data and make it easier to understand.

Discuss

Process


Plan

Collect


How safe is your neighbourhood?

TV, radio and newspapers regularly report crimes and crime statistics.

Collect Process Discuss

Crime in the Media

Plan

PlanCollect Process Discuss

Set the problem

How safe is your neighbourhood?

Are the crime figures as bad as some of the newspapers suggest?

What are the crime figures like in your neighbourhood?

Are crime figures increasing each year?

Should people be more/less concerned about certain crimes?

Where in the UK is the ‘safest’ place to live?

Where is the ‘crime capital’ of the UK?

In which areas of the UK is crime increasing?

Which places are improving?


Start screen

How can you find out?

Who should you ask?

What proportion of students worried about safety?

Do most fr

eshers

live in safe

neighbourhoods?

What should you ask them?

Plan


Crime in the Media

Plan

Is there any association between university town and attitude to

safety?

Do fresh

ers ch

oose

‘safe

’ neighbourh

oods

to liv

e in?

Are students at all

universities worried?

Use a questionnaire?

What crimes worry students most?


Eight categories

Plan

Develop a model of the population. One variable may depend on another. Turn the model into precise statistical hypotheses (null and alternative).

H0:

H1:

There is no association between university town and concern about being mugged

There is an association

CollectProcess Discuss

Plan

The questionnaire

Discuss

Process


Plan

Collect


You arenow here.

CollectProcess Discuss

Which data

Plan

You did this in your first seminars

Students at three other UK universities have completed the

questionnaire

Discuss

Process


Plan

Collect


You arenow here.

ProcessPlan Collect Discuss

Which processes

If University and scale of worry are INDEPENDENT

P(B and fairly worried) = P(B) х P(2)

250

45

250

65


Which processes

How does this compare with P(B and 2) 0560.0250

14

P(B and 2) = 0468.0250

45

250

65

How close are they??

Expected frequencies

How many would we have expected to be B and 2?

P(B and 2)

If B and 2 are independent

Expected frequency =

250

45

250

65 7.11

250

4565

row total х column total

overall total

х (total number)

250



Which processes

H0:

H1:

There is no association between university and worry about being mugged


We also need to choose the level α

Recall that α = P(reject H0 when H0 true)

What is the test statistic?

The test statistic

Expected frequency = row total х column total

overall totali is row number

j is column number

eij is expected frequency for cell (i, j)

oij is the observed (sample) frequency for cell (i, j)

ji ij

ijij

e

eoX

,

2

2 TEST STATISTIC

X2 has a distribution that is approximately

The approximation is good when all of eij ≥5

or when 80% of eij ≥ 5 and all eij ≥ 1

2 (Chi squared)


The distribution2

0 5 10 15

0.0

00

.05

0.1

00

.15

chisq

f(ch

isq)

)( 2f

2

ji ij

ijij

e

eoX

,

2

2

has a chi-squared distribution with (r-1)(c-1) degrees of freedom

(r-1)(c-1) = rc – r – c + 1

number of oij frequencies

number of row totals

number of column totals

(r-1)(c-1) df

Remove double counting


0 2 4 6 8 10 12

0.0

0.1

0.2

0.3

0.4

0.5

chisq

f(ch

isq

)

df = 2

Different 2 distributions

2 d.f.

0 5 10 15 20

0.0

00.

05

0.1

00.

15

chisq

f(ch

isq)

df = 5

5 d.f.

0 20 40 60 80 100

0.0

00

.01

0.0

20

.03

0.0

4

chisq

f(ch

isq

)

df = 50

50 d.f.

0 50 100 150

0.0

00

0.0

05

0.0

10

0.0

15

0.0

20

0.0

25

chisq

f(ch

isq

)

df = 100

100 d.f.


The decision rule2

0 5 10 15

0.0

00

.05

0.1

00

.15

chisq

f(ch

isq)

)( 2f

2

ji ij

ijij

e

eoX

,

2

2

If oij close to eij

(r-1)(c-1) df

2ijij eo will be close to zero and

X2 will be small

If oij very different from eij , 2ijij eo and X2 will be large

DECISION RULE

Reject H0 if X2 is too big



Which processes

Example

H0:

H1:

α = 0.05



DECISION RULE

Reject H0 if

28,05.0

22 )(

i ij

ijijcalc e

eoX

d.f. = (3-1)Χ(5-1) = 8


Which processes2

8,05.0

22 )(

i ij

ijijcalc e

eoX


Which processesExample

H0:

H1:

α = 0.05



DECISION RULE

Reject H0 if

d.f. = (3-1)Χ(5-1) = 8

From sample data …

507.15)( 2

8,05.0

22

i ij

ijijcalc e

eoX


Which processes

From Minitab

Expected frequencies

Contribution to test statistic

Test statistic

Discuss

Process


Plan

Collect


You arenow here.

H0 : there is no association between university attended and fear of being mugged

H1 : there is an association

α = 0.05

DECISION rule

Reject H0 if

DISCUSS

507.15)( 2

2

i ij

ijij

e

eoX

2f

2

d.f. = (r-1)Χ(c-1) = 8

REJECTDo not reject

From sample data

23.77722 calc

0 5 10 15

0.0

00

.05

0.1

00

.15

0.2

00

.25

chisq

f(ch

isq

)

8 df

DiscussPlan Collect Process

DiscussPlan Collect Process

Discussion

Other questions?

• about what is this due to

• about other questions/associations

What can we conclude?

Discuss

Process


Plan

Collect


You arenow here.

You can build on the first try by

continuing here...

Have you got all the evidence

you want?

plancollectprocessdiscuss start screen what sort of neighbourhood do you live in?

Documents

crime figures

safe neighbourhoods

approachhow safe

problemhow safe

crime statistics

crime capital

uk universities

universities worried