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

Plan Collect Process Discuss

Start screen

What sort of place do you live in?


Start screen

What sort of place do you live in?

Where do your

friends live?

Discuss

Process


Plan

Collect

DHCycleThe Problem Solving Approach


Start screen

How can you find out?

Who should you ask?

What proportion of students are freshers?Do most fr

eshers

live in university

accommodation?

What should you ask them?

Plan

Collect Process Discuss

Crime in the Media

Plan

Does the average rent paid depend on type of accommodation?

Do freshers prefer

private

accommodation?

Do third years live

in hall?

Use a questionnaire?

Do students pay a lot of rent?

Collect Process Discuss

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:

The average rent is the same for all types of accommodation

The average rents differ

CollectProcess Discuss

Plan

The questionnaire


Which data

Plan

Discuss

Process


Plan

Collect


You arenow here.


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

Analysis of variance

• Testing for– Differences between means

AN O VA

ANOVA

If we want to detect differences between means

why do we look at variances?


Which processes

10 15 20 25 30 35 40

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f(x)

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f(x)

H1 true

H0 true

Assume H0 true when H1

true

The null hypothesis is

H0 : the means are all equal

or μ1 = μ2 = μ3 …… = μk

The alternative hypothesis is

H1 : the means are not all equal

or μi ≠ μj for some i and j

Assume the variance σ2 is the same for all


Which processes

ANOVA10 15 20 25 30 35 40

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H0 : μ1 = μ2 = μ3 …… = μk

H1 : μi ≠ μj for some i and j Average the variances from these

And compare it with the variance from this


ANOVA10 15 20 25 30 35 40

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H0 : μ1 = μ2 = μ3 …… = μk

H1 : μi ≠ μj for some i and j Average the variances from these

And compare it with the variance from this

A big difference would support H1

Within groups

Between groups


Which processes

ANOVA

Measuring the variability within groups

1. Calculate individual sample means

2. Calculate sum of squared deviations from these sample means for each group

kixi ,,2,1,

j

iij xx 2

3. Calculate the total sum of squares across all groups the within groups sum of squares

i j

iijW xxSS 2

4. Then divide by the degrees of freedom n-k

kn

SSMS W

W

The within group mean square


Which processes

ANOVAMeasuring the variability between groups

1. Calculate individual sample means

2. Calculate the overall sample mean

kixi ,,2,1,

x

3. Calculate the between groups sum of squares as

To estimate we would use in

2

ii n

NX2

,~

2xxi

2xxn ii

because

So to estimate σ2 we use

i

iiB xxnSS 2

4. Then divide by the degrees of freedom k-1

1k

SSMS B

B

The between groups mean square


Which processes

The test statistic

We have two estimates of σ2

1k

SSMS B

B

The within group mean square

The between groups mean square

kn

SSMS W

W

If H0 is true they should be similar

We look at

W

B

MS

MSF The test

statistic

F has an F distribution with k-1 numerator AND

n-k denominator

degrees of freedom


Which processes

Different F distributions

0 2 4 6 8 10

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f(F)

3 and 179 d.f.

0 2 4 6 8 10

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f(F)

3 and 10 d.f.

0 2 4 6 8 10

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f(F)

10 and 10 d.f.

0 1 2 3 4

0.0

0.5

1.0

1.5

2.0

F

f(F)

100 and 179 d.f.

Discussion

0 2 4 6 8

0.0

0.2

0.4

0.6

0.8

1.0

F

f(F)

H0 : μ1 = μ2 = μ3

H1 : μi ≠ μj for some i and j

α = 0.05

The decision rule is Reject if

Can obtain this from Minitab

Reject H0

Do not reject

2 and 232 df

03475.305.0,232,2 FMS

MSF

W

B



Which processes

ANOVA table for rent versus type of accommodation

A random sample of n=235 students across 3 universities was taken

Type of accommodation classified as home, university or private

Numerator df = k - 1 = 2

Denominator df = n - k = 232


Which processes

From Minitab

Rent versus type

within group mean square MSW

between groups mean square MSB

92.69069

62784

W

Bcalc MS

MSF

Discuss

Process


Plan

Collect


You arenow here.

DISCUSSDiscussPlan Collect Process

Discussion

0 2 4 6 8

0.0

0.2

0.4

0.6

0.8

1.0

F

f(F)

H0 : μ1 = μ2 = μ3

H1 : μi ≠ μj for some i and j

α = 0.05

The decision rule is Reject if

3.03475F

92.6calcF

From sample data

Reject H0

Do not reject

2 and 232 df

DiscussPlan Collect Process

Discussion

Individual 95% CIs For Mean Based on Pooled StDev

Level N Mean StDev ----+---------+---------+---------+-----Home 5 319.60 251.78 (----------------*----------------)Private 117 248.36 85.78 (---*--)Uni 113 292.82 94.34 (---*--) ----+---------+---------+---------+----- 250 300 350 400Pooled StDev = 95.23

Can we say why?

What about students living at home?

Have we asked the right questions?

DiscussPlan Collect Process

Discussion

Other questions?

• about what is this due to

• about other questions/relationships

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 place do you live in?

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