Factorial Design analysis

Statistical analysis

for

Determining purchase intent of a customer while buying a vehicle.

Design and Analysis of ExperimentsNovember 20th, 2016

By,

Ashish Menkudale UIN: 656130575

Akash Tayal UIN: 661488456

Kshitij Nayak UIN: 657718376

Suhaas Nallacheru UIN: 673011149

Total slides: 29

Time: 8 minutes

Outline

• Defining problem statement and scope of project.

• Selecting response variable.

• Selecting factors and levels.

• Collecting data.

• Data cleaning and visualization.

• Selecting statistical analysis technique.

• Procedure of statistical analysis.

• Result analysis for factorial design without blocking.

• Result analysis for factorial design with blocking.

• Interpretation from effects plot.

• Conclusion.

Pre Experimental

planning

Experiment and

Model revision

2

Problem statement

“The selection of factors which are primarily responsible for determining the purchase intent of

a customer while buying a vehicle and study of interaction effect between those factors.”

Why we chose this problem statement?

• To understand how a generic problem like selection and purchase of a vehicle can be broken down

into a statistical analysis technique.

Scope of experiment

• Includes daily basis regular usage cars

• Excluded high end performance vehicles

3

Selection of response variable

• Initial response variable : Vehicle model preferred by the customer

• Disadvantages : Qualitative and difficult to measure

• Final selection : Price of the vehicle

4

• Initial selection

• Final selection

Selection of factors and levels

Factor Level 1 Level 2 level 3

1 Engine type IC Electric Hybrid

2 Segment Hatchback Sedan SUV/MUV

3 Features Aesthetic After sales service Luxury

5

Factor Level 1 Level 2 level 3

1 Engine power outputlow power

(below 150 hp)

Medium power

(150 hp-250 hp)

High power

(above 250 hp)

2 Segment Hatchback Sedan SUV/MUV

3 Features Aesthetic After sales service Luxury

Collecting data: Format of surveyQ1. Which range of engine power output would you prefer? (select one).

• Low Power (up to 150 hp).

• Medium power (150 hp to 250 hp).

• High Power (250 hp and above).

Q2. Which Vehicle segment would you prefer? (select one).

• Hatchback.

• Sedan.

• SUV / MUV.

Q3. Select preferred features you are looking for in your vehicle. (select one).

• Aesthetics.

• luxury.

• after sales service.

Q4. Please enter your preferred price estimate for above selected parameters.

• Price.

Q5. Please enter which brand of the vehicle you would prefer on the basis of the factors you chose above.

• Brand.6

Data cleaning: Initial screening

• Over 212 data points were obtained through survey.

• Visual screening.

• Removing illogical and incomplete inputs.

• Data frame of 189 data points.

Low Medium High Hatchback sedan SUV/MUV AestheticsAfterSales

serivceLuxury

1 ✔ ✔ ✔ 45000 Mercedes

2 ✔ ✔ ✔ 28000 Ford

3 ✔ ✔ ✔ 24500 Chevrolet

4 ✔ ✔ ✔ 20800 Toyota

5 ✔ ✔ ✔ 26500 Ford

6

7

Observati

on #

continued upto 189 data points

Engine power output Segment Features

Price $ Brand

Data frame

7

Probability distribution plot for price was plotted according to Anderson – Darling method.

Takeaway: Obtained data is normally distributed.

Data cleaning: Normality checks

P value should be greater than

0.05 so that we will fail to reject

our null hypothesis which

assumes our data is normally

distributed.

Probability plot of Response

Normal – 95 % CI

8

Data cleaning: Data visualizationDistribution in data according to brands

Takeaway: Honda, Toyota and Ford were most preferred brands. 9

10

Experimental procedure

1. Collect inputs from customers and get the desired combination and response variables via survey.

2. Check the Normality for the values of response variables using MINITAB.

3. Outline of experiment:

• A Full Factorial Design with 3 Factors and 3 Levels.

• 3 replicates and a total of 81 data points.

• Without blocking and with Blocking method (discussed later).

• Regression analysis

• Residual analysis for prices obtained from inputs and prices calculated from regression equation.

4. Check the significance of main effects and interaction effects with the help of P-value obtained from full

factorial design.

5. Residual analysis.

6. Conclude.

11

Formulation of theoretical model

H01: μHigh power = μmedium power = μlow power.

H a1: μHigh power ≠ μmedium power ≠ μlow power.

H 02: μhatchback = μsedan = μsuv/muv.

H a2: μhatchback ≠ μsedan ≠ μsuv/muv.

H 03: μaesthetics = μafter sales = μluxury.

H a3: μaesthetics ≠ μafter sales ≠ μluxury.

Main effect of factor Power output

Main effect of factor Segment

Main effect of factor feature

Interaction effect

between factor

power, segment

and feature

H 04: Power has no influence on how segment affects vehicle price.

H a4: There is an interaction between power and segment of the vehicle.

H 05: Power has no influence on how features affects vehicle price.

H a5: There is an interaction between power and features of the vehicle.

H 06: Segments has no influence on how features affects vehicle price.

H a6: There is an interaction between segment and features of the vehicle.

H 07: The three factors have no influence on vehicle price.

H a7: There is a three-factor interaction between Power, segment and features.

12

Formulation of theoretical modelInteraction effect

between factor

Power output

and segment

Interaction effect

between factor

Power output

and feature

Interaction effect

between factor

Segment and

feature

13

Results: Full factorial design analysisResults of analysis of variance (without blocking). Conclusion:

All main effects are significant as P value

is less than 0.05.

All two way interactions are not

significant.

Three way interaction is not significant.

Conclusion:

R square is 60%. It is slightly less than

moderate. Model does not have a good

fit over data.

Main effects

2-way interaction effects


Results: Full factorial design analysis

All the main effects (A, B and C) and a two

way interaction AB are significant as they do

not lie on normality spectrum.

14

Results of analysis of variance (without blocking).

15


Residuals are not

normally

distributed.

Residuals have

diverging trend as

fitted value

increases.

Mostly, residuals

lie on negative

side with respect

to observation

order which

concludes a

correlated error.

Residual analysis (without blocking).

16

Revised formulation of experiment

• Response Variable: Price

• A Full Factorial Design with 3 Factors and 3 Levels.

• 3 replicates and a total of 81 data points.

• Blocks on replicates.

• Regression analysis

• Residual analysis for prices obtained from inputs and prices calculated from regression equation.

Blocks Block 1 Block 2 Block 3

Brand Honda Toyota Ford

17

Results: Full factorial design analysisResults of analysis of variance (with blocking). Conclusion:

All main effects are significant as P value

is less than 0.05.

Two way interactions for power-segment

and segment-feature are significant.

Three way interaction is not significant.

Conclusion:

R square is 84%. Model has a good fit

over data.

Main effects




All the main effects (A-power, B-segment and

C-feature) are significant as they do not lie on

normality spectrum.

Also, two way interactions AB – power &

segment and BC – segment & feature are

significant as they lie slightly off from normality

spectrum.

Results of analysis of variance (with blocking).

18

19


Residuals are

normally

distributed.

Residuals do not

have any trend

with respect to

fitted values.

Residuals do not

have any trend

with respect to

observation order

which concludes a

non correlated

error.

Residual analysis (with blocking).

As data spread is large over regression line, it is

evident that model performance for experiment

without blocking is very poor. (R square = 60%). 20

Regression analysis: Actual vs. predicted

Compared to model performance for experiment

without blocking, this model performs way better

as R-square is significantly increased (84%).

Conclusion

For only Aesthetics, price is lowest

in factor features. Prices increases

for preference shifted to aftersales

service and it is highest for

preference as luxury. 21

Main effect analysisConclusion

Price increases as levels in power

changes from low power, medium

power to high power.

Conclusion

In factor segment, levels Sedan are

SUV have fairly similar prices and

those are higher than hatchbacks.

1 2 3

1

2

3

Main effects (with blocking).

22

Interaction effect analysis

From 1 and 3 (power and

segment interaction), it is

concluded that, interaction is

relatively more significant.

1

2

3

4

5

6

Interaction effects (with blocking).

From 4 and 6 (feature and

segment interaction), it is

concluded that, interaction is

relatively less significant.

From 2 and 5 (power and

feature), it is concluded that,

interaction is not significant at

all.

23

Conclusion

Conclusion# Term Experiment without blocking Experiment with blocking

1 Main effects Significant. Significant.

2 Two way interaction effectsNo two way interaction is

significant.

Two way interaction for Power

and segment is significant.

3 Three way interaction Not significacnt. Not significant.

4 R square 59.80% 84%

5 Adj. R square 40.50% 75.40%

6 Trend for residual distribution Not normal. Normally distributed.

7 Trend for fitted values Diverging trend. No trend.

8Performance (Actual vs.

Predicted)

Large spread (Poor

performance).

Less spread (good

performance).

24

Conclusion

H01: μHigh power = μmedium power = μlow power.

H a1: μHigh power ≠ μmedium power ≠ μlow power.

H 02: μhatchback = μsedan = μsuv/muv.

H a2: μhatchback ≠ μsedan ≠ μsuv/muv.

H 03: μaesthetics = μafter sales = μluxury.

H a3: μaesthetics ≠ μafter sales ≠ μluxury.

Main effect

of factor

Power

output

Main effect

of factor

Segment

Main effect

of factor

feature

We reject the null hypothesis.

i.e. there’s significant effect of

main effect power output.



main effect segment.



main effect feature.

H 04: Power has no influence on how segment affects vehicle price.

H a4: There is an interaction between power and segment of the vehicle.

H 05: Power has no influence on how features affects vehicle price.

H a5: There is an interaction between power and features of the vehicle.

H 06: Segments has no influence on how features affects vehicle price.

H a6: There is an interaction between segment and features of the vehicle.

H 07: The three factors have no influence on vehicle price.

H a7: There is a three-factor interaction between Power, segment and features.

25

Conclusion

We reject the

null hypothesis.

We fail to reject

the null

hypothesis.

We fail to reject

the null

hypothesis.

We fail to reject

the null

hypothesis.

Future scope

26

• Problem statement like this, usually involve a complex matrix of many factors with many different

levels.

• A more comprehensive model can be build for more factors and levels.

• Data transformation can be done to figure out better model fit.

Excel : Data collection from ‘formstack’ and Data sorting.

Rapid Miner : Data visualization.

Spotfire : Data visualization.

Minitab : factorial analysis, regression analysis, effects interpretation.

Design Expert : Half normality plots, Model performance analysis- predicted vs. actual

27

Software used

28

References

• Design and analysis Of experiments, Eighth edition, Douglas c. Montgomery, john wiley & sons, inc.

• Videos tutorials for Design Expert.

• Video tutorials for Rapid Miner.

29

Questions

Engineering

Factorial Design analysis