Factorial Design analysis
Download as PPTX, PDF3 likes1,961 views
The document presents a statistical analysis aimed at determining customer purchase intent for vehicles, focusing on factors like engine type, segment, and features. It details the experimental design, data collection, and analysis methods used, including factorial designs and regression analysis, ultimately concluding that main effects are significant while certain interactions are not. The model shows improved fit with blocking, achieving an R-squared of 84%, indicating better predictive performance compared to previous models.
Factorial Design analysis
- 1. Statistical analysis for Determining purchase intent of a customer while buying a vehicle. Design and Analysis of Experiments November 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
- 2. 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
- 3. 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
- 4. 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
- 5. • 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 output low 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
- 6. Collecting data: Format of survey Q1. 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
- 7. 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 Aesthetics AfterSales serivce Luxury 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
- 8. 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
- 9. Data cleaning: Data visualization Distribution in data according to brands Takeaway: Honda, Toyota and Ford were most preferred brands. 9
- 10. 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. 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
- 12. 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 model Interaction effect between factor Power output and segment Interaction effect between factor Power output and feature Interaction effect between factor Segment and feature
- 13. 13 Results: Full factorial design analysis Results 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 3-way interaction effects
- 14. 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. 15 Results: Full factorial design analysis 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. 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. 17 Results: Full factorial design analysis Results 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 2-way interaction effects 3-way interaction effects
- 18. Results: Full factorial design analysis 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. 19 Results: Full factorial design analysis 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).
- 20. 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%).
- 21. 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 analysis Conclusion 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. 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. 23 Conclusion Conclusion # Term Experiment without blocking Experiment with blocking 1 Main effects Significant. Significant. 2 Two way interaction effects No 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. 8 Performance (Actual vs. Predicted) Large spread (Poor performance). Less spread (good performance).
- 24. 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. We reject the null hypothesis. i.e. there’s significant effect of main effect segment. We reject the null hypothesis. i.e. there’s significant effect of main effect feature.
- 25. 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.
- 26. 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.
- 27. 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. 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. 29 Questions
Editor's Notes
- #7: Price being the quantitative variables, we asked people to input a number. Our
- #17: We observed that, our factors and selected levels were pretty basic and logically their interactions and they should significantly affect on the price of the vehicle. However, our model was not performing very well in terms of R square. While trying to figure out the reason behind this abnormality, we concluded that, in the received inputs, for a particular selection of levels of different factors, the price for a vehicle in one replicate was very much different from the price of the vehicle in other replicates for same combinations of levels of factors. When a person was providing input, they had some specific brand in their mind and due to different brands, there was this price difference. Hence, we decided to run our experiment with brands as our blocking variables.
- #18: Considering 3 brands which were mostly preferred in obtained data, we had Toyota, Ford and Honda as blocks. In the results, main effects turned out as significant as earlier. In addition to that, we found two two-way interactions were also significant after blocking. And that was logical. Also, R square was improved significantly from 60% to 84%. Which shows a better fit on data.
- #19: To confirm our results, we plotted this half normal probability plot in Design Expert. And we got all the main effects and two way interactions AB and BC outside normality spectrum which confirmed their significance.
- #20: Also, residuals were normally distributed and in the versus fits plot, there wasn’t any trend in scatter plot. Which confirmed the absence of constant variance in residuals. Also the scatter for observation order does not have any trend as desired.
- #21: In the regression analysis, actual vs predicted graph for experiment with blocking had less scatter and that shows improvised fit of the model than the one without blocking.
- #22: After finalizing our model, we analyzed main effects model with blocking. We observed, higher the power of the vehicle, the price also increases. Also, Sedans and SUV’s has almost similar price which are more than Hatchbacks. And Luxury was the more expensive feature than After sales service and mere Aesthetics.
- #23: In the interaction effects analysis, it is observed from graphs 1 and 3 that interaction effect for power and segment, has non parallel lines. Also, Interaction 4 and 6 has fairly non parallel lines. However, interaction in between, power and feature is not significant.
- #24: To conclude our experiment, blocking resulted in better fit of the model. Main effects remained significant in both analyses. However, a two way interaction was turned out to be significant and another two way interaction had p value just more than 0.5. Three way interaction remained insignificant in both analyses. R square and adjusted R-square increased significantly after blocking. Residuals were normally distributed after blocking. Also diverging trend in fitted value disappeared after blocking. For regression analysis, actual vs predicted graph showed less spread in scatter plot for the blocked experiment.
- #25: To conclude our theoretical model, we reject the null hypotheses for all of our main effects which states that they are not significant.
- #26: Also, we reject the null hypothesis for one two way interaction, i.e. power and segment. For rest two way interactions and three way interaction, we fail to reject the null hypotheses.
- #27: With the current analysis, we observed that the R-square has been significantly improved from 60% to 84%. Which shows a good correlation in between factors and response variables. Although, there’s a lot of scope for improvising the model to capture the variation in response variables by means of variation of input variables. For the sake of simplicity, we considered the model with 3 factors and 3 levels. But it is logical to conclude that, there are a lot of other factors as well which can significantly affect the purchase intent of the customer which consequently affects the price of the vehicle. For example, the income of the customer, age of the customer, gender of the customer etc. Including these variables might increase the model fit . A complex matrix comprising of different factors with different levels can be built to have a better control over the variation in the response variable. Also, after analysis, data transformations can be performed to get more accurate estimated prices of the vehicles.
- #28: These were the software used for different purposes.
- #29: These are the references.
- #30: Thank you. Any question.