1. 6/3/20151 FROM DATA TO GRAPHS TO WORDS - BUT WHERE ARE THE MODELS? K. Larry Weldon Simon Fraser University Canada 1 10.3 12.2 2 15.4 27.6.. …. …. Findings from the Data The data shows that higher Y’s are associated with higher x’s. But note the predictive assumption of the line shown. It is for predicting Y from X, not the other way round. Clearly, the line is not a fit to the data since two different lines cannot be equally good fits.

2. 6/3/20152 Outline Ex 1 - A time series Ex 2 - A two-variable prediction problem Ex 3 - A three-variable interaction Ex 4 - A two-group comparison Theme: Graphs can analyze & summarize, and are easy to report in words. Conclusion: We need to give this material more emphasis, and less emphasis on parametric models.

3. 6/3/20153 Ex 1: A time series

4. 6/3/20154 Verbal report? Petrol Consumption varies with the season - high in winter and low in summer. Petrol Consumption varies sinusoidally with the season - high in winter and low in summer.

5. 6/3/20155 So what? Parametric approach was unreachable for many undergraduates Parametric approach would not necessarily find the important information Graphical approach adequate for both analysis and summary display, and was easy to verbalize. On to Example #2 …

6. 6/3/20156 Ex#2: Relationship between two variables Density=1.1627-.0042*BMI 40% 17% 26% 8% %FAT

7. 6/3/20157 Read the Graph Directly 1.06 1.0140% FAT 17% FAT

8. 6/3/20158 Verbal Report? BMI is not a good enough predictor of Body Density (and % FAT) to be useful clinically, in this population.

9. 6/3/20159 So what? Parametric approach would not necessarily find the important information Graphical approach all that was needed for both analysis and summary On to Example #3 …

10. 6/3/201510 Ex#3: More than two variables - Interaction What is Interaction? Correlation? Association? Interdependence? Conversation!? Example: Tire Rubber data: Y = Abrasion Loss X1= Hardness X2=Tensile Strength Explain with Anova or Regression?

11. 6/3/201511 Regression on Rubber Data Abrasion.loss = 1204.3 - 10.92*Hardness -3.21*Tensile.Strength +.0253 * H.TS Interaction Term not at all significant, yet …

12. 6/3/201512 Interaction? Data and co-plot method described in Wm. Cleveland’s 1993 text “Visualizing Data” Probably Yes!

13. 6/3/201513 A verbal report? “Samples of rubber with low tensile strength may still have low abrasion loss if the hardness is great enough.”

14. 6/3/201514 So what? Parametric approach was unreachable for many undergraduates Parametric approach would not necessarily find the important information Graphical approach all that was needed for both analysis and summary On to Example #4 …

15. 6/3/201515 Ex#4: A two-group comparison Old Treatment Response - % Improvement New Treatment Response - % Improvement Parametric Summary? n 1 = 25 n 2 = 25 Independent samples of patients

16. 6/3/201516 Parametric Summary Mean-Old = 27% improvement SD-Old = 11% Mean-New= 39% SD-New= 23% Verbal Report? Difficult to give a useful one.

17. 6/3/201517 A two-group comparison Old Treatment Response - % Improvement New Treatment Response - % Improvement n 1 = 25 n 2 = 25 Independent samples of patients Verbal Report?….

18. 6/3/201518 Verbal Report? The new treatment has a superior response for most of the patients, but may be inferior for a few patients. i.e. promising! Note: If check for shift in mean equivocal conclusion. Use a Graph! Need the whole distribution.

19. 6/3/201519 So what? Parametric approach would not necessarily contain the important information Graphical approach all that was needed for both analysis and summary

20. 6/3/201520 Conclusion We need to increase the proportion of our courses that focus on this process - for all categories of students. 1 10.3 12.2 2 15.4 27.6.. …. …. Findings from the Data The data shows that higher Y’s are associated with higher x’s. But note the predictive assumption of the line shown. It is for predicting Y from X, not the other way round. Clearly, the line is not a fit to the data since two different lines cannot be equally good fits. DataGraphsWords