DATA ANALYSIS

1. DATA ANALYSIS Making Sense of Data ZAIDA RAHAYU YET

3. Types of Data The type(s) of data collected in a study determine the type of statistical analysis used.

4. Types of Data Qualitative Data Quantitative Data Discrete Continuous Nominal Ordinal Interval Ratio

5. Terms Describing Data • Quantitative Data: • Deals with numbers. • Data which can measured. • (can be subdivided into interval and ratio data) • Example:- length, height, weight, volume • Qualitative Data (Categorical data ): • Deals with descriptions. • Data can be observed but not measured. • (can be subdivided into nominal and ordinal data) • Example:- Gender, Eye color, textures

6. Discrete data -- Gaps between possible values 0 1 2 3 4 5 6 7 Discrete Data • A quantitative data is discrete if its possible values form a set of separate numbers: 0,1,2,3,…. • Examples: • Number of pets in a household • Number of children in a family • Number of foreign languages spoken by an individual

7. Continuous data -- Theoretically, no gaps between possible values 0 1000 Continuous Data • A quantitative data is continuous if its possible values form an interval • Measurements • Examples: • Height/Weight • Age • Blood pressure

8. Qualitative (Categorical) data Nominal data : • A type of categorical data in which objects fall into unorderedcategories. • To classify characteristics of people, objects or events into categories. • Example: Gender (Male / Female). Ordinal data (Ranking scale) : • Characteristics can be put into ordered categories. • Example: Socio-economic status (Low/ Medium/ High).

9. Displaying Categorical & Quantitative Data

10. Which graph to use? • Depends on type of data: • For categorical you will typically use either a bar or pie graph • For quantitative you can use dotplot, stemplot, histogram, boxplot.

11. Displaying Categorical & Quantitative Data(MINITAB)

12. Parametric Assumptions • Independent samples • Data normally distributed • Equal variances

13. Normality test (MINITAB)

14. Equal variances test(MINITAB)

16. Regression analysis (MINITAB)

18. Correlation analysis (MINITAB)

20. Example One-way ANOVA

21. One-way ANOVA(MINITAB)

22. ANOVA(MINITAB output)

24. 2 samples t-test (MINITAB)

26. 2 Samples Dependent (MINITAB)

27. OPTIMIZATION

28. OPTIMIZATION FLOWCHART

29. RSM Example • In the article “Sealing Strength of Wax-Polyethylene Blends” by Brown, Turner, & Smith, the effects of three process variables (A) seal temperature, (B) cooling bar temperature, & (C) % polyethylene additive on the seal strength y of a bread wrapper stock were studied using a central composite design.

30. RSM Design(MINITAB)

31. RSM Design(MINITAB)

32. RSM Analysis(MINITAB)

33. RSM-Regression Analysis (MINITAB) Response Surface Regression: Response versus temp, cooling, polyethylene The analysis was done using uncoded units. Estimated Regression Coefficients for Response TermCoef SE Coef T P Constant -28.7877 11.3798 -2.530 0.030 temp 0.1663 0.0646 2.573 0.028 cooling 0.6120 0.1914 3.198 0.010 polyethylene 5.4495 2.4698 2.206 0.052 temp*temp -0.0003 0.0001 -2.647 0.024 cooling*cooling -0.0045 0.0013 -3.633 0.005 polyethylene*polyethylene -1.1259 0.2813 -4.003 0.003 temp*cooling -0.0005 0.0005 -0.909 0.385 temp*polyethylene -0.0098 0.0076 -1.298 0.223 cooling*polyethylene 0.0098 0.0252 0.389 0.705 S = 1.089 R-Sq = 85.6% R-Sq(adj) = 72.6%

34. RSM-Analysis of Variance(MINITAB) Analysis of Variance for Response Source DF Seq SS Adj SS Adj MS F P Regression 9 70.305 70.305 7.8116 6.58 0.003 Linear 3 30.960 18.654 6.2181 5.24 0.020 Square 3 36.184 36.184 12.0615 10.17 0.002 Interaction 3 3.160 3.160 1.0533 0.89 0.480 Residual Error 10 11.865 11.865 1.1865 Lack-of-Fit 5 6.905 6.905 1.3811 1.39 0.363 Pure Error 5 4.960 4.960 0.9920 Total 19 82.170

35. Surface Plot & Contour Plot (MINITAB)

36. RSM-Response Optimization(MINITAB)

37. Thank you