1. DATA ANALYSIS Making Sense of Data ZAIDA RAHAYU YET

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

4. Types of Data Qualitative DataQuantitative Data Nominal Ordinal Discrete Continuous IntervalRatio

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

7. Continuous Data  A quantitative data is continuous if its possible values form an interval  Measurements  Examples: 1. Height/Weight 2. Age 3. Blood pressure Continuous data -- Theoretically, no gaps between possible values 0 1000

8. Qualitative (Categorical) data Nominal data : A type of categorical data in which objects fall into unordered categories. 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).

10.  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.

12. Parametric Assumptions 1.Independent samples 2.Data normally distributed 3.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)

28. OPTIMIZATION FLOWCHART

29.  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. FactorRange A. Seal Temp225 - 285 B. Cooling Bar Temp46 - 64 C. Polyethylene Content0.5 – 1.7

31. RSM Design (MINITAB)

32. RSM Analysis (MINITAB)

33. Response Surface Regression: Response versus temp, cooling, polyethylene The analysis was done using uncoded units. Estimated Regression Coefficients for Response Term Coef 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. 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

37. Thank you