DATA ANALYSISMaking Sense of Data

ZAIDA RAHAYU YET

Types of Data

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

Types of Data

Qualitative Data Quantitative Data

Nominal Ordinal Discrete Continuous

Interval Ratio

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

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

Continuous Data

A quantitative data is continuous if its possible values form an interval

Measurements Examples:

1. Height/Weight2. Age3. Blood pressure

Continuous data -- Theoretically,no gaps between possible values

0 1000

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).

Displaying Categorical & Quantitative Data

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.

Displaying Categorical & Quantitative Data (MINITAB)

Parametric Assumptions

1. Independent samples2. Data normally distributed3. Equal variances

Normality test (MINITAB)

Equal variances test(MINITAB)

Regression analysis (MINITAB)

Correlation analysis (MINITAB)

Example One-way ANOVA

One-way ANOVA(MINITAB)

ANOVA (MINITAB output)

2 samples t-test (MINITAB)

2 Samples Dependent (MINITAB)

OPTIMIZATION

OPTIMIZATION FLOWCHART

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.

Factor Range

A. Seal Temp 225 - 285

B. Cooling Bar Temp 46 - 64

C. Polyethylene Content 0.5 – 1.7

RSM Design(MINITAB)

RSM Design(MINITAB)

RSM Analysis(MINITAB)

RSM-Regression Analysis (MINITAB)

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 PConstant -28.7877 11.3798 -2.530 0.030temp 0.1663 0.0646 2.573 0.028cooling 0.6120 0.1914 3.198 0.010polyethylene 5.4495 2.4698 2.206 0.052temp*temp -0.0003 0.0001 -2.647 0.024cooling*cooling -0.0045 0.0013 -3.633 0.005polyethylene*polyethylene -1.1259 0.2813 -4.003 0.003temp*cooling -0.0005 0.0005 -0.909 0.385temp*polyethylene -0.0098 0.0076 -1.298 0.223cooling*polyethylene 0.0098 0.0252 0.389 0.705

S = 1.089 R-Sq = 85.6% R-Sq(adj) = 72.6%

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

Surface Plot & Contour Plot (MINITAB)

RSM-Response Optimization(MINITAB)

Thank you