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