Experimental Designs (Introduction)

By

Fan Shenghua, Kelly

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Example: What are the factors affecting the taste of a soft drink

beverage?

• Type of sweetener• Ratio of syrup to water• Carbonation level• Temperature• Others??

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What is an experiment?

• An inquiry in which an investigator chooses the levels (values) of input or independent variables and observes the values of the output or dependent variable(s).

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What is a statistical experimental design?

• What is the output variable?

• Which (input) factors should we study?

• What are the levels of these factors?

• What combinations of these levels should be studied?

• How should we assign the studied combinations to experimental units?

Determine the levels of independent variables (factors) and the number of experimental units at each combination of these levels according to the experimental goal.

Experimental unit: the unit we apply the factors on to get the response.

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Example (Cont.): soft drink beverage

• Type of sweetener• Ratio of syrup to

water• Carbonation level• Temperature

•What is the output variable?

Taste of the drink; score 1 to 10 (from poor to good)

•What factors and at which levels should we study?A, B

Low, High

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Example (Cont.): soft drink beverage

•What combinations of factors should be studied?

All 2x2x2x2 combinations.

•How should we assign the studied combinations to experimental units?

Assign equal number of units to each combination.

(unit: the “null” beverage or say the plain water)

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The Six Steps of Experimental Design

• Plan the experiment.

• Design the experiment.

• Perform the experiment.

• Analyze the data from the experiment.

• Confirm the results of the experiment.

• Evaluate the conclusions of the experiment.

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Plan the Experiment

• Identify the dependent or output variable(s).• Translate output variables to measurable

quantities.• Determine the factors (input or independent

variables) that potentially affect the output variables that are to be studied.

• Identify potential combined actions between factors.

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Example: Which brand of battery should we buy?

Three available brands; Prices etc.

•What is the output variable?

•What are the input variables (factors)?

Battery life. (in hours)

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Design topics vs. variable types

Response (output)

Predictor (input)

Continuous Categorical

Continuous

•Response surfaces (RS)•Uniform designs (UD)•Optimal designs (OD)

•Standard ANOVA designs (eg. factorial designs)

Categorical UD,OD

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Prior experimental information

The model is known but the parameters are not:

Optimal designs

The shape of the model is somewhat clear:

Response surfaces

The model is completely unknown:

Uniform designs