Notes on Data Collectionand Analysis

Dale WeberPLTW EDDFall 2009

Things to Consider

Experiment Planning• Replication• Randomization• Blocking

Data Analysis• Strength of “Effects”

– Individual Factors– Factor/Factor Interaction

• Modeling• Linear Regression

Replication

1. Using mean of replicate data gives more precise results

2. Comparing mean to raw data gives an estimate of experimental error

– Standard Deviation of data is commonly used– Also, can identify Outliers

Typically 3 Replicates are considered sufficent

Equal Means2x Variance Outliers

2 close pts- suggests dropping outliers- performing another experiment

Randomization and Blocking

Want to “average out” the impact of extraneous factors

Ex. Weather, pressure variation, cone smoothness, etc.

Compile a list of all experiments to be performed (including replicates)

Perform tests in random orderRoll dice or use computer (Excel –RAND) to generate

random sequence

Strength of Effects

Montgomery, D.C. Design and Analysis of Experiments, 2001.

Effect of A: Average of High A value minus Average of Low A value

Factor/Factor Interaction

Montgomery, D.C. Design and Analysis of Experiments, 2001.

Effect of A at Low B:50 - 20 = 30

Effect of A at High B:12 – 40 = -28

Another way to view it

Since the Effect of A depends on value of B: There is Interaction

Modeling

• Regression Model

y 0 1x 1 2x 2 12x 1x 2 ...

Measured output

Random NoiseCoefficients Mean

Factor Values

Interaction Term

Can add other terms to model:

23 ixx

3214 xxxx and so on.

(Multiple) Linear Regression

• You know Linear Regression from using adding trend-lines to plots in Excel

• For multiple independent variables, need to use LINEST function in spreadsheet

1.Make table of model terms in columns with output in last column:

(Multiple) Linear Regression (2)

2. Enter LINEST Command in blank cell

Measured Data

Model Input Data (Exp

Factor values and combos)

Force const ( to 0?T = No F = Yes

Calculate Fit Statistics

Least Squares Fit Coefficients’s – in reverse

order!

R2 – value(Goodness of

Fit)

(Multiple) Linear Regression (3)

3. Drag LINEST cell and Filli. Drag box needs as many Columns as factors and

factor combos in the model + 1ii. Drag box needs 5 Rows.

4. Press F2 to convert LINEST formula and Drag box to an array.

5. Press CTRL+SHIFT+ENTER to fill

(Multiple) Linear Regression (4)

6. Use Least Squares Model to make predictions

ˆ y ˆ 0 ˆ 1x1 ˆ 2x2 ˆ 12x1x2 ...Note: 1. There is no noise term in the fit model

2. A hat (^) signifies model estimate

ANY QUESTONS?Don’t Forget:- LINEST Help File Handout- Montgomery Handout