1. Notes on Data Collectionand Analysis Dale Weber PLTW EDD Fall 2009

2. Things to Consider Experiment Planning Data Analysis Strength of “Effects” Individual Factors Factor/Factor Interaction Modeling Linear Regression • Replication • Randomization • Blocking

3. Replication • Using mean of replicate data gives more precise results • 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

4. Equal Means 2x Variance Outliers 2 close pts - suggests dropping outliers - performing another experiment

5. 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 order Roll dice or use computer (Excel –RAND) to generate random sequence

6. Strength of Effects Effect of A: Average of High A value minus Average of Low A value Montgomery, D.C. Design and Analysis of Experiments, 2001.

7. Factor/Factor Interaction Effect of A at Low B: 50 - 20 = 30 Effect of A at High B: 12 – 40 = -28 Since the Effect of A depends on value of B: There is Interaction Another way to view it Montgomery, D.C. Design and Analysis of Experiments, 2001.

8. Modeling • Regression Model Random Noise Measured output Mean Factor Values Coefficients Interaction Term Can add other terms to model: and so on.

9. (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 • Make table of model terms in columns with output in last column:

10. (Multiple) Linear Regression (2) • Enter LINEST Command in blank cell Calculate Fit Statistics Model Input Data (Exp Factor values and combos) Force const (b0) to 0? T = No F = Yes Measured Data Least Squares Fit Coefficients b’s – in reverse order! R2 – value (Goodness of Fit)

11. (Multiple) Linear Regression (3) • Drag LINEST cell and Fill • Drag box needs as many Columns as factors and factor combos in the model + 1 • Drag box needs 5 Rows. • Press F2 to convert LINEST formula and Drag box to an array. • Press CTRL+SHIFT+ENTER to fill

12. (Multiple) Linear Regression (4) • Use Least Squares Model to make predictions 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