notes on data collection and analysis dale weber pltw edd fall 2009
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Notes on Data Collectionand Analysis
Dale WeberPLTW EDDFall 2009
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Things to Consider
Experiment Planning• Replication• Randomization• Blocking
Data Analysis• Strength of “Effects”
– Individual Factors– Factor/Factor Interaction
• Modeling• Linear Regression
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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
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Equal Means2x Variance Outliers
2 close pts- suggests dropping outliers- performing another experiment
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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
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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
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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
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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.
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(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:
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(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)
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(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
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(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