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Notes on Data Collection
and Analysis
Dale Weber
PLTW EDD
Fall 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 Means
2x 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 order
Roll dice or use computer (Excel –RAND) to generate
random sequence
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.
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.
Modeling
• Regression Model
y  0  1x1  2 x2  12 x1x2  ... 
Measured
output
Coefficients
Random
Noise
Mean
Factor
Values
Interaction Term
x3  xi2
Can add other terms to model:
x4  x1 x2 x3
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
Calculate Fit Statistics
Measured
Data
Least Squares
Fit Coefficients
’s – in reverse
order!
R2 – value
(Goodness of
Fit)
Model Input Force const (0) to 0?
Data (Exp
T = No
F = Yes
Factor values
and combos)
(Multiple) Linear Regression (3)
3. Drag LINEST cell and Fill
i.
Drag box needs as many Columns as factors and
factor combos in the model + 1
ii. 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  
ˆ x  
ˆ x  
ˆ x x  ...
yˆ  
0
1 1
2 2
12 1 2
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