Notes on Data Collection and Analysis

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Notes on Data Collection and Analysis Dale Weber PLTW EDD Fall 2009

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Notes on Data Collection and Analysis. Dale Weber PLTW EDD Fall 2009. Things to Consider. Experiment Planning. Data Analysis. Strength of “Effects” Individual Factors Factor/Factor Interaction Modeling Linear Regression. Replication Randomization Blocking. Replication. - PowerPoint PPT Presentation

Transcript of Notes on Data Collection and Analysis

Page 1: Notes on Data Collection and Analysis

Notes on Data Collectionand Analysis

Dale WeberPLTW EDDFall 2009

Page 2: Notes on Data Collection and Analysis

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