Home / DOE / Charts / Main Effects Plots / Main Effects Plots How-To
Main Effects Plots How-To¶
This walkthrough draws a main effects panel for each of three factors and checks every point on it against the coefficient table, which is the cleanest way to see what a coefficient means.
Every chart in this family is drawn from a fitted model, so the walkthrough starts by building one. The same experiment is used on all ten chart walkthroughs, so once you have the regression sheet you can work through any of the others without setting the data up again.
The data is on this page rather than in a file to download. Press Copy for Excel, then paste it into a blank worksheet.
The data¶
A three factor experiment on a bonding process, run twice through. Temp is in degrees C, Press in psi and Time in seconds, and the response Strength is the peel strength of the finished bond. Each of the eight factor combinations was run twice, giving 16 runs.
| Temp | Press | Time | Strength |
|---|---|---|---|
| 180 | 40 | 10 | 49.5 |
| 220 | 40 | 10 | 65.4 |
| 180 | 60 | 10 | 61.8 |
| 220 | 60 | 10 | 66.8 |
| 180 | 40 | 20 | 52.3 |
| 220 | 40 | 20 | 70.7 |
| 180 | 60 | 20 | 60.7 |
| 220 | 60 | 20 | 70.0 |
| 180 | 40 | 10 | 50.6 |
| 220 | 40 | 10 | 66.4 |
| 180 | 60 | 10 | 61.2 |
| 220 | 60 | 10 | 67.2 |
| 180 | 40 | 20 | 51.4 |
| 220 | 40 | 20 | 67.1 |
| 180 | 60 | 20 | 61.9 |
| 220 | 60 | 20 | 71.6 |
Each factor takes exactly two values, so this is a full factorial of the three at two levels each, replicated once. That matters for more than one chart: a factor with exactly two observed values is the only kind that can carry a Cube Plot axis, and a design with centre points would have failed that test.
Steps¶
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Put the data in Excel
Press Copy for Excel above the table. In Excel, open a blank worksheet, click cell A1, and press Ctrl+V. You should have headers in row 1 and the 16 runs in rows 2 through 17.
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Make a design sheet to hold it
From the Excel ribbon: QXL DOE New > Create Design > Special > Create Custom Design.
On the first page set the number of factors to 3 and the number of runs to 16. On the second page set the number of outputs to 1. That gives you an empty design sheet of the right shape, which is how data collected outside Quantum XL gets analysed.
-
Fill in the design sheet
Copy the four columns of data into the three factor columns and the one output column. Name the factors Temp, Press and Time, and the output Strength, so the names on your charts match the ones quoted below.
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Check the model holds the three two-factor interactions
The charts below assume a model of the three main effects plus AB, AC and BC. Add any that are missing with QXL DOE New > Modify Design > Inputs > Add/Remove Interactions.
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Run the regression
QXL DOE New > Analyze Design > Run Regression. A worksheet called Regression is added after the design sheet. Every chart in this family reads that sheet.
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Draw the main effects panels
QXL DOE New > Charts > Analysis > Main Effects Plot.
In the Outputs tree tick Strength Y-Hat. Leave all three factors ticked in Factors to plot, and leave the set points alone. Press Create.
Check the fit first¶
Before drawing anything, check the coefficient table on the Regression sheet against this. If these numbers match, every chart number quoted further down will match too; if they do not, the design was not entered the way this walkthrough assumes and nothing below will line up.
| Term | Coefficient | Standard error | t | p |
|---|---|---|---|---|
| Constant | 62.1625 | 0.2912 | 213.477 | 0.000000 |
| Temp (A) | 5.9875 | 0.2912 | 20.562 | 0.000000 |
| Press (B) | 2.9875 | 0.2912 | 10.260 | 0.000003 |
| Time (C) | 1.0500 | 0.2912 | 3.606 | 0.005696 |
| AB | -2.2375 | 0.2912 | -7.684 | 0.000030 |
| AC | 0.6500 | 0.2912 | 2.232 | 0.052506 |
| BC | -0.1500 | 0.2912 | -0.515 | 0.618877 |
The fitted equation is
Strength = 62.1625 + 5.9875 A + 2.9875 B + 1.0500 C - 2.2375 AB + 0.6500 AC - 0.1500 BC
in coded units, where each factor runs from -1 at its low value to +1 at its high value.
Every standard error is the same 0.2912. That is not a coincidence and it is a useful sign that the design was entered correctly: on a balanced full factorial every coded column is orthogonal to every other and carries the same amount of information, so every coefficient is estimated equally precisely.
What you should see¶
One worksheet holding three panels, one per ticked factor, each with two points joined by a line.
| Panel | Low point | High point | Rise |
|---|---|---|---|
| Temp (A), 180 to 220 | 56.1750 | 68.1500 | 11.9750 |
| Press (B), 40 to 60 | 59.1750 | 65.1500 | 5.9750 |
| Time (C), 10 to 20 | 61.1125 | 63.2125 | 2.1000 |
Every rise is exactly twice its coefficient. Temp's coefficient is 5.9875 and its panel rises 11.9750. Press is 2.9875 against 5.9750, and Time is 1.0500 against 2.1000. That is the clearest statement of what a coded coefficient is: the change in the fitted response for a one unit change in the coded factor, and the coded factor runs from -1 to +1, which is two units end to end.
If your panels rise by those three amounts, the design and the model are right.
The three panels share one value axis. All three are drawn against the same scale, so the Temp panel visibly climbs while the Time panel is nearly flat. That comparison is the point of drawing them together, and it only works because the axis is computed once from every panel's points rather than per panel.
Each point is an average of eight runs. The low Temp point at 56.1750 is the mean of the eight runs made at 180 C, whatever Press and Time were doing in them. Add the eight and divide: 49.5, 61.8, 52.3, 60.7, 50.6, 61.2, 51.4 and 61.9 average to 56.175.
Where a main effect can mislead you¶
Temp rises 11.9750 on this panel, and that number is an average over a real disagreement. The Interaction Plots How-To draws the same data split by Press, and finds Temp gaining 16.4500 at Press 40 but only 7.5000 at Press 60. The main effects panel reports the average of those two, and shows no sign that they differ.
That is not a fault in the chart. A main effects panel answers "what does this factor do on average", and this model's AB coefficient of -2.2375 is the product saying that on average is hiding something. Both charts are drawn from the same fit.
Things to try next¶
- Draw the same three panels from the raw data. They will not move. On a balanced design with every held factor at its default set point, the two chart sources agree exactly, which is a property of this design rather than a general rule.
- Move a set point and redraw. Set Time to 20 instead of its default 15 and the Temp and Press panels shift, because their held factor moved. The Time panel does not, because a factor's own set point is overwritten on the panel that plots it.
- Compare with the Pareto. Pareto How-To ranks the same coefficients as bars, where these panels show them as slopes.